Abstract:
An optical transport system configured to transmit information using two or more modulated optical carriers spaced at spectral intervals that are smaller than the baud rate. An example optical receiver in the optical transport system includes a signal equalizer configured to implement frequency-diversity multiple-input/multiple-output signal processing directed at canceling the effects of inter-carrier interference caused by the spectral overlap between adjacent modulated optical carriers to enable the optical receiver to recover individual data streams encoded onto the different modulated optical carriers at the corresponding optical transmitter(s). Some embodiments of the optical transport system may advantageously be capable of achieving a higher spectral efficiency than the spectral efficiency supported by the optical orthogonal-frequency-division-multiplexing transmission format.

Description:
BACKGROUND 
     1. Field 
     The present invention relates to optical communication equipment and, more specifically but not exclusively, to an optical transmission scheme using frequency-diversity (FD) multiple-input/multiple-output (MIMO) signal processing. 
     2. Description of the Related Art 
     This section introduces aspects that may help facilitate a better understanding of the invention(s). Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is in the prior art or what is not in the prior art. 
     Telecommunications companies face continuing demands for increased capacity in their metro, regional, and long-haul optical networks, e.g., due to the proliferation of high-speed data services, video services, and business and residential broadband connections. While optical fiber has a very large intrinsic capacity for transporting data, the spectral efficiency realized in modern optical networks still has significant room for improvement. For example, one of the most spectrally efficient optical-transport techniques employed today is optical orthogonal frequency-division multiplexing (OFDM), which uses modulated subcarriers that are spaced exactly at the baud rate. However, a higher spectral efficiency than that supported by optical OFDM is likely to be required to meet the capacity demands in the future. 
     In telecommunications and electronics, the term “baud rate” refers to the data rate expressed in the units of symbols per second or pulses per second. Baud rate, also sometimes referred to as “modulation rate,” is therefore the number of distinct symbol changes or signaling events applied to the transmission medium per second using a digitally modulated signal or line code. The corresponding bit rate is a product of the baud rate and the number of bits per symbol in the employed modulation format or constellation. 
     SUMMARY OF SOME SPECIFIC EMBODIMENTS 
     Disclosed herein are various embodiments of an optical transport system configured to transmit information using two or more modulated optical carriers spaced at spectral intervals that are smaller than the baud rate. An example optical receiver in the disclosed optical transport system includes a signal equalizer configured to implement FD-MIMO signal processing directed at canceling the effects of inter-carrier interference caused by the spectral overlap between adjacent modulated optical carriers to enable the optical receiver to recover individual data streams encoded onto the different modulated optical carriers at the corresponding optical transmitter(s). Advantageously, some embodiments of the optical transport system may be capable of achieving a higher spectral efficiency than the spectral efficiency supported by the optical OFDM transmission format. 
     In some embodiments, the disclosed optical transport system may be configured to transmit polarization-division-multiplexed optical signals. 
     According to one embodiment, provided is an optical receiver comprising an optical detector configured to generate a first filtered electrical signal and a second filtered electrical signal based on a received modulated optical signal, wherein the received modulated optical signal has (i) a first modulated optical carrier having encoded thereon a first data stream at a selected baud rate, said first modulated optical carrier having a first carrier frequency, and (ii) a second modulated optical carrier having encoded thereon a second data stream at the selected baud rate, said second modulated optical carrier having a second carrier frequency, wherein the first and second carrier frequencies are separated from one another by a frequency interval that is smaller than the selected baud rate. The optical receiver further comprises a signal processor configured to process the first and second filtered electrical signals to recover the first data stream and the second data stream. 
     According to another embodiment, provided is an apparatus comprising: a first optical transmitter configured to generate a first modulated optical carrier having encoded thereon a first data stream at a selected baud rate, said first modulated optical carrier having a first carrier frequency; a second optical transmitter configured to generate a second modulated optical carrier having encoded thereon a second data stream at the selected baud rate, said second modulated optical carrier having a second carrier frequency, wherein the first and second carrier frequencies are separated from one another by a frequency interval that is smaller than the selected baud rate; and an optical combiner configured to combine the first modulated optical carrier and the second modulated optical carrier for transmission over a fiber-optic link. 
     According to yet another embodiment, provided is an optical transmitter comprising: a plurality of electrical intermediate-frequency generators, each configured to generate a respective electrical carrier wave having a respective intermediate frequency, wherein spacing between neighboring intermediate frequencies is smaller than a selected baud rate; a plurality of electrical modulators, each configured to modulate the respective electrical carrier wave, at the selected baud rate and using a respective one of a plurality of data streams to generate a respective one of a plurality of modulated electrical carriers; an electrical signal combiner configured to combine the plurality of modulated electrical carriers to generate a modulated multi-carrier electrical signal; and an optical modulator configured to generate a modulated optical signal by modulating an optical carrier wave based on the modulated multi-carrier electrical signal. 
     According to yet another embodiment, provided is an optical receiver comprising: an optical detector configured to generate a first filtered electrical signal and a second filtered electrical signal based on a received modulated optical signal, wherein the received modulated optical signal has (i) a first modulated optical carrier having encoded thereon a first data stream at a selected baud rate, said first modulated optical carrier having a first carrier frequency, and (ii) a second modulated optical carrier having encoded thereon a second data stream at the selected baud rate, said second modulated optical carrier having a second carrier frequency; and a signal processor configured to: convert the first filtered electrical signal into a first electrical baseband signal; convert the second filtered electrical signal into a second electrical baseband signal; apply MIMO equalization processing to the first and second electrical baseband signals to mitigate an effect of inter-carrier interference due to partial spectral overlap of the first modulated optical carrier and the second modulated optical carrier, said MIMO equalization processing configured to receive, as a first input, the first electrical baseband signal, and further configured to receive, as a second input, the second electrical baseband signal, wherein said MIMO equalization processing is configured to generate a first equalized electrical signal, as a first output thereof, and a second equalized electrical signal, as a second output thereof; recover the first data stream based on the first equalized electrical signal; and recover the second data stream based on the second equalized electrical signal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other aspects, features, and benefits of various embodiments of the invention will become more fully apparent, by way of example, from the following detailed description and the accompanying drawings, in which: 
         FIG. 1  shows a block diagram of an optical transport system according to an embodiment of the disclosure; 
         FIGS. 2A-2C  graphically show spectra of intermediate-frequency signals generated in the optical transport system of  FIG. 1  according to an embodiment of the disclosure; 
         FIG. 3  shows a flowchart of a signal processing method that can be used in the optical transport system of  FIG. 1  according to an embodiment of the disclosure; 
         FIG. 4  shows a block diagram of an optical transmitter that can be used in the optical transport system of  FIG. 1  according to an embodiment of the disclosure; 
         FIG. 5  shows a block diagram of an optical heterodyne detector that can be used in the optical transport system of  FIG. 1  according to an embodiment of the disclosure; 
         FIG. 6  shows a block diagram of a digital signal processor that can be used in the optical transport system of  FIG. 1  according to an embodiment of the disclosure; 
         FIG. 7  shows a block diagram of a finite-impulse-response filter that can be used in the digital signal processor of  FIG. 6  according to an embodiment of the disclosure; 
         FIG. 8  shows a block diagram of a MIMO equalizer that can be used in the digital signal processor of  FIG. 6  according to an embodiment of the disclosure; 
         FIG. 9  shows a block diagram of an optical transmitter  900  that can be used in the optical transport system of  FIG. 1  according to an alternative embodiment of the disclosure; and 
         FIG. 10  shows a block diagram of an optical intradyne detector that can be used instead of the optical heterodyne detector shown in  FIG. 5  according to an embodiment of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows a block diagram of an optical transport system  100  according to an embodiment of the disclosure. Optical transport system  100  is configured to use frequency-diversity multiple-input/multiple-output (FD-MIMO) signal processing, e.g., as further explained below. Briefly, optical transport system  100  is configured to transport (at least) two modulated optical carriers having encoded thereon (at least) two data streams, data1 and data2, respectively. Said modulated optical carriers are transmitted in parallel over a fiber-optic link  140 , where they overlap in time and space, and are then processed at the egress end of the fiber-optic link, e.g., as further described below, to recover data streams data1 and data2. 
     The relationship between the carrier frequencies of the two modulated optical carriers used in optical transport system  100  is described by Eq. (1):
 
| f   1   −f   2   |&lt;R   (1)
 
where f 1  and f 2  are the first and second carrier frequencies, respectively; and R is the baud rate. In one embodiment, |f 1 −f 2 |/R is smaller than about 0.9 but greater than about 0.2. In an alternative embodiment, |f 1 −f 2 |/R is smaller than about 0.7 but greater than about 0.4. In yet another alternative embodiment, |f 1 −f 2 |/R≈0.6. In an example embodiment, the values of f 1  and f 2  are on the order of 200 THz, and the value of R is on the order of 10÷100 GHz (but is typically given using the units of Gbaud).
 
     Optical transport system  100  has two optical transmitters (labeled  110   1  and  110   2 ) coupled to the ingress end of fiber-optic link  140  as indicated in  FIG. 1 . Optical transmitter  110   1  is configured to receive data stream data1 via an electrical input port  102   1 . Optical transmitter  110   2  is similarly configured to receive data stream data2 via an electrical input port  102   2 . 
     Optical transmitter  110   1  applies data stream data1 to a digital signal processor (DSP)  112   1 . DSP  112   1  processes data stream data1 to generate electrical digital signals  114   1  and  114   2 . Such processing may include, but is not limited to forward-error-correction (FEC) encoding, constellation mapping, electronic dispersion pre-compensation, and pulse shaping, e.g., implemented as known in the art. The constellation used in the step of constellation mapping can be, e.g., a quadrature-amplitude-modulation (QAM) constellation or a quadrature-phase-shift-keying (QPSK) constellation. 
     In each signaling interval (also referred to as a symbol period or a time slot corresponding to an optical symbol), signals  114   1  and  114   2  carry digital values that represent the in-phase (I) component and quadrature (Q) component, respectively, of a corresponding constellation point (symbol) selected based on the respective portion of data from data stream data1. Digital-to-analog converters (DACs)  118   1  and  118   2  transform digital signals  114   1  and  114   2  into an analog form to generate electrical drive signals I 1  and Q 1 , respectively. Drive signals I 1  and Q 1  are then used, in a conventional manner, to drive an optical I-Q modulator  124   1 . Based on drive signals I 1  and Q 1 , optical I-Q modulator  124   1  modulates a light beam  122   1  supplied by a laser source  120   1  to generate a modulated optical signal  126   1 . Light beam  122   1  has carrier frequency f 1 , and modulated optical signal  126   1  is therefore the first of the above-mentioned two modulated optical carriers. 
     Optical transmitter  110   2  is generally analogous to optical transmitter  110   1  and is configured to apply similar (to the above-described) processing to data stream data2 to generate a modulated optical signal  126   2 . More specifically, the elements of optical transmitters  110   2  and  110   1  designated using similar alphanumerical labels have similar functions, and the description of those functions is not repeated here in reference to optical transmitter  110   2 . However, one difference between optical transmitters  110   1  and  110   2  is that a light beam  122   2  generated by a laser source  120   2  in optical transmitter  110   2  has carrier frequency f 2 . Modulated optical signal  126   2  is therefore the second of the above-mentioned two modulated optical carriers. 
     A beam combiner  128  combines modulated optical signals  126   1  and  126   2  to generate an optical output signal  130 , which is then applied to the ingress end of fiber-optic link  140  and transported therethrough to the egress end thereof, where it emerges as an optical signal  142 . Optical signal  142  has the same two modulated optical carriers as optical signal  130 , but is additionally affected by noise and various linear and nonlinear distortions and impairments imposed in fiber-optic link  140 . 
     Optical transport system  100  further has an optical receiver  150  coupled to the egress end of fiber-optic link  140  as indicated in  FIG. 1 . Optical receiver  150  comprises an optical heterodyne detector  154  configured to convert optical signal  142  into an intermediate-frequency electrical signal  158  using a local-oscillator signal  122   3  generated by a laser source  120   3 . In one embodiment, local-oscillator signal  122   3  has an optical frequency f 3  that has the following relationship with carrier frequencies f 1  and f 2 :
 
| f   3 −0.5×| f   1   −f   2 ∥≧2 R   (2)
 
where R is the baud rate. Example optical heterodyne detectors that can be used as optical heterodyne detector  154  are disclosed, e.g., in U.S. Pat. Nos. 6,535,289, 6,646,746, and 7,162,165, all of which are incorporated herein by reference in their entirety.
 
       FIGS. 2A-2C  graphically show spectra of intermediate-frequency electrical signal  158  ( FIG. 1 ) according to an embodiment of the disclosure. More specifically,  FIG. 2A  shows a spectrum of intermediate-frequency signal  158  when only optical transmitter  110   1  is transmitting, and optical transmitter  110   2  is turned OFF.  FIG. 2B  shows a spectrum of intermediate-frequency signal  158  when only optical transmitter  110   2  is transmitting, and optical transmitter  110   1  is turned OFF.  FIG. 2C  shows a spectrum of intermediate-frequency signal  158  when both optical transmitters  110   1  and  110   2  are transmitting. The measurements presented in  FIGS. 2A-2C  correspond to the following configuration of optical transport system  100 :
         QPSK modulation at R=10 Gbaud;   |f 1 −f 2 |≈6 GHz; and   |f 3 −0.5×|f 1 −f 2 ∥≈28 GHz.       

     Referring back to  FIG. 1 , optical receiver  150  further comprises band-pass filters  160   1  and  160   2 , each configured to receive a respective copy of intermediate-frequency electrical signal  158 . Band-pass filter  160   1  filters the received copy of intermediate-frequency signal  158  to generate a filtered electrical signal  162   1 . Band-pass filter  160   2  similarly filters the received copy of intermediate-frequency signal  158  to generate a filtered electrical signal  162   2 . 
     In an example embodiment, band-pass filters  160   1  and  160   2  have different respective pass bands. For example, band-pass filter  160   1  may be configured to pass a spectral band that is approximately centered at intermediate frequency f IF1 =|f 3 −f 1 | and has a 3-dB width of about R. Band-pass filter  160   2  may similarly be configured to pass a spectral band that is approximately centered at intermediate frequency f IF2 =|f 3 −f 2 | and has a 3-dB width of about R. 
     In one embodiment, band-pass filters  160   1  and  160   2  may have transfer functions F 1 (f) and F 2 (f), respectively, that are described by Eqs. (3a)-(3b):
 
 F   1 ( f )= F   0 ( f−f   IF1 )  (3a)
 
 F   2 ( f )= F   0 ( f−f   IF2 )  (3b)
 
where f is frequency, and F 0 (f) is a transfer function that has a maximum at the zero frequency and is approximately symmetrical with respect to the zero frequency.
 
     Analog-to-digital converters (ADCs)  168   1  and  168   2  convert filtered electrical signals  162   2  and  162   2  into digital form and apply the resulting digital electrical signals  170   1  and  170   2  to a DSP  172  for processing. DSP  172  processes digital electrical signals  170   1  and  170   2  using an FD-MIMO signal-processing method, an example embodiment of which is described below in reference to  FIG. 3 . Based on said processing, DSP  172  recovers data streams data1 and data2 and directs the recovered data stream to external circuits via electrical output ports  176   1  and  176   2 , respectively. 
       FIG. 3  shows a flowchart of a signal processing method that can be used in DSP  172  ( FIG. 1 ) according to an embodiment of the disclosure. 
     At step  302 , DSP  172  performs down-conversion of digital electrical signals  170   1  and  170   2  to baseband. Recall that digital electrical signals  170   1  and  170   2  are digital forms of filtered electrical signals  162   1  and  162   2 , which are intermediate-frequency signals. In the digital domain, frequency down-conversion can be implemented, e.g., by converting digital electrical signals  170   1  and  170   2  into a complex-valued form and then multiplying the corresponding complex values by the factor of exp[−jπ(f IF1 +f IF2 )t], where t is time. In this manner, the spectral bands corresponding to the two modulated optical carriers received by optical transmitter  150  via fiber-optic link  140  (see  FIG. 1 ) are shifted down in frequency to symmetrical positions with respect to the zero frequency. For example, f IF1 &gt;f IF2 , then the down-converted complex-valued digital signal derived from digital electrical signal  170   1  is spectrally located at positive frequencies, and the down-converted complex-valued digital signal derived from digital electrical signal  170   2  is spectrally located at negative frequencies. 
     At step  304 , DSP  172  performs individual frequency-offset correction for each of the two down-converted complex-valued digital signals generated at step  302 . More specifically, the down-converted complex-valued digital signal having positive frequencies is multiplied by the factor of exp[−jπ|f IF1 −f IF2 |t]. The down-converted complex-valued digital signal having negative frequencies is similarly multiplied by the factor of exp[jπ|f IF1 −f IF2 |t]. Step  304  can qualitatively be interpreted as a step of removing the carrier-frequency diversity of the two detected baseband signals. 
     At step  306 , DSP  172  applies MIMO-equalization processing to mitigate the effects of inter-carrier interference present in the signals generated at step  306 . Such effects are present due to the spectral overlap of the intermediate-frequency bands, which is illustrated, e.g., by the spectra shown in  FIGS. 2A and 2B . That spectral overlap, in turn, is a consequence of the carrier-frequency relationship expressed by Eq. (1) and a similar spectral overlap of modulated optical signals  126   2  and  126   2 . 
     The MIMO-equalization processing of step  306  can qualitatively be viewed as being directed at solving, e.g., approximately, the following mathematical problem. Suppose that the digital baseband signals corresponding to modulated optical signals  126   2  and  126   2  are X 1 (f) and X 2 (f), respectively. Let us denote as Y 1 (f) and Y 2 (f) the two digital baseband signals generated at step  304 . The MIMO-equalization processing implemented in DSP  172  then needs to recover (X 1 (f), X 2 (f)) based on (Y 1 (f), Y 2 (f)). 
     The relationship between (X 1 (f), X 2 (f)) and (Y 1 (f), Y 2 (f)) can be understood by tracing the signal propagation and processing implemented in optical transport system  100 . In one embodiment, this relationship can be expressed, for example, as follows: 
                     (             Y   1     ⁡     (   f   )                   Y   2     ⁡     (   f   )             )     =       (             aF   0     ⁡     (   f   )               bF   0     ⁡     (     f   -              f     IF   ⁢           ⁢   1       -     f     IF   ⁢           ⁢   2              2       )                   aF   0     ⁡     (     f   +              f     IF   ⁢           ⁢   1       -     f     IF   ⁢           ⁢   2              2       )               bF   0     ⁡     (   f   )             )     ⁢     (             X   1     ⁡     (   f   )                   X   2     ⁡     (   f   )             )               (   4   )               
where a and b are the complex numbers that describe the propagation of the first and second modulated carriers, respectively, through fiber-optic link  140  ( FIG. 1 ); and F 0 (f) is the filter transfer function already introduced and described above in reference to Eqs. (3a)-(3b). Thus, to find (X 1 (f), X 2 (f)), DSP  172  needs to find the inverse of the 2×2 matrix that appears in Eq. (4). If we denote said inverse matrix as H −1 (f), then the original baseband signals can be calculated using Eq. (5) as follows:
 
     
       
         
           
             
               
                 
                   
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                               f 
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                         H 
                         
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                                 Y 
                                 1 
                               
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                                 f 
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                                 Y 
                                 2 
                               
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     Note that Eqs. (4) and (5) describe the MIMO-equalization processing in the frequency domain. Equivalently, this processing can also be implemented in the time domain, e.g., using one or more multi-tap finite-impulse-response (FIR) filters. Once the equations for time-domain equalization are formulated, a properly constructed cost or error function can be used to drive a suitable (e.g., a least-mean squares, LMS, or a constant-modulus, CMA) algorithm for properly configuring the FIR filters for blind MIMO equalization. An example of the error function that can be used for this purpose is described below in reference to  FIG. 6 . Example CMA implementations that can be used in the MIMO-equalization processing of step  306  are disclosed, e.g., in U.S. Pat. Nos. 8,335,440, 7,260,370, and 6,993,311, all of which are incorporated herein by reference by their entirety. 
     At step  308 , the equalized digital signals generated at step  306  are used to estimate the corresponding original constellation symbols generated by DSPs  112   1  and  112   2  during the step of constellation mapping. 
     At step  310 , the estimated constellation symbols generated at step  308  are converted, using the operative constellation, into the corresponding data streams, and said data streams are subjected to FEC decoding to remove possible errors and recover data streams data1 and data2. 
       FIGS. 4-7  show block diagrams of the various circuits/devices that can be used to modify optical transport system  100  ( FIG. 1 ) in order to adapt it for transmission of polarization-division-multiplexed (PDM) optical signals. More specifically,  FIG. 4  shows a block diagram of an optical transmitter  400  that can be used to replace each of optical transmitters  110   1  and  110   2  ( FIG. 1 ).  FIG. 5  shows a block diagram of an optical heterodyne detector  500  that can be used to replace optical heterodyne detector  154  ( FIG. 1 ).  FIG. 6  shows a block diagram of a DSP  600  that can be used to replace DSP  172  ( FIG. 1 ).  FIG. 7  shows a block diagram of a FIR filter  700  that can be used in DSP  172  ( FIG. 1 ) or DSP  600  ( FIG. 6 ). 
       FIG. 4  shows a block diagram of an optical transmitter  400  that can be used in optical transport system  100  ( FIG. 1 ) according to an embodiment of the disclosure. Optical transmitter  400  is illustratively shown in  FIG. 4  as being coupled between an electrical input port  102  and beam combiner  128  (see  FIG. 1 ). In an example embodiment, a first instance (copy) of optical transmitter  400  can be coupled between electrical input port  102   1  and beam combiner  128  to replace optical transmitter  110   1 , and a second instance of optical transmitter  400  can be coupled between electrical input port  102   2  and beam combiner  128  to replace optical transmitter  110   2  (see  FIG. 1 ). A laser source  420  in the first instance of optical transmitter  400  is then configured to generate light having carrier frequency f 1 , and a laser source  420  in the second instance of optical transmitter  400  is similarly configured to generate light having carrier frequency f 2 . 
     Optical transmitter  400  has a DSP  412  configured to receive an input data stream from electrical input port  102 . DSP  412  processes the received input data stream to generate electrical digital signals  414   1 - 414   4 . In each signaling interval, signals  414   1  and  414   2  carry digital values that represent the I and Q components, respectively, of a corresponding constellation symbol intended for transmission using X-polarized light. Signals  414   3  and  414   4  similarly carry digital values that represent the I and Q components, respectively, of the corresponding constellation symbol intended for transmission using Y-polarized light, where the Y-polarization is approximately orthogonal to the X-polarization. 
     An electrical-to-optical (E/O) converter (also sometimes referred to as a front-end circuit)  416  of optical transmitter  400  transforms digital signals  414   1 - 414   4  into modulated optical output signal  430 . More specifically, DACs  418   1  and  418   2  transform digital signals  414   1  and  414   2  into an analog form to generate drive signals I X  and Q X , respectively. Drive signals I X  and Q X  are then used, in a conventional manner, to drive an I-Q modulator  424   X . Based on drive signals I X  and Q X , I-Q modulator  424   X  modulates an X-polarized beam  422   X  of light supplied by laser source  420 , thereby generating a modulated optical signal  426   X . 
     DACs  418   3  and  418   4  similarly transform digital signals  414   3  and  414   4  into an analog form to generate drive signals I Y  and Q Y , respectively. Based on drive signals I Y  and Q Y , an I-Q modulator  424   Y  modulates a Y-polarized beam  422   Y  of light supplied by laser source  420 , thereby generating a modulated optical signal  426   Y . 
     A polarization beam combiner  428  combines modulated optical signals  426   X  and  426   Y  to generate optical output signal  430 , which is directed to beam combiner  128  ( FIG. 1 ). 
       FIG. 5  shows a block diagram of an optical heterodyne detector  500  that can be used in optical transport system  100  ( FIG. 1 ) according to an embodiment of the disclosure. Similar to optical heterodyne detector  154  shown in  FIG. 1 , optical heterodyne detector  500  can be configured to receive its optical inputs from laser  120   3  and the egress end of fiber-optic link  140  (see  FIG. 1 ). Each of intermediate-frequency electrical signals  558   X  and  558   Y  generated by optical heterodyne detector  500  can be filtered and digitized similar to intermediate-frequency electrical signal  158  (see  FIG. 1 ). 
     Optical heterodyne detector  500  comprises two instances (copies) of optical heterodyne detector  154 , which instances are labeled in  FIG. 5  as  154   X  and  154   Y , respectively. Polarization beam splitters  502   1  and  502   2  operate to provide X-polarized inputs to heterodyne detector  154   X  and Y-polarized inputs to heterodyne detector  154   Y , as indicated in  FIG. 5 . More specifically, polarization beam splitter  502   1  is configured to (i) separate the X- and Y-polarizations of the modulated optical signal received from the remote optical transmitter(s), such as optical transmitters  400  ( FIG. 4 ) or optical transmitter  900  ( FIG. 9 ), and (ii) feed the resulting polarized optical signals into the respective signal ports of heterodyne detectors  154   X  and  154   Y . Polarization beam splitter  502   2  is similarly configured to (i) separate the X- and Y-polarizations of the local-oscillator signal received from laser  120   3  ( FIG. 1 ) and (ii) feed the resulting polarized local-oscillator signals into the respective local-oscillator ports of heterodyne detectors  154   X  and  154   Y . 
       FIG. 6  shows a block diagram of a DSP  600  that can be used in optical transport system  100  ( FIG. 1 ) according to an embodiment of the disclosure. More specifically, DSP  600  is designed to operate in conjunction with optical heterodyne detector  500  ( FIG. 5 ) and is configured to receive (filtered intermediate-frequency) digital electrical signals  602   1 - 602   4 . Digital electrical signals  602   1  and  602   3  correspond to the X-polarization and are generated from signal  558   X  ( FIG. 5 ) in the same manner as that used in the process of generating digital electrical signals  170   1  and  170   2 , respectively, from signal  158  (see  FIG. 1 ). Digital electrical signals  602   2  and  602   4  correspond to the Y-polarization and are generated from signal  558   Y  ( FIG. 5 ) also in the same manner as that used in the process of generating digital electrical signals  170   1  and  170   2 , respectively, from signal  158 . 
     Digital electrical signals  602   1 - 602   4  are applied to a down-converter  610 , which is configured to implement step  302  of method  300  ( FIG. 3 ). In an example embodiment, down-converter  610  includes four complex-value multipliers (not explicitly shown in  FIG. 6 ), each configured to multiply the respective complex-valued signal by exp[−jπ(f IF1 +f IF2 )t]. The resulting complex-valued baseband signals are signals  612   1 - 612   4 . 
     Baseband signals  612   1 - 612   4  are applied to multipliers  616   1 - 616   4 , which are configured to implement step  304  of method  300  ( FIG. 3 ). More specifically, multipliers  616   1  and  616   2  operate to multiply baseband signals  612   1  and  612   2 , respectively, by exp[−jπ(f IF1 −f IF2 )t]. The resulting frequency-offset-corrected signals are signals  618   1  and  618   2 , respectively. Multipliers  616   3  and  616   4  similarly operate to multiply baseband signals  612   3  and  612   4 , respectively, by exp[jπ(f IF1 −f IF2 )t]. The resulting frequency-offset-corrected signals are signals  618   3  and  618   4 , respectively. 
     Frequency-offset-corrected signals  618   1 - 618   4  are applied to a bank  630  of configurable FIR filters (not individually shown in  FIG. 6 , see  FIG. 7 ), which are configured to implement step  306  of method  300  ( FIG. 3 ). In this particular embodiment, bank  630  has sixteen configurable FIR filters of the same length that are interconnected, e.g., as indicated in  FIG. 8 . The resulting equalized signals generated by filter bank  630  are signals  634   1 - 634   4 . 
     In an example embodiment, filter bank  630  is configured to perform signal processing that corresponds to a time-domain equivalent of Eq. (5) formulated for a four-component input and a four-component output, as expressed by Eq. (6): 
                     (           x   1               x   2               x   3               x   4           )     =       (             h   →     11             h   →     12             h   →     13             h   →     14                 h   →     21             h   →     22             h   →     23             h   →     24                 h   →     31             h   →     32             h   →     33             h   →     34                 h   →     41             h   →     42             h   →     43             h   →     44           )     ⁢     (             y   →     1                 y   →     2                 y   →     3                 y   →     4           )               (   6   )               
where x 1 -x 4  are the values of equalized signals  634   1 - 634   4  generated by bank  630  in a single symbol period; each of vectors {right arrow over (h)} mn  (where m=1, 2, 3, 4 and n=1, 2, 3, 4) represents a respective one of the sixteen configurable FIR filters from bank  630 ; and each of vectors {right arrow over (y)} 1 -{right arrow over (y)} 4  represents a string of values from a respective one of frequency-offset-corrected signals  618   1 - 618   4 . Each of vectors {right arrow over (h)} mn  and {right arrow over (y)} 1 -{right arrow over (y)} 4  has N components, with N being the number of taps in the FIR filters of bank  630 . More specifically, each of vectors {right arrow over (y)} 1 -{right arrow over (y)} 4  consists of the values supplied during the last N symbol periods by the respective one of frequency-offset-corrected signals  618   1 - 618   4 . Each of vectors {right arrow over (h)} mn  consists of the filter coefficients C 1 -C N  used in the respective FIR filter of bank  630  (also see  FIG. 7 ). The values of filter coefficients C 1 -C N  can be changed over time and are set by a filter controller  626  via a control signal  628  generated based on an error-update signal  624 . In operation, different FIR filters in bank  630  are typically configured to use different respective sets of coefficients C 1 -C N .
 
     In one embodiment, error-update signal  624  is generated based on error estimates derived by an error estimator  640  from signals  618   1 - 618   4  and  634   1 - 634   4 . Error estimator  640  is configured to generate sixteen such error estimates, each of which is then used to enable filter controller  626  to appropriately adjust coefficients C 1 -C N  of a respective one of the sixteen FIR filters in bank  630 . For example, for a PDM-QPSK constellation, error estimator  640  can be configured to generate a set of error estimates e mn  (where m=1, 2, 3, 4 and n=1, 2, 3, 4) as follows:
 
 e   mn ( k )=(1−| y   m ( k )| 2 ) y   m ( k ) x   n *( k )  (7)
 
where k is the counter of symbol periods; y m (k) is the value of signal  618   m  in the k-th symbol period; x n (k) is the value of signal  634   n  in the k-th symbol period; and the “*” symbol denotes the complex conjugate. The circuit coupled between error estimator  640  and filter controller  626  tracks average estimated errors E mn  by recursively updating them based on error estimates e mn  as follows:
 
 E   mn ( k )= E   mn ( k −1)+μ e   mn ( k )  (8)
 
where μ is an error-weighting coefficient. In each symbol period, average estimated errors E mn  are provided to filter controller  626  via error-update signal  624 . Filter controller  626  then uses average estimated errors E mn  to adaptively select coefficients C 1 -C N  for each of the sixteen FIR filters in bank  630 .
 
     Equalized signals  634   1 - 634   4  are applied to a constellation mapper  650 , which is configured to implement step  308  of method  300  ( FIG. 3 ). In one embodiment, constellation mapper  650  may be configured to (i) calculate distances between a value supplied by equalized signal  634   n  and the various constellation points of the operative constellation and (ii) select the nearest constellation point as an estimate of the corresponding transmitted symbol. The resulting sequences of estimated constellation symbols are sequences  654   1 - 654   4 . 
     Sequences  654   1 - 654   4  are applied to an error correction module  660 , where they are subjected to FEC decoding to remove possible errors (if any). After the errors are corrected, error correction module  660  generates output data streams data1 X , data1 Y , data2 X , and data2 Y , where the subscripts X and Y indicate the polarization using which the corresponding data stream was transmitted over fiber-optic link  140  ( FIG. 1 ). Taken together, data streams data1 X  and data1 Y  have all the data of data stream data1 (see  FIG. 1 ). Data streams data2 X  and data2 Y  similarly have all the data of data stream data2. 
       FIG. 7  shows a block diagram of a finite-impulse-response (FIR) filter  700  that can be used to implement any or each of the sixteen FIR filters in filter bank  630  ( FIG. 6 ) according to an embodiment of the disclosure. 
     Filter  700  is configured to receive an input signal  702  and generate a filtered output signal  732 . Filter  700  is an N-tap FIR filter comprising: (i) N−1 delay elements  710   1 - 710   N-1 ; (ii) N multipliers  720   1 - 720   N ; and (iii) an adder  730 . Each of delay elements  710   1 - 710   N-1  is configured to introduce a time delay τ, which is equal in duration to the symbol period. Each of multipliers  720   1 - 720   N  is configured to multiply a corresponding delayed copy of input signal  702  by a respective complex-valued coefficient C i , where i=1, 2, . . . , N. Adder  730  is configured to sum the output signals generated by multipliers  720   1 - 720   N  to generate filtered output signal  732 . In one embodiment, the number (N) of taps in FIR filter  700  can be between two and twelve. In an alternative embodiment, a significantly larger number of taps, e.g., about five hundred, may also be used. 
       FIG. 8  shows a block diagram of a MIMO equalizer  800  that can be used to implement filter bank  630  ( FIG. 6 ) according to an embodiment of the disclosure. More specifically, an embodiment of MIMO equalizer  800  corresponding to K=4 can be configured to operate as filter bank  630  in DSP  600  ( FIG. 6 ). In various alternative embodiments, parameter K can be selected to be any positive integer greater than one. 
     In operation, each of input terminals IN 1 -IN K  receives a digital input signal, such as one of signals  618   1 - 618   4  ( FIG. 6 ). Each of output terminals OUT 1 -OUT K  then outputs a respective output signals, such as one of signals  634   1 - 634   4  ( FIG. 6 ). Each of the processing blocks labeled h ij  (where i=1, 2, . . . K and j=1, 2, . . . K) represents a respective FIR filter, such as filter  700  ( FIG. 7 ). The filter coefficients C 1 -C N  for each filter h 1  are programmed by a corresponding controller, such as filter controller  626  ( FIG. 6 ), via a control-signal bus  802 . As indicated above, by using appropriate respective sets of filter coefficients C 1 -C N  in different filters h ij , MIMO equalizer  800  can substantially cancel the adverse effects of inter-carrier interference, and also possibly perform some other useful operations, such as polarization de-multiplexing. 
       FIG. 9  shows a block diagram of an optical transmitter  900  that can be used in optical transport system  100  ( FIG. 1 ) according to an alternative embodiment of the disclosure. More specifically, a modulated optical signal  930  generated by optical transmitter  900  can be applied to the ingress end of fiber-optic link  140  instead of optical signal  130  ( FIG. 1 ). Modulated optical signal  930  has K modulated optical carriers. When received at the egress end of fiber-optic link  140 , modulated optical signal  930  can be processed in the corresponding optical receiver, e.g., using a DSP that employs MIMO equalizer  800  ( FIG. 8 ). 
     Optical transmitter  900  includes intermediate-frequency (IF) generators  906   1 - 906   K , each configured to generate an electrical carrier wave having a respective intermediate frequency. The spacing between the neighboring intermediate frequencies is smaller than the baud rate R. Each electrical carrier wave generated by IF generators  906   1 - 906   K  is then modulated, using a respective one of data streams data1-dataK, in a respective one of electrical modulators  910   1 - 910   K . Each of the resulting modulated electrical carriers  912   1 - 912   K  has baud rate R. 
     Modulated electrical carriers  912   1 - 912   K  are combined in an electrical signal combiner  914 , and a resulting modulated multi-carrier electrical signal  916  is applied to a driver circuit  918 . Driver circuit  918  operates to convert modulated multi-carrier electrical signal  916  into a corresponding electrical drive signal  922  suitable for driving an I-Q modulator  924 . The conversion process may include, e.g., amplifying signal  916  and applying an appropriate dc bias to the resulting amplified signal. I-Q modulator  924  operates to up-convert electrical drive signal  922  to an optical frequency range, e.g., around 190 THz, by modulating an optical carrier wave supplied by a laser source  920 . The optical output signal generated by I-Q modulator  924  is optical signal  930 . As already indicated above, optical signal  930  has K modulated optical carriers. The spacing between the modulated optical carriers in optical signal  930  is approximately the same as the spacing between the frequencies of the electrical carrier waves generated by IF generators  906   1 - 906   K . 
     Although various embodiments have been described above in reference to optical heterodyne detection at the corresponding optical receiver (e.g.,  150 ,  FIG. 1 ), some embodiments can also be configured to work using optical intradyne detection, e.g., as described below in reference to  FIG. 10 . 
       FIG. 10  shows a block diagram of an optical intradyne detector  1000  that can be used instead of optical heterodyne detector  500  ( FIG. 5 ) according to an embodiment of the disclosure. Detector  1000  is configured to receive a PDM optical signal from fiber-optic link  140  (see  FIG. 1 ) and operates to convert this PDM optical signal into four electrical signals  1038   a - 1038   d , wherein electrical signals  1038   a  and  1038   b  represent the I- and Q-components of the X-polarization of the received PDM optical signal, and electrical signals  1038   c  and  1038   d  represent the I- and Q-components of the Y-polarization of the received PDM optical signal Each of signals  1038   a - 1038   d  may then be split into two copies, and each of the copies may be subjected to filtering similar to that applied to electrical signal  158  ( FIG. 1 ). However, one change in the filtering is that the corresponding filters now have pass-bands that are relatively close to or in the baseband, and not in the intermediate frequency range as filters  160  ( FIG. 1 ). The resulting filtered electrical signals may be converted into digital complex values and processed in an appropriately modified embodiment of DSP  600  ( FIG. 6 ). One of the modifications may be that down-converter  610  ( FIG. 6 ) may be omitted or bypassed. Another modification may be that multipliers  616   1 - 616   4  ( FIG. 6 ) may be configured to apply other appropriate multiplication factors to perform the frequency-offset correction. 
     Detector  1000  implements a polarization-diversity intradyne-detection scheme using an optical local-oscillator signal that can be generated by the appropriately tuned laser source  120   3 . Polarization beam splitters (PBSs)  1022   a - 1022   b  decompose the optical input signals into respective X- and Y-polarized components, labeled  1002   X ,  1012   X ,  1002   Y , and  1012   Y . These polarization components are then directed to an optical hybrid  1026 . 
     In optical hybrid  1026 , each of polarization components  1002   X ,  1012   X ,  1002   Y , and  1012   Y  is split into two (attenuated) copies, e.g., using a conventional 3-dB power splitter (not explicitly shown in  FIG. 10 ). A relative phase shift of about 90 degrees (π/2 radian) is then applied to one copy of component  1012   X  and one copy of component  1012   Y  using phase shifters  1028   a - 1028   b , respectively. The various copies of signals  1002   X ,  1012   X ,  1002   Y , and  1012   Y  are optically mixed with each other as shown in  FIG. 10  using four optical signal mixers  30 , and the mixed signals produced by the mixers are detected by eight photo-detectors (e.g., photodiodes)  1036 . Photo-detectors  1036  are arranged in pairs, as shown in  FIG. 10 , and the output of each photo-detector pair is a corresponding one of electrical signals  1038   a - 1038   d . This configuration of photo-detectors  1036  is a differential configuration that helps to reduce noise and improve DC balancing. In an alternative embodiment, detector  1000  may have four photo-detectors  1036 , one per optical signal mixer  30 , configured for single-ended detection of the corresponding optical signals. 
     Exemplary optical hybrids that are suitable for use in detector  1000  are described, e.g., in U.S. Patent Application Publication Nos. 2007/0297806 and 2011/0038631, both of which are incorporated herein by reference in their entirety. 
     According to an embodiment disclosed above in reference to  FIGS. 1-10 , provided is an apparatus comprising an optical detector (e.g., a combination of 154, 160 1 - 160   2 , and  168   1 - 168   2 ;  FIG. 1 ) configured to generate a first filtered electrical signal (e.g.,  170   1 ,  FIG. 1 ) and a second filtered electrical signal (e.g.,  170   2 ,  FIG. 1 ) based on a received modulated optical signal (e.g.,  142 ;  FIG. 1 ). The received modulated optical signal has (i) a first modulated optical carrier (e.g.,  126   1 ,  FIG. 1 ) having encoded thereon a first data stream (e.g., data1,  FIG. 1 ) at a selected baud rate (e.g., R; Eq. (1)), said first modulated optical carrier having a first carrier frequency (e.g., f 1 ; Eq. (1)), and (ii) a second modulated optical carrier (e.g.,  126   2 ,  FIG. 1 ) having encoded thereon a second data stream (e.g., data2,  FIG. 1 ) at the selected baud rate, said second modulated optical carrier having a second carrier frequency (e.g., f 2 ; Eq. (1)), wherein the first and second carrier frequencies are separated from one another by a frequency interval that is smaller than the selected baud rate. The second filtered electrical signal is different from the first filtered electrical signal. The apparatus further comprises a signal processor (e.g.,  172 ;  FIG. 1 ) configured to process the first and second filtered electrical signals to recover the first data stream and the second data stream. 
     In some embodiments of the above apparatus, the frequency interval is smaller than about 90% of the selected baud rate. 
     In some embodiments of any of the above apparatus, the frequency interval is smaller than about 80% of the selected baud rate but greater than about 20% of the selected baud rate. 
     In some embodiments of any of the above apparatus, the optical detector comprises: a first heterodyne detector (e.g.,  154 ;  FIGS. 1 and 5 ) configured to convert the received modulated optical signal into a first intermediate-frequency electrical signal (e.g.,  158 ,  FIG. 1 ;  558   X ,  FIG. 5 ) by mixing the received modulated optical signal with an optical local-oscillator signal (e.g.,  122   3 ;  FIG. 1 ); a first band-pass filter (e.g.,  160   1 ;  FIG. 1 ) configured to filter a first copy of the first intermediate-frequency electrical signal to generate the first filtered electrical signal; and a second band-pass filter (e.g.,  160   2 ;  FIG. 1 ) configured to filter a second copy of the first intermediate-frequency electrical signal to generate the second filtered electrical signal. 
     In some embodiments of any of the above apparatus, the optical detector comprises an optical intradyne detector (e.g.,  1000 ;  FIG. 10 ). 
     In some embodiments of any of the above apparatus, the optical local-oscillator signal has a third carrier frequency (e.g., f 3 ; Eq. (2)) that is detuned from a middle of the frequency interval by at least 2R, where R is the selected baud rate. 
     In some embodiments of any of the above apparatus, the first band-pass filter is configured to pass a first spectral band approximately centered at a first intermediate frequency (e.g., f IF1 ; Eq. (3a)); and the second band-pass filter is configured to pass a second spectral band approximately centered at a second intermediate frequency (e.g., f IF2 ; Eq. (3b)) different from the first intermediate frequency. 
     In some embodiments of any of the above apparatus, the first intermediate frequency and the second intermediate frequency are separated from one another by a frequency interval that is smaller than the selected baud rate; and each of the first and second spectral bands has a 3-dB width of about the selected baud rate. 
     In some embodiments of any of the above apparatus, the optical detector further comprises: a polarization beam splitter (e.g.,  502   1 ;  FIG. 5 ) configured to split the received modulated optical signal into a first (e.g., X) polarization component and a second (e.g., Y) polarization component; and a second heterodyne detector (e.g.,  154   Y ;  FIG. 5 ) configured to convert the second polarization component into a second intermediate-frequency electrical signal (e.g.,  558   Y ;  FIG. 5 ) by mixing the second polarization component with a respective (e.g., Y-pol.;  FIG. 5 ) polarization component of the optical local-oscillator signal. The first heterodyne detector (e.g.,  154   X ;  FIG. 5 ) is configured to convert the first polarization component into the first intermediate-frequency electrical signal (e.g.,  558   X ;  FIG. 5 ). 
     In some embodiments of any of the above apparatus, the optical detector further comprises: a third band-pass filter (e.g., an additional copy of  160   1 ;  FIG. 1 ) configured to filter a first copy of the second intermediate-frequency electrical signal to generate a third filtered electrical signal; and a fourth band-pass filter (e.g., an additional copy of  160   2 ;  FIG. 1 ) configured to filter a second copy of the second intermediate-frequency electrical signal to generate a fourth filtered electrical signal. The signal processor (e.g.,  600 ;  FIG. 6 ) is further configured to process the third and fourth filtered electrical signals to recover the first data stream and the second data stream. 
     In some embodiments of any of the above apparatus, the signal processor comprises: an electronic circuit (e.g.,  610 ,  616   1 - 616   4 ;  FIG. 6 ) configured to individually down-convert, by different respective frequency amounts (e.g., using steps  302 - 304 ,  FIG. 3 ), the first filtered electrical signal and the second filtered electrical signal to generate a first electrical baseband signal (e.g.,  618   1 ;  FIG. 6 ) and a second electrical baseband signal (e.g.,  618   3 ;  FIG. 6 ); and a MIMO equalizer (e.g.,  630 ,  FIG. 6 ;  800 ,  FIG. 8 ) configured to apply equalization processing (e.g., corresponding to Eqs. (5) and (6)) to the first and second electrical baseband signals to at least partially remove an effect of inter-carrier interference due to spectral overlap of the first modulated optical carrier and the second modulated optical carrier. The signal processor is configured to recover the first data stream and the second data stream based on a plurality of equalized electrical signals (e.g.,  634   1 - 634   4 ;  FIG. 6 ) generated by the MIMO equalizer as a result of said equalization processing. 
     In some embodiments of any of the above apparatus, the MIMO equalizer comprises a plurality of configurable finite-impulse-response filters (e.g.,  700 ,  FIG. 7 ; h 1 ,  FIG. 8 ). The signal processor further comprises a filter controller (e.g.,  626 ;  FIG. 6 ) configured to adaptively program, based on one or more error estimates, respective sets of filter coefficients (e.g., C 1 -C N ;  FIG. 7 ) used to configure different filters of said plurality of configurable finite-impulse-response filters, with said one or more error estimates being generated (e.g., as expressed by Eqs. (7)-(8)) based on the first and second electrical baseband signals and the plurality of equalized electrical signals. 
     In some embodiments of any of the above apparatus, the received modulated optical signal further has one or more additional modulated optical carriers (e.g., generated by  900 ;  FIG. 9 ) having encoded thereon one or more respective additional data streams (e.g., . . . dataK,  FIG. 9 ) at the selected baud rate; a respective carrier frequency of each of said one or more additional modulated optical carriers is separated from a carrier frequency of a nearest (in terms of the frequency) modulated optical carrier in the received modulated optical by a respective frequency interval that is smaller than the selected baud rate; the optical detector is further configured to generate one or more additional filtered electrical signals (e.g., corresponding to IN 1 -IN K ,  FIG. 8 ) based on the received modulated optical signal; and the signal processor is further configured to process said one or more additional filtered electrical signals together with the first and second filtered electrical signals to recover the one or more respective additional data streams. 
     In some embodiments of any of the above apparatus, the apparatus further comprises an optical transmitter (e.g.,  900 ,  FIG. 9 ) optically coupled to the optical detector via a fiber-optic link (e.g.,  140 ,  FIG. 1 ) and configured to apply the received modulated optical signal to the optical detector. 
     In some embodiments of any of the above apparatus, the fiber-optic link (e.g.,  140 ,  FIG. 1 ) comprises a single-mode fiber or a multimode fiber. 
     In some embodiments of any of the above apparatus, the apparatus further comprises at least a portion of the fiber-optic link (e.g.,  140 ,  FIG. 1 ). 
     In some embodiments of any of the above apparatus, the optical transmitter comprises: a plurality of electrical intermediate-frequency generators (e.g.,  906   1 - 906   K ,  FIG. 9 ), each configured to generate a respective electrical carrier wave having a respective intermediate frequency, wherein spacing between neighboring intermediate frequencies is smaller than the selected baud rate; a plurality of electrical modulators (e.g.,  910   1 - 910   K ;  FIG. 9 ), each configured to modulate the respective electrical carrier wave using a respective one of the first data stream, the second data stream, and the one or more additional data streams to generate a respective one of a plurality of modulated electrical carriers (e.g.,  912   1 - 912   K ;  FIG. 9 ); an electrical signal combiner (e.g.,  914 ;  FIG. 9 ) configured to combine the plurality of modulated electrical carriers to generate a modulated multi-carrier electrical signal (e.g.,  916 ;  FIG. 9 ); and an optical modulator (e.g.,  924 ;  FIG. 9 ) configured to generate the received modulated optical signal by modulating an optical carrier wave based on the modulated multi-carrier electrical signal. 
     In some embodiments of any of the above apparatus, the signal processor further comprises: a constellation mapper (e.g.,  650 ;  FIG. 6 ) configured to convert each of the plurality of equalized electrical signals into a respective sequence (e.g.,  654   1 - 654   4 ;  FIG. 6 ) of estimated constellation symbols; and an error correction module (e.g.,  660 ;  FIG. 6 ) configured to apply error-correction processing to the sequences of estimated constellation symbols generated by the constellation mapper to recover the first data stream and the second data stream. 
     In some embodiments of any of the above apparatus, the apparatus further comprises one or more optical transmitters (e.g.,  110   1 - 110   2 ,  FIG. 1 ;  400 ,  FIG. 4 ;  900 ,  FIG. 9 ) optically coupled to the optical detector via a fiber-optic link (e.g.,  140 ,  FIG. 1 ) and configured to apply the received modulated optical signal to the optical detector. 
     In some embodiments of any of the above apparatus, the one or more optical transmitters include: a first optical transmitter (e.g.,  110   1 ,  FIG. 1 ) configured to generate the first modulated optical carrier; and a second optical transmitter (e.g.,  110   2 ,  FIG. 1 ) configured to generate the second modulated optical carrier. The apparatus further comprises an optical combiner (e.g.,  128 ;  FIG. 1 ) configured to combine the first and second modulated optical carriers to generate the received modulated optical signal. 
     In some embodiments of any of the above apparatus, the one or more optical transmitters include: a plurality of electrical intermediate-frequency generators (e.g.,  906   1 - 906   K ,  FIG. 9 ), each configured to generate a respective electrical carrier wave having a respective intermediate frequency, wherein spacing between neighboring intermediate frequencies is smaller than the selected baud rate; a plurality of electrical modulators (e.g.,  910   1 - 910   K ;  FIG. 9 ), each configured to modulate the respective electrical carrier wave using a respective one of the first data stream, the second data stream, and one or more additional data streams to generate a respective one of a plurality of modulated electrical carriers (e.g.,  912   1 - 912   K ;  FIG. 9 ); an electrical signal combiner (e.g.,  914 ;  FIG. 9 ) configured to combine the plurality of modulated electrical carriers to generate a modulated multi-carrier electrical signal (e.g.,  916 ;  FIG. 9 ); and an optical modulator (e.g.,  924 ;  FIG. 9 ) configured to generate the received modulated optical signal by modulating an optical carrier wave based on the modulated multi-carrier electrical signal. 
     According to another embodiment disclosed above in reference to  FIGS. 1-10 , provided is an apparatus comprising: a first optical transmitter (e.g.,  110   1 ,  FIG. 1 ) configured to generate a first modulated optical carrier (e.g.,  126   1 ,  FIG. 1 ) having encoded thereon a first data stream (e.g., data1,  FIG. 1 ) at a selected baud rate (e.g., R; Eq. (1)), said first modulated optical carrier having a first carrier frequency (e.g., f 1 ; Eq. (1)); a second optical transmitter (e.g.,  110   2 ,  FIG. 1 ) configured to generate a second modulated optical carrier (e.g.,  126   2 ,  FIG. 1 ) having encoded thereon a second data stream (e.g., data2,  FIG. 1 ) at the selected baud rate, said second modulated optical carrier having a second carrier frequency (e.g., f 2 ; Eq. (1)), wherein the first and second carrier frequencies are separated from one another by a frequency interval that is smaller than the selected baud rate; and an optical combiner (e.g.,  128 ;  FIG. 1 ) configured to combine the first modulated optical carrier and the second modulated optical carrier for transmission over a fiber-optic link (e.g.,  140 ;  FIG. 1 ). 
     In some embodiments of the above apparatus, the frequency interval is smaller than about 90% of the selected baud rate. 
     In some embodiments of any of the above apparatus, the frequency interval is smaller than about 80% of the selected baud rate but greater than about 20% of the selected baud rate. 
     In some embodiments of any of the above apparatus, the first data stream comprises a first sub-stream (e.g., data1 X ;  FIG. 6 ) and a second sub-stream (e.g., data1 Y ;  FIG. 6 ); and the first optical transmitter (e.g.,  400 ;  FIG. 4 ) is configured to encode the first sub-stream onto a first (e.g., X) polarization of the first modulated optical carrier and encode the second sub-stream onto a second (e.g., Y) polarization of the first modulated optical carrier, said second polarization being approximately (e.g., within 10 degrees) orthogonal to the first polarization. 
     According to yet another embodiment disclosed above in reference to  FIGS. 1-10 , provided is an apparatus comprising: a plurality of electrical intermediate-frequency generators (e.g.,  906   1 - 906   K ,  FIG. 9 ), each configured to generate a respective electrical carrier wave having a respective intermediate frequency, wherein spacing between neighboring intermediate frequencies is smaller than a selected baud rate (e.g., R; Eq. (1)); a plurality of electrical modulators (e.g.,  910   1 - 910   K ;  FIG. 9 ), each configured to modulate the respective electrical carrier wave, at the selected baud rate and using a respective one of a plurality of data streams (e.g., data1-dataK;  FIG. 9 ) to generate a respective one of a plurality of modulated electrical carriers (e.g.,  912   1 - 912   K ;  FIG. 9 ); an electrical signal combiner (e.g.,  914 ;  FIG. 9 ) configured to combine the plurality of modulated electrical carriers to generate a modulated multi-carrier electrical signal (e.g.,  916 ;  FIG. 9 ); and an optical modulator (e.g.,  924 ;  FIG. 9 ) configured to generate a modulated optical signal (e.g.,  930 ;  FIG. 9 ) by modulating an optical carrier wave based on the modulated multi-carrier electrical signal. 
     In some embodiments, the FD-MIMO processing described above can be adapted for transmission format that exhibit relatively strong inter-carrier interference when the relationship between the carrier frequencies of the two modulated optical carriers used in optical transport system  100  is described by Eq. (9):
 
 R&lt;|f   1   −f   2 |&lt;5 R   (9)
 
A corresponding embodiment provides an apparatus comprising an optical detector (e.g., a combination of  154 ,  160   1 - 160   2 , and  168   1 - 168   2 ;  FIG. 1 ;  500  and the corresponding filters configured to filter signals  558   X  and  558   Y ,  FIG. 5 ; or  1000  and the corresponding filters configured to filter signals  1038   a - 1038   d ,  FIG. 10 ) configured to generate a first filtered electrical signal and a second filtered electrical signal based on a received modulated optical signal, wherein the received modulated optical signal has (i) a first modulated optical carrier having encoded thereon a first data stream at a selected baud rate, said first modulated optical carrier having a first carrier frequency, and (ii) a second modulated optical carrier having encoded thereon a second data stream at the selected baud rate, said second modulated optical carrier having a second carrier frequency. The apparatus further comprises a signal processor (e.g.,  600 ,  FIG. 6 ) configured to: (i) convert the first filtered electrical signal into a first electrical baseband signal; (ii) convert the second filtered electrical signal into a second electrical baseband signal; (iii) apply MIMO equalization processing (e.g., using  630 ,  FIG. 6 ) to the first and second electrical baseband signals to mitigate an effect of inter-carrier interference due to partial spectral overlap of the first modulated optical carrier and the second modulated optical carrier, said MIMO equalization processing configured to receive, as a first input, the first electrical baseband signal (e.g., one of  618 ,  FIG. 6 ), and further configured to receive, as a second input, the second electrical baseband signal (e.g., another one of  618 ,  FIG. 6 ), wherein said MIMO equalization processing is configured to generate a first equalized electrical signal (e.g., one of  634 ,  FIG. 6 ), as a first output thereof, and a second equalized electrical signal (e.g., another one of  634 ,  FIG. 6 ), as a second output thereof; (iv) recover the first data stream based on the first equalized electrical signal; and (v) recover the second data stream based on the second equalized electrical signal.
 
     In some embodiments of the above apparatus, the signal processor comprises a plurality of configurable finite-impulse-response filters (e.g.,  700 ,  FIG. 7 ;  800 ,  FIG. 8 ). The signal processor further comprises an electronic filter controller (e.g.,  626 ,  FIG. 6 ) configured to adaptively program, based on one or more error estimates, respective sets of filter coefficients used to configure different filters of said plurality of configurable finite-impulse-response filters, with said one or more error estimates being generated based on the first and second electrical baseband signals and the first and second equalized electrical signals. 
     In some embodiments of any of the above apparatus, the first and second carrier frequencies are separated from one another by a frequency interval that is greater than the selected baud rate. 
     In some embodiments of any of the above apparatus, the first and second carrier frequencies are separated from one another by a frequency interval that is smaller than 3R, where R is the selected baud rate. 
     While this invention has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various modifications of the described embodiments, as well as other embodiments of the invention, which are apparent to persons skilled in the art to which the invention pertains are deemed to lie within the principle and scope of the invention as expressed in the following claims. 
     Unless explicitly stated otherwise, each numerical value and range should be interpreted as being approximate as if the word “about” or “approximately” preceded the value of the value or range. 
     It will be further understood that various changes in the details, materials, and arrangements of the parts which have been described and illustrated in order to explain the nature of this invention may be made by those skilled in the art without departing from the scope of the invention as expressed in the following claims. 
     The use of figure numbers and/or figure reference labels in the claims is intended to identify one or more possible embodiments of the claimed subject matter in order to facilitate the interpretation of the claims. Such use is not to be construed as necessarily limiting the scope of those claims to the embodiments shown in the corresponding figures. 
     Although the elements in the following method claims, if any, are recited in a particular sequence with corresponding labeling, unless the claim recitations otherwise imply a particular sequence for implementing some or all of those elements, those elements are not necessarily intended to be limited to being implemented in that particular sequence. 
     Reference herein to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the invention. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments necessarily mutually exclusive of other embodiments. The same applies to the term “implementation.” 
     Also for purposes of this description, the terms “couple,” “coupling,” “coupled,” “connect,” “connecting,” or “connected” refer to any manner known in the art or later developed in which energy is allowed to be transferred between two or more elements, and the interposition of one or more additional elements is contemplated, although not required. Conversely, the terms “directly coupled,” “directly connected,” etc., imply the absence of such additional elements. 
     The description and drawings merely illustrate the principles of the invention. It will thus be appreciated that those of ordinary skill in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the invention and the concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to encompass equivalents thereof. 
     The functions of the various elements shown in the figures, including any functional blocks labeled as “processors” and “controllers,” may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared. Moreover, explicit use of the term “processor” or “controller” should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASIC), field programmable gate array (FPGA), read only memory (ROM) for storing software, random access memory (RAM), and non volatile storage. Other hardware, conventional and/or custom, may also be included. Similarly, any switches shown in the figures are conceptual only. Their function may be carried out through the operation of program logic, through dedicated logic, through the interaction of program control and dedicated logic, or even manually, the particular technique being selectable by the implementer as more specifically understood from the context. 
     It should be appreciated by those of ordinary skill in the art that any block diagrams herein represent conceptual views of illustrative circuitry embodying the principles of the invention. Similarly, it will be appreciated that any flow charts, flow diagrams, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.