Patent Publication Number: US-9838133-B2

Title: Compensation of non-linear transmitter impairments in optical communication networks

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional application of U.S. patent application Ser. No. 14/341,373 filed on Jul. 25, 2014 by Clarence Kan, et al., and titled “Compensation of Non-Linear Transmitter Impairments in Optical Communication Networks,” which is incorporated by reference. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not applicable. 
     REFERENCE TO A MICROFICHE APPENDIX 
     Not applicable. 
     BACKGROUND 
     Optical communication networks serve an important function in worldwide communication. They have increasingly replaced copper wire communications due to various advantages that they offer. Optical communication networks may include various nodes connected by optical fibers or free space. As users demand higher data rates, it is becoming increasingly important to transmit and receive optical data more accurately. 
     SUMMARY 
     In one embodiment, the disclosure includes an optical transceiver comprising a transmitter configured to transmit a first signal, and a receiver coupled to the transmitter and configured to receive a first compensation, wherein the first compensation is based on a pattern-dependent analysis of the first signal, and provide the first compensation to the transmitter, wherein the transmitter is further configured to compensate a second signal based on the first compensation to form a first compensated signal, and transmit the first compensated signal. 
     In another embodiment, the disclosure includes an optical transmitter comprising a digital signal processor (DSP) comprising a compensator, a digital-to-analog converter (DAC) coupled to the DSP, a radio frequency amplifier WA) coupled to the DAC, and an electrical-to-optical converter (EOC) coupled to the RFA. 
     In yet another embodiment, the disclosure includes an optical receiver comprising an optical-to-electrical converter (OEC), an analog-to-digital converter (ADC) coupled to the OEC, and a digital signal processor (DSP) coupled to the ADC and comprising a calibrator. 
     In yet another embodiment, the disclosure includes a method comprising transmitting a first optical signal, receiving a first compensation, wherein the first compensation is based on a pattern-dependent analysis of the first optical signal, compensating a second optical signal based on the first compensation to form a first compensated optical signal, and transmitting the first compensated optical signal. 
     These and other features will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings and claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of this disclosure, reference is now made to the following brief description, taken in connection with the accompanying drawings and detailed description, wherein like reference numerals represent like parts. 
         FIG. 1  is a schematic diagram of a network device. 
         FIG. 2  is a schematic diagram of an optical network according to an embodiment of the disclosure. 
         FIG. 3  is a schematic diagram of an optical modulator according to an embodiment of the disclosure. 
         FIG. 4  is a schematic diagram of an optical network according to another embodiment of the disclosure. 
         FIG. 5  is a schematic diagram of the calibrator in the optical network in  FIG. 4  according to an embodiment of the disclosure. 
         FIG. 6  is an example of a pattern-dependent look-up table (PD-LUT) according to an embodiment of the disclosure. 
         FIG. 7  is a schematic diagram of the compensator in the optical network in  FIG. 4  according to an embodiment of the disclosure. 
         FIG. 8  is a message sequence diagram illustrating iterative calibration and compensation scheme according to an embodiment of the disclosure. 
         FIG. 9  is a graph of a modeled bit error rate (BER) for the optical network in  FIG. 4 . 
         FIG. 10  is another graph of a modeled BER for the optical network in  FIG. 4 . 
         FIG. 11  is a graph of an experimental symbol constellation for the optical network in  FIG. 4 . 
         FIG. 12  is another graph of an experimental symbol constellation for the optical network in  FIG. 4 . 
         FIG. 13  is a graph of experimental optical signal-to-noise ratio (OSNR) versus BER for the optical network in  FIG. 4 . 
         FIG. 14  is a graph of experimental pattern length versus BER for the optical network in  FIG. 4 . 
         FIG. 15  is a flowchart illustrating a method of transmitter impairment compensation according to an embodiment of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     It should be understood at the outset that, although an illustrative implementation of one or more embodiments are provided below, the disclosed systems and/or methods may be implemented using any number of techniques, whether currently known or in existence. The disclosure should in no way be limited to the illustrative implementations, drawings, and techniques illustrated below, including the exemplary designs and implementations illustrated and described herein, but may be modified within the scope of the appended claims along with their full scope of equivalents. 
       FIG. 1  is a schematic diagram of a network device  100 . The network device  100  may be suitable for implementing the disclosed embodiments. The network device  100  may comprise ingress ports  110  and receiver units (Rx)  120  for receiving data; a processor, logic unit, or central processing unit (CPU)  130  to process the data; transmitter units (Tx)  140  and egress ports  150  for transmitting the data; and a memory  160  for storing the data. The network device  100  may also comprise optical-to-electrical (OE) components and electrical-to-optical (EO) components coupled to the ingress ports  110 , receiver units  120 , transmitter units  140 , and egress ports  150  for egress or ingress of optical or electrical signals. 
     The processor  130  may be implemented by hardware and software. The processor  130  may be implemented as one or more CPU chips, cores (e.g., as a multi-core processor) field-programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), and digital signal processors (DSPs). The processor  130  may be in communication with the ingress ports  110 , receiver units  120 , transmitter units  140 , egress ports  150 , and memory  160 . 
     The memory  160  may comprise one or more disks, tape drives, and solid-state drives; may be used as an over-flow data storage device; may be used to store programs when such programs are selected for execution; and may be used to store instructions and data that are read during program execution. The memory  160  may be volatile and non-volatile and may be read-only memory (ROM), random-access memory (RAM), ternary content-addressable memory (TCAM), and static random-access memory (SRAM). 
       FIG. 2  is a schematic diagram of an optical network  200 . The network  200  may comprise a first transceiver  205  and a second transceiver  250  in communication with each other via a medium  245 . The components of the optical network  200  may be arranged as shown or in any other suitable manner. Some of the components may comprise multiple inputs and multiple outputs that may, for instance, run in parallel; however, the components may be simplified for easier understanding. 
     As an example, the first transceiver  205  may be located in any node in an optical network and the second transceiver  250  may be located in any other node in the optical network. Alternatively, the TX  210  and the RX  255  may be part of a single transceiver in a fiber loop-back configuration. Furthermore, the first transceiver  205  and the second transceiver  250  may be located in any optical communication network, including a long-haul network, a metropolitan network, a passive optical network (PON), or another optical network using high-order modulation. 
     The first transceiver  205  may be any transceiver suitable for transmitting and receiving optical signals. The first transceiver  205  may comprise a transmitter (TX)  210  and a receiver (RX)  240  coupled to each other via a coupler  235 . The TX  210  may comprise modules, including a digital signal processor (DSP)  215 , a digital-to-analog converter (DAC)  220 , a radio frequency amplifier (RFA)  225 , and an electrical-to-optical converter (EOC)  230 . The components of the first transceiver  205  may be arranged as shown or in any other suitable manner. 
     The medium  245  may be any medium suitable for providing communication between the first transceiver  205  and the second transceiver  250 . For instance, the medium  245  may be an optical fiber cable. In that case, the medium  245  may comprise one or more optical fibers that each comprises a core and a cladding layer, and the medium  245  may be contained in a tube to protect from the environment. 
     The second transceiver  250  may be any transceiver suitable for transmitting and receiving optical signals. The second transceiver  250  may comprise an RX  255  and a TX  280  coupled to each other via a coupler  275 . The RX  255  may comprise various modules, including a DSP  260 , an analog-to-digital converter (ADC)  265 , and an optical-to-electrical converter (OEC)  270 . The components of the second transceiver  250  may be arranged as shown or in any other suitable manner. The first transceiver  205  and the second transceiver  250  may comprise additional components known in the art in order for the first transceiver  205  and the second transceiver  250  to communicate with each other. 
     The first transceiver  205  may need to transmit signals to the second transceiver  250 . In order to generate a high-order modulation signal over an in-phase (I) and quadrature-phase (Q) optical modulator, first, the DSP  215  may form multi-level I and Q digital electrical signals and pre-condition those digital electrical signals. Second, the DAC  220  may convert the digital electrical signals to analog electrical signals. The DAC  220  may have a finite resolution and frequency response. Third, the RFA  225  may amplify the analog electrical signals. The RFA.  225  may have a finite bandwidth. Fourth, the EOC  230 , which may comprise a Mach-Zehnder modulator, may convert the analog electrical signals into optical signals. Fifth, the first transceiver  205  may transmit the optical signals through the coupler  235  and the medium  245  to the second transceiver  250 . 
     The second transceiver  250  may first receive the optical signals over the medium  245  and through the coupler  275 . Second, the OEC  270  may convert the optical signals to analog electrical signals. Third, the ADC  265  may convert the analog electrical signals into digital electrical signals. Fourth, the DSP  260  may process the digital electrical signals as appropriate. 
       FIG. 3  is a schematic diagram of an optical modulator  300 . The modulator  300  may be a polarization-multiplexed I and Q Mach-Zehnder and may be used in the EOC  230 . The modulator  300  may comprise a polarization beam splitter (PBS)  310 , a first Mach-Zehnder modulator array  320 , a second Mach-Zehnder modulator array  330 , and a polarization beam coupler (PBC)  340 . The components of the modulator  300  may be arranged as shown or in any other suitable manner. 
     The PBS  310  may split a laser into an X polarization component and a Y polarization component. The first Mach-Zehnder modulator array  320  may split the X polarization component into a first component and second component and modulate the first component as an X I  component and the second component as an X Q  component. The X Q  component may he voltage-biased to have π/2 optical phase shift compared to the X I  component. The first Mach-Zehnder modulator array  320  may then multiplex the X I  component and the X Q  component together to form a modulated X component. The second Mach-Zehnder modulator array  330  may split the Y polarization component into a first component and second component and modulate the first component as a Y I  component and the second component as a Y Q  component. The X Q  component may be voltage-biased to have π/2 optical phase shift compared to the X I  component. The second Mach-Zehnder modulator array  320  may then multiplex the Y I  component and the Y Q  component together to form a modulated Y component. Finally, the PBC  340  may couple, or multiplex, the modulated X component and the modulated Y component to form a polarization-multiplexed signal. 
     High-order modulation is a promising technology to achieve spectrally-efficient terabit (Tb) transmission in optical networks such as the network  200 . High-order modulated signals can be generated by modulators such as the optical modulator  300 . By modulating both the X polarization component and the Y polarization component, the optical modulator  300  may double the spectral efficiency. 
     Using existing approaches to pre-conditioning of the digital electrical signals in the DSP  215  in the first transceiver  205 , the signals can substantially deviate from the expected values due to non-linear responses of the electrical and optical components of the TX  210  in the first transceiver  205 . Those deviations, or impairments, may cause a poor BER at a coherent receiver such as the RX  255  in the second transceiver  250 . A poor BER may shorten transmission distances, which may increase the need for signal regeneration, thus resulting in higher infrastructure costs. 
     The impairments may comprise two parts, a static part that does not depend on the data pattern and a dynamic part that does depend on the data pattern. The dynamic part that does depend on the data pattern may be caused by a memory effect. With application of a near-Nyquist pulse-shaping filter such as a raised-root-cosine (RRC) filter with a roll-off factor of less than 0.2, the level deviation becomes essentially pattern dependent due to filtering-induced inter-symbol interference (ISI). 
     DSP techniques may at leak partially equalize, or compensate, the impairments. At the TX  210  in the first transceiver  205 , a frequency-domain equalizer (FDEQ) and a finite impulse response pre-equalizer (FIR) may compensate linear impairments such as radio frequency (RF) bandwidth limitations or I-Q delays. At the RX  255  in the second transceiver  250 , an FDEQ may compensate for fiber chromatic dispersion and perform frequency filtering optimization, including bandwidth compensation. A time-domain equalizer (TDEQ) and carrier recovery (CR) module may recover the transmitted X polarization and Y polarization and compensate for polarization mode dispersion, and carrier phase recovery. Those DSP techniques may not, however, compensate for non-linear, pattern-dependent impairments. 
     Prior approaches to compensate for non-linear, pattern-dependent impairments include Joel L. Dawson, “Power Amplifier Linearization Techniques: An Overview,” Feb. 4, 2001 (“Dawson”); Shawn P. Stapleton, “Presentation on Digital Predistortion of Power Amplifiers,” June 2001 (“Stapleton”); Jian Hong Ke, et al., “Three-carrier 1 Tbit/s Dual Polarization 16-QAM Superchannel Using Look-Up Table Correction and Optical Pulse Shaping,” Optics Express, Vol. 22, No. 1, Jan. 13, 2014 (“Ke 1”); and Jian Hong Ke, et al., “400 Gbit/s single-carrier and 1 Tbit/s three-carrier superchannel signals using dual polarization 16-QAM with look-up table correction and optical pulse shaping,” Optics Express, Vol. 22, No. 1, Dec. 20, 2013 (“Ke 2”), which are incorporated by reference. Ke 1&#39;s and Ke 2&#39;s first approach uses a digitally sampled signal at the transmitter to generate a PD-LUT. The sampled signal is then adjusted based on the PD-LUT to produce an equalized, or compensated, driver amplitude. First, that approach may require additional hardware, including an RF splitter and an ADC at the transmitter to acquire the sampled drive signal. Second, that approach may result in driver power loss. Third, that approach may incorrectly compensate intentional pre-distortion such as pulse shaping, bandwidth pre-compensation, and dispersion pre-compensation, which may be used to compensate transmission impairments after the point where the signal is sampled. Ke 1&#39;s and Ke 2&#39;s second approach generates the PD-LUT and compensates the signal at the receiver DSP. Both approaches describe a single iteration of calibration and compensation. 
     Disclosed herein are embodiments for improved compensation of transmitter impairments. Those impairments may be non-linear, pattern-dependent impairments. The disclosed embodiments may provide for calibration by generating a compensation, which may be a PD-LUT, based on a pattern-dependent analysis of data received at a receiver, then pattern-dependent level equalization (PD-LEQ) or compensation, in a transmitter based on the PD-LUT. There may be multiple iterations of calibration and compensation with each successive iteration providing improved compensation. The disclosed embodiments may be suitable for any optical communication network, including a PON, a long-haul network, a metropolitan network, or another optical network using high-order modulation. The disclosed embodiments may provide at least three benefits. First, by generating the PD-LUT based on the pattern-dependent analysis of data received at the receiver and not the transmitter, the transmitter may not require any additional hardware, which may reduce transmitter size and cost. Second, there may be less or no undesired compensation of intentional pre-distortion such as bandwidth pre-compensation, pulse shaping, and dispersion pre-compensation. Third, by calibrating in the receiver after the DSP, including after the TDEQ, then compensating in the transmitter, the impairments may be more accurately compensated because the data sequence is error-free and the data patterns can be accurately determined at the transmitter. Fourth, multiple iterations of calibration and compensation may further improve compensation and thus further reduce the BER at the receiver. 
       FIG. 4  is a schematic diagram of an optical network  400  according to an embodiment of the disclosure. As can be seen, the network  400  may be the same as, and function the same as, the network  200  with a few exceptions. First, the DSP  260  in the second transceiver  250  may comprise an additional module, a calibrator  410 . Second, the RX  255  may communicate with the TX  280  in the second transceiver  250  to, for instance, provide a PD-LUT. Third, the DSP  215  in the first transceiver  205  may comprise an additional module, a compensator  420 . The TX  210  may not comprise any additional signal processing modules before the compensator  420 . Fourth, the TX  210  may communicate with the RX  240  in the first transceiver  205  to, for instance, receive the PD-LUT. The components of the optical network  400  may be arranged as shown or in any other suitable manner. 
     The calibrator  410  may generate the PD-LUT, and the RX  255  may provide the PD-LUT to the TX  280 . The TX  280  may transmit the PD-LUT to the first transceiver  205  via the coupler  275  and the medium  245 . The RX  240  may receive the PD-LUT via the medium  245  and the coupler  235 . The RX  240  may provide the PD-LUT to the TX  210 , and the compensator  420  may compensate signals in the TX  210  based on the PD-LUT. The operation of the calibrator  410  and the compensator  420  are described more fully below. 
       FIG. 5  is a schematic diagram of the calibrator  410  in the optical network  400  in  FIG. 4  according to an embodiment of the disclosure. The calibrator  410  may comprise modules, including a multiple-input and multiple-output (MIMO) TDEQ and CR module  510 ; a slicer  520 ; a pattern matcher  530 ; a mean calculator  540 ; an adjustment calculator  550 ; and a PD-LUT generator  560 . The components of the calibrator  410  may be arranged as shown or in any other suitable manner. Some of the components may comprise multiple inputs and multiple outputs that may, for instance, run in parallel; however, the components may be simplified for easier understanding. 
     The calibrator  410  may output four PD-LUTs, one for each of an X I  component, an X Q  component, a Y I  component, and a Y Q  component. The X I  component may correspond to an X-polarization and I component of a signal, the X Q  component may correspond to an X-polarization and Q component of the signal, the Y I  component may correspond to a Y-polarization and component of the signal, and the Y Q  component may correspond to a Y-polarization and Q component of the signal. The calibrator  410  is described further below with respect to an arbitrary component of the signal. 
     The MIMO TDEQ and CR module  510  may receive an input from the DSP  260  of the RX  255 . The input from the DSP  260  may result from known digital signal processing (DSP) techniques applied in, for instance, upstream modules of the DSP  260 . The MIMO portion of the MIMO TDEQ and CR module  510  may demultiplex the X and Y components of the input from the DSP  260 . The TDEQ portion of the MIMO TDEQ and CR module  510  may equalize linear distortion of the signal. The CR portion of the MIMO TDEQ and CR module  510  may recover a phase of modulation. For instance, the signal may have been modulated using quadrature amplitude modulation (QAM). The output of the MIMO TDEQ and CR module  510  may be a soft signal comprising the X I  component, the X Q  component, the Y I  component, and the Y Q  component. A soft signal may refer to the signal actually received. In other words, the soft signal may result from noise and distortion and thus may not correspond to the discrete levels of the modulation scheme. 
     The slicer  520  may compare the soft signal to the discrete levels of the modulation scheme. The slicer  520  may then convert the soft signal to a hard signal based on the comparison. A hard signal may refer to a signal with symbols corresponding to the discrete levels of the modulation scheme. 
     The pattern matcher  530  may compare the hard signal to mapped levels, which may be based on an arbitrary scheme. The arbitrary scheme may have the same number of levels as the modulation scheme, but use different levels. The pattern matcher  530  may then convert the hard signal to a matched signal based on the comparison. The pattern matcher  530  may also calculate a pattern index by multiplying the first symbol in the first sequence of the signal by the number of matched levels raised to the power of the symbol number, multiplying the second symbol in the first sequence of the signal by the number of matched levels raised to the power of the symbol number, and so on for each symbol, then adding the quantities together. 
     The mean calculator  540  may calculate a mean of the center symbol of each sequence of the soft signal. The adjustment calculator  550  may subtract the mean from the center symbols of the hard signal to obtain the adjustment. The center symbol for each of the sequences corresponding to a pattern index will be the same. 
     Finally, the PD-LUT generator  560  may generate a PD-LUT based on the pattern index and the adjustment. The PD-LUT may further comprise additional pattern indices with their respective adjustments. The PD-LUT generator  560  may similarly generate PD-LUTs for each X I  component, X Q  component, Y I  component, and Y Q  component of the signal inputted from the DSP  260 . The RX  255  may provide the PD-LUTs to the TX  280 , and the TX  280  may transmit the PD-LUTs to the first transceiver  205  via the coupler  275  and the medium  245 . 
     As an example, the calibrator  410  may receive from the DSP  260  a signal with sequences comprising five consecutive symbols (i.e., a pattern length of five) and modulated using 16-QAM, which may yield four discrete levels (e.g., −3, −1, 1, and 3). The number of unique patterns may therefore be 4 5 , or 1,024. The range of the pattern index may therefore be 0-1,023 or 1-1,024. After performing its functions, the MIMO TDEQ and CR module  510  may then output the soft signal as follows:
 
(−3.1, −2.8, −1.2, 1.2, 3.2)
 
(−3.2, −2.9, −1.1, 1.4, 2.9)
 
(−2.9, −2.7, −0.8, 1.1, 3.1).  (1)
 
     The slicer  520  may compare the soft signal ( 1 ) to the four discrete levels, −3, −1, 1, and 3. For instance, −3.1 in the first symbol of the first sequence may be closer to −3 than to any other discrete level, −2.8 in the second symbol of the first sequence may be closer to −3 than to any other discrete level, −1.2 in the third symbol of the first sequence may be closer to −1 than to any other discrete level, 1.2 in the fourth symbol of the first sequence may be closer to 1 than to any other discrete level, and 3.2 in the fifth symbol of the first sequence may be closer to 3 than to any other discrete level. The slicer  520  may similarly compare the remaining sequences to obtain the following hard signal:
 
(−3, −3, −1, 1, 3)
 
(−3, −3, −1, 1, 3)
 
(−3, −3, −1, 1, 3).  (2)
 
     The pattern matcher  530  may match the hard signal ( 2 ) to a matched signal based on four mapped levels 0, 1, 2, and 3). The hard signal ( 2 ) may therefore become the following matched signal:
 
(0, 0, 1, 2, 3)
 
(0, 0, 1, 2, 3)
 
(0, 0, 1, 2, 3).  (3)
 
The pattern matcher  530  may also calculate the pattern index of the matched signal ( 3 ) by multiplying the first symbol in the first sequence of the signal by the number of matched levels (i.e., 4) raised to the power of the symbol number (i.e., 0), multiplying the second symbol in the first sequence of the signal by the number of matched levels (i.e., 4) raised to the power of the symbol number i.e., 1), and so on for each symbol, then adding the quantities together as follows:
 
(0×4 0 )±(0×4 1 )+(1×4 2 )+(2×4 3 )+(3×4 4 )=912.  (4)
 
     The mean calculator  540  may then calculate the mean of the center (i.e., third) symbol of each sequence of the soft signal ( 1 ) as follows: 
                         (     -   1.2     )     +     (     -   1.1     )     +     (     -   0.8     )       3     =     -     1.03   .               (   5   )               
The adjustment calculator  550  may subtract the mean ( 5 ) from the center symbol of the hard signal ( 2 ) to obtain the adjustment as follows:
 
(−1)−(−1.03)=0.03.  (6)
 
Finally, the PD-LUT generator  560  may generate a PD-LUT based on the pattern index ( 4 ), 912, and the adjustment ( 6 ), 0.03.
 
       FIG. 6  is an example of a PD-LUT  600  according to an embodiment of the disclosure. The PD-LUT  600  may be, for instance, a PD-LUT generated by the PD-LUT generator  560 . As shown, the PD-LUT  600  may comprise the pattern index ( 4 ), 912, and the adjustment ( 6 ), 0.03. The PD-LUT  600  may further comprise, for instance, pattern indices  896  and  976  and their respective adjustments, 0.06 and 0.04. Finally, the PD-LUT  600  may further comprise additional pattern indices and their respective adjustments as indicated by the ellipses. As described above, there may be up to 1,024 unique pattern indices. 
       FIG. 7  is a schematic diagram of the compensator  420  in the optical network  400  in  FIG. 4  according to an embodiment of the disclosure. The compensator  420  may comprise modules, including a pattern matcher  710 , and an adjuster  720 . The components of the compensator  420  may be arranged as shown or in any other suitable manner. Some of the components may comprise multiple inputs and multiple outputs that may, for instance, run in parallel; however, the components may be simplified for easier understanding. The compensator  420  may output an X I  component, an X Q  component, a Y-I component, and a Y Q  component. The compensator  420  is described further below with respect to an arbitrary component of the signal. 
     The pattern matcher  710  may receive an input from the DSP  215  of the TX  210 . The input from the DSP  215  may result from known DSP techniques applied in, for instance, upstream modules of the DSP  260 . Such upstream modules may comprise a slicer similar to the slicer  520  so that the input from the DSP  215  is a hard signal. The pattern matcher  710  may compare the hard signal to mapped levels, which may be based on an arbitrary scheme. The arbitrary scheme may have the same number of levels as the modulation scheme, but use different levels. The pattern matcher  710  may then convert the hard signal to a matched signal based on the comparison. The pattern matcher  710  may also calculate a pattern index by multiplying the first symbol in the first sequence of the signal by the number of matched levels raised to the power of the symbol number, multiplying the second symbol in the first sequence of the signal by the number of matched levels raised to the power of the symbol number, and so on for each symbol, then adding the quantities together. 
     The adjuster  720  may input a PD-LUT, for instance the PD-LUT  600 , from the RX  240  in the first transceiver  205 , which the RX  240  may have received from the TX  280  in the second transceiver  250 . The adjuster  720  may then look up in the PD-LUT the pattern index calculated by the pattern matcher  710 , then determine the adjustment in the PD-LUT corresponding to that pattern index. The adjuster  720  may then adjust the center symbol of each sequence of the hard signal by the adjustment. 
     It is known that calculating an adjustment of the center symbol in a sequence of a signal, then compensating that center symbol, may reduce impairments. If, however, a sequence has an even number of symbols, then the center two symbols may be compensated. Similarly, symbols other than the center symbol or symbols may be compensated in other applications. 
     As an example, the pattern matcher  710  may input the following hard signal:
 
(−3, −3, −1, 1, 3)  (7)
 
The pattern matcher  710  may match the hard signal ( 7 ) to a matched signal based on the four mapped levels, 0, 1, 2, and 3, to obtain the following matched signal:
 
(0, 0, 1, 2, 3).  (8)
 
In the same way as described for the pattern matcher  530 , the pattern matcher  710  may also calculate the pattern index of the matched signal ( 8 ) as follows:
 
(0×4 0 )+(0×4 1 )+(1×4 2 )+(2×4 3 )+(3×4 4 )=912.  (9)
 
The adjuster  720  may then look up in the PD-LUT  600  the pattern index ( 9 ) and determine a corresponding adjustment for that pattern index. As described above and as shown in  FIG. 6 , 0.03 is the adjustment corresponding to the pattern index of 912. Accordingly, the adjuster  720  may adjust the center symbol of the hard signal ( 7 ) by 0.3 to obtain the following adjusted signal:
 
(−3, −3, −0.97, 1, 3).  (10)
 
Finally, the adjuster  720  may provide the adjusted signal ( 10 ) to the DSP  215 . For instance, the adjuster  720  may provide the adjusted signal ( 10 ) to downstream modules of the DSP  215 . Such downstream modules may apply known DSP techniques.
 
       FIG. 8  is a message sequence diagram illustrating iterative calibration and compensation scheme  800  according to an embodiment of the disclosure. The optical network  400  may implement the scheme  800 . Specifically, the first transceiver  205  and the second transceiver  250  may implement the scheme  800 , though the same principles may apply between any suitable transmitter and receiver. 
     At step  805 , the first transceiver  205  may transmit a first signal to the second transceiver  250 . At step  810 , the second transceiver  250  may perform a first calibration, for instance in the calibrator  410 , to produce a PD-LUT, for instance the PD-LUT  600 . The calibrator  410  may perform the first calibration based on the first signal. At step  815 , the second transceiver  250  may transmit the PD-LUT  600  to the first transceiver  205 . At step  820 , the first transceiver  205  may perform a first compensation, for instance in the compensator  420 . For instance, the compensator  420  may compensate subsequent transmissions by applying to those transmissions the adjustments in the PD-LUT  600 . Steps  805  to  820  may comprise a first iteration of calibration and compensation. 
     The first iteration may not, however, fully compensate the signals that the first transceiver  205  transmits. The scheme  800  may therefore comprise additional iterations of calibration and compensation. Accordingly, at step  825 , the first transceiver  205  may transmit a second signal to the second transceiver  250 . The second signal may be compensated based on the PD-LUT  600 . At step  830 , the calibrator  410  may perform a second calibration to produce a PD-LUT Δ 2 . The PD-LUT Δ 2  may provide adjustments to be added to the adjustments from the PD-LUT  600  to form anew PD-LUT 2 . For instance, for a pattern index of 912, the PD-LUT Δ 2  may provide an adjustment of 0.005 to add to the adjustment of 0.03 in the PD-LUT  600  to form a new PD-LUT 2  with an adjustment of 0.035 for a pattern index of 912. The calibrator  410  may perform the second calibration in the same manner that it performed the first calibration, except that the calibrator may do so based on the second signal. At step  835 , the second transceiver  250  may transmit the PD-LUT 2  to the first transceiver  205 . At step  840 , the compensator  420  may perform a second compensation. For instance, the compensator  420  may compensate subsequent transmissions by applying to those transmissions the adjustments in the PD-LUT 2 . Steps  825  to  840  may comprise a second iteration of calibration and compensation. 
     The scheme  800  may comprise similar additional iterations of calibration and compensation until an ith iteration at steps  845  to  860 . I may be any positive integer. Each successive iteration may provide a finer granularity of compensation. The first transceiver  205 , the second transceiver  250 , or another component may request a first or subsequent iteration. 
       FIG. 9  is a graph  900  of a modeled BER for the optical network  400  in  FIG. 4 . As shown, the x-axis represents calibration and compensation iterations as constants, and the y-axis represents BER as constants or arbitrary units. Non-linearity of the RFA  225  may be modeled using the Rapp model, which is well-known in the art and described in many sources, including in John Liebetreu, et al., “Proposed System Impairment Models,” IEEE 802.16 Broadband Wireless Access Working Group, Mar. 8, 2000, which is incorporated by reference. The graph  900  shows BERs for a pattern length of five and for different saturation voltages, which are represented as V S  and described in Rapp. V S  may be inversely proportional to the non-linearity of the RFA  225 . The solid line may represent a linear RFA  225 . 
     As can be seen, the BER may decrease for each successive iteration, though improvement may begin to level off around three iterations. A V S  of 0.75 volts (V) yields a relatively low BER, while lower V S  values yield relatively higher BERs. The successive iterations may not fully compensate the non-linearity, particularly for the lower V S  values. That inability to compensate may be due to the relatively short pattern length of five used in this example, which may not fully compensate for the patterning effects. 
       FIG. 10  is another graph  1000  of a modeled BER for the optical network  400  in  FIG. 4 . As shown, the x-axis represents calibration and compensation iterations as constants, and the y-axis represents BER as constants or arbitrary units. Once again, the Rapp model may be used. Compared to the graph  900 , however, the graph  1000  shows BERs for a V S  of 0.5 V, a pre-compensation dispersion at the DSP  215  of 300 picoseconds (ps)/nanometer (nm), a post-compensation dispersion at the DSP  260  of −300 ps/nm, and different pattern lengths, which are represented as PL. Once again, the solid line may represent a linear RFA  225 . 
     As can be seen, a higher pattern length yields a lower BER, particularly after successive iterations. Once again, however, the BER improvement may begin to level off around three iterations. A pattern length of nine may nearly fully compensate the patterning effects due to a combination of pre-compensation dispersion and RFA  225  non-linearity. 
       FIG. 11  is a graph  1100  of an experimental symbol constellation for the optical network  400  in  FIG. 4 .  FIG. 12  is another graph  1200  of an experimental symbol constellation for the optical network  400  in  FIG. 4 . The graph  1100  is shown before applying the disclosed calibration and compensation, and the graph  1200  is shown after applying the disclosed calibration and compensation. As shown, for both the graph  1100  and the graph  1200 , both the x-axis and the y-axis represent constants or arbitrary units. The graph  1100  and the graph  1200  are obtained experimentally based on the following:
         polarization-multiplexed 16-QAM (PM-16QAM) transmission;   36 gigabaud (Gbaud) transmission;   a polarization-multiplexed I and Q (PM-IQ) modulator;   driving signals for the modulators generated electrically from eight-bit, four-channel, high-speed DACs with sampling rates up to 65 Gbaud;   a 2 15 -1 pseudo-random bit sequence (PRBS);   Nyquist RRC pulse-shaping with a roll-off factor of 0.1;   detection of the signal by a polarized, diversified, coherent detector;   recordation of the signal using a 50 Gbaud Tektronix real-time digital sampling oscilloscope (DSO) with a 20 gigahertz (GHz) electrical bandwidth; and   signal processing using an offline DSP code package comprising an FDEQ, a TDEQ, and a CR module.       

     As can be seen, the symbols in the graph  1100  are grouped together in 16 circles, but the circles are not neatly defined. In the graph  1200 , however, the 16 circles are more neatly defined, compact, and equally spaced apart. In other words, the symbols are more closely aligned with the PM-16QAM grid. The experimental BER in  FIG. 11  is 1.67e −4 , while the experimental BER in  FIG. 12  is 6.3e −5 , thus showing substantial improvement in BER. 
       FIG. 13  is a graph  1300  of experimental OSNR versus BER for the optical network  400  in  FIG. 4 . As shown, the x-axis represents OSNR in decibels (dB), and the y-axis represents BER in constants or arbitrary units. The graph  1300  is based on a V G  of 2 V, where V G  is a voltage related to the RFA  225 . The graph  1300  shows OSNR versus BER before applying the disclosed calibration and compensation and after applying the disclosed calibration and compensation. As can be seen, the disclosed calibration and compensation may significantly decrease the BER, particularly as the OSNR increases. 
       FIG. 14  is a graph  1400  of experimental pattern length versus BER for the optical network  400  in  FIG. 4 . As shown, the x-axis represent pattern length in constants or arbitrary units, and the y-axis represents BER in constants or arbitrary units. The graph  1400  is based on a single iteration of calibration and compensation. As can be seen, the BER may significantly decrease as the pattern length increases, though improvement may begin to level off around a pattern length of four to five. The BER may begin to decrease as the pattern length increases beyond seven. 
       FIG. 15  is a flowchart illustrating a method  1500  of transmitter impairment compensation according to an embodiment of the disclosure. The method  1500  may be implemented in the first transceiver  205 , for instance in the TX  210 . At step  1510 , a first optical signal may be transmitted. At step  1520 , a first compensation may be received. For instance, the TX  210  may receive the PD-LUT  600  from the second transceiver  250 , for instance from the RX  255 . The first compensation may be based on a pattern-dependent analysis of the first optical signal. At step  1530 , a second optical signal may be compensated based on the first compensation to form a first compensated optical signal. For instance, the compensator  420  may compensate the second optical signal based on the PD-LUT  600 . At step  1540 , the first compensated optical signal may be transmitted. 
     At least one embodiment is disclosed and variations, combinations, and/or modifications of the embodiment(s) and/or features of the embodiment(s) made by a person having ordinary skill in the art are within the scope of the disclosure. Alternative embodiments that result from combining, integrating, and/or omitting features of the embodiment(s) are also within the scope of the disclosure. Where numerical ranges or limitations are expressly stated, such express ranges or limitations may be understood to include iterative ranges or limitations of like magnitude falling within the expressly stated ranges or limitations (e.g., from about 1 to about 10 includes, 2, 3, 4, etc.; greater than 0.10 includes 0.11, 0.12, 0.13, etc.). For example, whenever a numerical range with a lower limit, R 1 , and an upper limit, R u , is disclosed, any number falling within the range is specifically disclosed. In particular, the following numbers within the range are specifically disclosed: R=R 1 +k*(R u −R 1 ), wherein k is a variable ranging from 1 percent to 100 percent with a 1 percent increment, i.e., k is 1 percent, 2 percent, 3 percent, 4 percent, 5 percent, 50 percent, 51 percent, 52 percent, 95 percent, 96 percent, 97 percent, 98 percent, 99 percent, or 100 percent. Moreover, any numerical range defined by two R numbers as defined in the above is also specifically disclosed. The use of the term “about” means +/−10% of the subsequent number, unless otherwise stated. Use of the term “optionally” with respect to any element of a claim means that the element is required, or alternatively, the element is not required, both alternatives being within the scope of the claim. Use of broader terms such as comprises, includes, and having may be understood to provide support for narrower terms such as consisting of, consisting essentially of, and comprised substantially of. Accordingly, the scope of protection is not limited by the description set out above but is defined by the claims that follow, that scope including all equivalents of the subject matter of the claims. Each and every claim is incorporated as further disclosure into the specification and the claims are embodiment(s) of the present disclosure. The discussion of a reference in the disclosure is not an admission that it is prior art, especially any reference that has a publication date after the priority date of this application. The disclosure of all patents, patent applications, and publications cited in the disclosure are hereby incorporated by reference, to the extent that they provide exemplary, procedural, or other details supplementary to the disclosure. 
     While several embodiments have been provided in the present disclosure, it may be understood that the disclosed systems and methods might be embodied in many other specific forms without departing from the spirit or scope of the present disclosure. The present examples are to be considered as illustrative and not restrictive, and the intention is not to be limited to the details given herein. For example, the various elements or components may be combined or integrated in another system or certain features may be omitted, or not implemented. 
     In addition, techniques, systems, subsystems, and methods described and illustrated in the various embodiments as discrete or separate may be combined or integrated with other systems, modules, techniques, or methods without departing from the scope of the present disclosure. Other items shown or discussed as coupled or directly coupled or communicating with each other may be indirectly coupled or communicating through some interface, device, or intermediate component whether electrically, mechanically, or otherwise. Other examples of changes, substitutions, and alterations are ascertainable by one skilled in the art and may be made without departing from the spirit and scope disclosed herein.