Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
  • H04B10/07—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems
  • H04B10/075—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems using an in-service signal
  • H04B10/079—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems using an in-service signal using measurements of the data signal
  • H04B10/0795—Performance monitoring; Measurement of transmission parameters
  • H04B10/07955—Monitoring or measuring power
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
  • H04B10/07—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems
  • H04B10/075—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems using an in-service signal
  • H04B10/079—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems using an in-service signal using measurements of the data signal
  • H04B10/0799—Monitoring line transmitter or line receiver equipment
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
  • H04B10/50—Transmitters
  • H04B10/516—Details of coding or modulation
  • H04B10/54—Intensity modulation
  • H04B10/541—Digital intensity or amplitude modulation

Definitions

• the disclosure relates generally to the field of optical communication.
• One embodiment provides an apparatus that includes an optical transmitter configured to provide an optical signal amplitude-modulated among M different levels.
• a constellation control module is configured to provide a drive signal to control the optical signal.
• a feedback module is configured to receive a measure of spacing between amplitude peaks of a signal constellation of the optical signal and to adjust the optical signal in response to the measure of symbol spacing.
• Another embodiment provides a method, e.g. for forming an optical transmitter.
• the method includes configuring an optical transmitter to provide an optical signal amplitude- modulated among M different levels.
• the method further includes configuring a constellation control module to control a drive signal to control the optical signal.
• the method still further includes configuring a feedback module to receive a measure of spacing between amplitude peaks of a symbol constellation of the optical signal.
• the feedback module is further configured to adjust the optical signal in response to the measure of spacing.
• the constellation control module and feedback controller may be configured to substantially equalize spacing between symbols of an amplitude-shift keyed symbol constellation.
• the optical transmitter may include a vertical cavity surface-emitting laser (VCSEL) configured to generate the optical signal in response to the drive signal.
• the drive signal may indicate an amplitude, a bias level and an amplitude peak spacing.
• the feedback module may be configured to provide an amplitude peak spacing adjustment signal.
• the optical transmitter may include an electro-absorption modulator configured to modulate light from the laser into the M different levels in response to the drive signal.
• the optical transmitter may include a Mach-Zehnder modulator (MZM) configured to modulate light from a laser into the M different levels in response to the drive signal.
• MZM Mach-Zehnder modulator
• Any embodiment may further include a coherent optical receiver.
• the receiver may be configured to determine a spacing between amplitude peaks of the symbol constellation, and may be further configured to produce the measure of symbol spacing therefrom.
• two lasers may be configured to provide polarization-multiplexed signals on first and second different polarizations of the optical signal.
• the apparatus includes an optical detector and a constellation characterization module.
• the optical detector is configured to demodulate a received optical signal and to produce therefrom a received symbol constellation.
• the constellation characterization module is configured to determine a spacing between amplitude peaks of the received symbol constellation, and to provide a measure of the symbol spacing.
• the optical receiver may include a local oscillator and optical hybrid configured to determine in-phase and quadrature components of the optical signal.
• the optical receiver may include an optical 120-degree hybrid configured to determine in-phase and quadrature components of the optical signal.
• each symbol of the symbol constellation may be represented by a closed curve in the in-phase /quadrature (I/Q) plane.
• the amplitude detector may determine a spacing between the closed curves.
• FIG. 3 illustrates an embodiment of the disclosure in which an optical communication system includes 1) a transmitter, the transmitter including lasers directly modulated with M- level, e.g. 4-level, electrical signals to generate an M-ASK optical signal, and 2) a receiver that employs an optical hybrid to demodulate the optical signal to recover data without employing carrier and phase recovery;
• M- level e.g. 4-level, electrical signals to generate an M-ASK optical signal
• receiver that employs an optical hybrid to demodulate the optical signal to recover data without employing carrier and phase recovery
• FIG. 4 illustrates an alternate embodiment of the receiver of FIG. 3 in which optical 120-degree hybrids, e.g. 3X3 optical couplers, provide some functionality of the optical hybrids of FIG. 3;
• optical 120-degree hybrids e.g. 3X3 optical couplers
• FIG. 5 illustrates an alternate embodiment of the transmitter of FIG. 3, in which Mach Zehnder modulators are employed to produce the transmitted optical signal of FIGs. 3 and 4 ;
• FIG. 6 illustrates an alternate embodiment of the transmitter of FIG. 3, wherein electro-absorption modulators are employed to produce the transmitted optical signal of FIGs. 3 and 4 ;
• FIGs. 7A-7C illustrate aspects of a received constellation, wherein FIG. 7A illustrates an embodiment in which the constellation includes continuous closed curves, and wherein FIGs. 7B and 7C illustrate embodiments in which the constellation includes open arcs;
• FIG. 8 illustrates an experimental configuration, including a shaping filter between the transmitter and receiver, that may be used to determine the characteristics presented in FIGs. 9A/B, 10, 11 and 12;
• FIGs. 9A and 9B respectively illustrate I/Q characteristics of the signal transmitted by the embodiment of FIG. 8 with and without the shaping filter;
• FIG. 10 illustrates peak intensity characteristics of the signal transmitted by the embodiment of FIG. 3 with and without the shaping filter and an example response of the shaping filter;
• FIG. 11 illustrates experimental performance of the embodiment of FIG. 8 for back-to-back operation (e.g. negligible optical path length between the transmitter and receiver);
• FIG. 12 illustrates bit error rate (BER) characteristics of the embodiment of FIG. 8 as a function of launch power for three span lengths, e.g. 320 km, 640 km and 960 km;
• BER bit error rate
• FIG. 13 illustrates a embodiment of a PAM transmission system configured to about equalize spacing between constellation symbols, such as the symbol rings of FIG. 7A;
• FIG. 14 illustrates an embodiment of a method of operating the system of FIG. 13 to equalize symbol spacing
• FIG. 15 illustrates experimental performance of a test system configured to implement the embodiment illustrated in FIG. 13 in a 4-PAM transmission system in back-to-back operation (e.g. negligible optical path length between the transmitter and receiver ) .
• VCSELs are used widely in short-reach and low-data- rate applications due to their relative low cost, energy efficiency, and small footprint. Recent developments have enabled 40 Gb/s operation of single-mode 1.5- ⁇ VCSELs and a maximum transmission distance of 60 km at 10 Gb/s. A 100 Gb/s short-reach link using VCSELs with direct modulation has also been demonstrated recently, with 4-level pulse amplitude modulation (PAM) , polarization-division multiplexing (PDM) and direct detection. However, only a 100 m transmission distance was achieved. For this and other considerations, directly modulated VCSELs are conventionally not generally considered to be suited for metro networks with transmission distances between 100 km and 1000 km at high data rates.
• PAM polarization-division multiplexing
• FIG. 1 illustrates a first prior art implementation that uses multiple transmitters and receivers.
• a system may include ten 10 Gb/s transmitters 110 and receivers 120, or as illustrated, four 25 Gb/s transmitters HOa-llOd and receivers 120a-120d (4 x 25 Gb/s) .
• One deficiency of such an implementation is that it occupies a large bandwidth, e.g. typically cannot fit into a 50-GHz channel spacing.
• such a system typically cannot transmit over a distance greater than about a few hundred kilometers without using optical dispersion compensation.
• FIG. 2 illustrates a second prior art implementation that directly modulates two lasers 210a, 210b with 4-level signals.
• the laser outputs are differently, e.g. orthogonally, polarized, and combined using a polarization beam combiner (PBC) 220.
• the signal is received by a polarization beam splitter (PBS) 230 that separates the two polarizations.
• PBS polarization beam splitter
• Two direct- detection receivers 240a and 240b then receive the separated polarized signals.
• optical polarization tracking is typically needed, which is generally bulky.
• optical dispersion compensation is typically needed for distances of more than a few tens of kilometers .
• a third prior art implementation uses subcarrier modulation.
• Polarization division multiplexing PDM
• PDM Polarization division multiplexing
• optical polarization tracking is typically needed.
• PMD polarization-mode dispersion
• Embodiments within the scope of the disclosure overcome some of the deficiencies of the aforementioned prior art implementations .
• optical sources e.g. lasers
• M may be directly modulated with M-level electrical signals to generate M amplitude-shift keyed (ASK) optical signals.
• ASK amplitude-shift keyed
• M is shown without limitation as being equal to four.
• the complexity of the optical transmitter is significantly reduced relative to a coherent transmitter.
• Polarization division multiplexing (PDM) is used in some embodiments to reduce the bandwidth of the signal.
• PDM-4ASK modulated system may implement a 100 Gb/s transmission rate using a 25 Gbaud symbol rate.
• the received symbol stream may be coherently detected, which can optionally provide chromatic dispersion compensation and polarization demultiplexing in the electrical domain with digital signal processing (DSP) .
• DSP digital signal processing
• the transmitted signal is ASK modulated, no carrier frequency and phase recoveries are needed, which significantly reduces the complexity and power consumption of the receivers.
• the lasers are VCSELs, further reducing cost.
• FIG. 3 illustrates a block diagram of a system 300 in a nonlimiting embodiment.
• the system 300 includes a transmitter 310 and a receiver 320.
• the transmitter 310 includes two lasers 330a and 330b.
• the lasers 330a and 330b are not limited to any particular laser type, and each may be, e.g. an edge-emitting distributed feedback (DFB) , distributed Bragg reflector (DBR) or Fabry-Perot (FP) laser, a VCSEL, or a laser followed by an external modulator such as an electro-absorption modulator or an interference-based modulator.
• DBR distributed Bragg reflector
• FP Fabry-Perot
• VCSEL Fabry-Perot
• embodiments including this laser type may be advantageous in that, e.g., the VCSEL may be lower cost and have greater reliability than a comparable edge-emitting laser diode.
• polarization components of the signal 350 which may be arbitrarily rotated with respect to the polarization at the output of the transmitter 310, are separated by a PBS 355.
• a local oscillator (LO) 360 produces two polarization components, e.g. H and V, which are separated by a PBS 365.
• Each polarization component from the PBS 355 beats with a corresponding polarization component from the PBS 365 in a corresponding one of two polarization diverse 90° optical hybrids 370a, 370b.
• Unreferenced photo-detectors e.g.
• a DSP 380 provides chromatic dispersion (CD) compensation, polarization demultiplexing and intersymbol interference (ISI) equalization.
• CD chromatic dispersion
• ISI intersymbol interference
• the symbol identification may be performed directly after the equalizers. Notably, no carrier frequency and phase recoveries are needed by or are used in the illustrated embodiment .
• FIG. 4 illustrates an alternate embodiment, e.g. a receiver 400, that includes a receiver 410.
• optical 120-degree hybrids e.g. 3x3 couplers, 420a, 420b replace the 90° optical hybrids 370a and 370b of the system 300.
• appropriately configured 3x3 couplers may be used in lieu of optical hybrids in optical receivers. See, e.g. in C. Xie, et al, "Colorless coherent receiver using 3x3 coupler hybrids and single-ended detection," Optics Express, Vol. 20, No. 2, pp. 1164-1171, 2012, incorporated herein by reference.
• the couplers 420a-b are expected to provide significantly lower cost relative to embodiments using optical hybrids, e.g. the receiver 320.
• Three single-ended detectors 430 are used for each 3x3 coupler, and additional signal processing may be needed to obtain I and Q components.
• a DSP 440 may include the functionality of the DSP 380 and additional functionality to determine I and Q of each received polarization channel.
• the optical signal field E s and LO field E L at the input of the coupler, output photocurrents of the detectors 430, e.g. single-ended detectors, are described by
• Eq. (1) the direct- detection term
• the second term is the beat term.
• the direct- detection term can become relatively large compared to the beat term if local-oscillator-to-signal power ratio (LOSPR) is small and/or there are many wavelength-division multiplexed (WDM) channels (
• LOSPR local-oscillator-to-signal power ratio
• WDM wavelength-division multiplexed
• the transmitter 510 includes an unmodulated (CW) laser source 520, Mach-Zehnder modulators (MZMs) 530a, 530b, the previously referenced PR 335 and the previously referenced PBC 340.
• the PR 335 rotates the polarization of the modulated light from the MZM 530b relative to the light from the MZM 530a by, e.g. n/2 radians, and the signals are recombined by the PBC 340.
• FIG. 6 illustrates another alternate embodiment of an
• EAMs electro-absorption modulators
• an EAM may modulate the intensity of an optical signal propagating therethrough in response to an applied voltage, wherein the voltage modulates the bandgap of the propagation medium.
• the EAMs 620a/b thereby may be used to modulate the intensity of the CW light received from the laser 520.
• the remaining elements of the transmitter 610 may operate as previously described.
• FIGs. 7A-7C illustrate aspects of received signal constellations 700A, 700B and 700C in various embodiments. Each figure show a complex I-Q space, e.g. a plane, with in-phase (horizontal axis) and quadrature (vertical axis) components of the constellations 700A-700C.
• the constellation 700A includes a number of closed curves 710, e.g. concentric rings, and a symbol point 720.
• This constellation represents data simulated in one embodiment after equalization for one polarization of a dual-polarized transmitted signal, wherein each of the closed curves 710 and the symbol point 720 represent a transmitted symbol, as further described below.
• the closed curves 710 may be viewed as arcs having an angle measure of 2 ⁇ .
• the linewidths of the transmitter lasers (e.g. lasers 330a/b) and the LO laser (e.g. laser 360) are 500 MHz and 10 MHz, respectively, without limitation thereto.
• the frequency offsets between the transmitter and LO lasers are 1 GHz and 2 GHz for x and y polarizations, respectively, without limitation thereto.
• the constellation 700B illustrates aspects of the received signal constellation when the concentric rings of the constellation 700A are not fully closed, e.g. are open arcs.
• This constellation includes open arcs 730 and the symbol point 720.
• Each of the open arcs 730 and the point 720 represent a transmitted symbol.
• the open arcs 730 each have an angle measure less than 2 ⁇ , in this example about 11 ⁇ /6.
• Each open arc 730 may extrapolated along its radius to form closed curves, or rings, 740 that are analogous to the closed curves 710.
• the constellation 700C illustrates aspects of the received signal constellation, wherein arcs 750 have an angle measure substantially less than 2 ⁇ , e.g. about ⁇ /4.
• the arcs 750 may be also extrapolated to form closed curves, or rings, 760 that are analogous to the closed curves 710.
• the angle measure of the constellation arcs is determined at least in part by the linewidth of the laser 330. It is expected that lasers 330 having a smaller linewidth produce constellation arcs having a smaller angle measure, while lasers 330 having a larger linewidth produce constellation arcs having a larger angle measure. For instance, when the laser 330 linewidth is large enough the constellation includes closed curves, such as in FIG. 7A. In the limit of very small linewidth the constellation may include points, e.g. arcs with very small angle measure.
• the constellations 700B and 700C illustrate examples between these two extremes, in which the arcs are open arcs .
• the angular position of one of the symbol arcs in the constellations 700B and 700C may be indeterminate with respect to the others of the symbol arcs. This may occur when, e.g., the polarization rotation of the transmitted light that is resolved into each symbol arc is unconstrained.
• Each closed curve 710 may be referred to as a "symbol ring”.
• each arc 730, 750 may be referred to as a symbol ring, even if the arc has an angle measure less than 2 ⁇ , e.g. is an open arc, by virtue of the extrapolation of each arc onto a closed curve such as one of the rings 740 or 760.
• the term "concentric" as applied to two or more symbol rings, closed curves or arcs means that one symbol ring, closed curve or arc is located within the other symbol ring, closed curve or arc.
• a first arc is located within a second arc when the first arc extrapolates to a closed curve with a smaller radius than a closed curve to which the second arc extrapolates.
• the constellations 700A-700C each include three concentric symbol rings, as well as a symbol located at the about the origin.
• the symbol ring having a smaller radius is referred to herein as a lower-order symbol ring
• the symbol ring having a larger radius is referred to herein as a higher-order symbol ring.
• symbols are represented by entire rings here, i.e., the meaning of a symbol in these constellations is independent of the optical field value on the ring.
• concentric symbol rings need not exactly share an origin, though the term is inclusive of embodiments in which the symbol rings share an origin.
• the symbol rings 710 are about circular, embodiments include symbol rings that are not circular, e.g. a closed path such, but not limited to, about oval.
• one symbol ring may have a small radius such that that symbol ring is effectively a symbol point, at about the origin of the other symbol rings.
• Such a symbol point e.g. the symbol point 720, may be regarded as a concentric symbol ring when wholly contained within one or more other symbol rings.
• the constellation 700 represents four received symbols.
• FIG. 8 illustrates an experimental configuration of another embodiment, e.g. a system 800.
• the system 800 includes a laser 810, digital-to-analog converter (DAC) 820, polarization multiplexer 830, amplifiers 840, shaping filter 850, optical path 855, amplifier LO 860, coherent receiver 870, digital sampling oscilloscope 880 and offline processing 890.
• DAC digital-to-analog converter
• polarization multiplexer 830 amplifiers 840, shaping filter 850, optical path 855, amplifier LO 860, coherent receiver 870, digital sampling oscilloscope 880 and offline processing 890.
• the embodiment may be referred to as "back-to-back".
• the length of the optical path 855 may be on the order of hundreds of kilometers (km) .
• the driver 820 provides 35 Gbaud 3-level amplitude direct modulation of the laser 810, e.g.
• the optical filter 850 is configured to reduce the intensity of a proper subset of the plurality of concentric symbol rings. This aspect is described further below.
• the laser 810 is a VCSEL it may have a large linewidth, e.g. >500 MHz. However, this has little effect on system performance, and no carrier frequency and phase recoveries are needed in the processing 890, which further reduces complexity and power consumption of the coherent receiver .
• the filter 850 may operate to reduce the intensity of a proper subset of the concentric symbol rings. For example, inspection of FIGs. 9A and 9B indicate that the intensity of the lower-order symbol ring 910 located about at the origin of the I-Q plane (the lowest-order symbol ring) is reduced by the presence of the filter 850, thereby enhancing the contrast between the symbol rings of the set. Further comparing of the unfiltered (FIG. 9A) and filtered (FIG. 9B) characteristics, the filtering provides significant contrast enhancement of concentric symbol rings 920 and 930 of the constellation, which is expected to improve the performance of the detected signal.
• the filter 850 suppresses the lower-level amplitude and increases the amplitude difference between different signal in the I/Q space.
• the presence of the filter 850, by enhancing the signal contrast, is expected to significantly improve system performance in some embodiments, as further illustrated below.
• F I G . 10 illustrates intensity of the signal output by the amplifier 840a in the embodiment of F I G . 8 as a function of wavelength without filtering (1010) and with filtering (1020) using the previously described 0.67-nm filter.
• An overlying filter response 1030 illustrates operation of the filter 850 to reduce the intensity of the optical signal at wavelengths above and below about 1526 nm. The reduction has the effect of, e.g. the aforementioned intensity reduction of a proper subset of the symbol rings, e.g. the lowest order symbol ring.
• the filtered characteristic also illustrates significant reduction of the off-peak optical noise floor, consistent with the improved constellation characteristics shown in F I G . 9B.
• the filter 850 In a directly modulated laser, e.g. the lasers 330a and 330b, higher-intensity symbols are typically blue shifted relative to lower-intensity symbols.
• the red shifted signal portion e.g. lower-intensity symbols
• the blue shifted signal portion e.g. higher-intensity symbols
• the spectrum of the signal is located at a wavelength at which the filter response has a negative slope, e.g. increasing attenuation with the increasing of wavelength.
• the peak filter response is located at about 1526.1 nm, while the peak signal intensity, or the signal center frequency, is located at about 1526.7 nm.
• the filter response may be shifted relative to the signal center wavelength by about 0.5 nm in the direction of shorter wavelength, e.g. in the blue direction.
• the wavelength difference ⁇ between the peak filter response and the signal center wavelength is about 0.5 nm.
• this relationship between the peak filter response wavelength and the signal center wavelength results in conversion from frequency modulation (FM) to amplitude modulation (AM) . This conversion is expected to increase the eye-opening of the signal and thus the performance of the system.
• ⁇ is chosen such that the entire signal spectrum is located within the region of the filter response having negative slope, e.g., the wavelength of the whole signal spectrum is larger than center wavelength of the filter.
• the signal spectrum 1010 is substantially located at wavelengths greater than 1526 nm and thus is coincident with the portion of the filter response 1030 having negative slope.
• bit error rate (BER) of the system 800 in back-to-back operation is illustrated versus optical signal-to-noise ratio (OSNR) .
• OSNR optical signal-to-noise ratio
• This characteristic shows that in this particular embodiment there is an error floor at a BER of about 2.0xl0 ⁇ 3 .
• FEC forward- error-correction
• substantially error-free operation may be expected with an OSNR larger than about 26 dB .
• substantially error-free operation is expected with an OSNR larger than 20.3 dB .
• an embodiment denoted 1300 is illustrated, e.g. an optical transmission system, that includes an optical transmitter 1305 and an optical receiver 1310.
• the transmitter 1305 is configured to transmit a modulated optical signal 1315 to the receiver 1310 by way of an optical path.
• the optical path is not limited to any particular type, but may in some embodiments include an optical fiber.
• a laser 1330 is configured to provide an optical signal that is amplitude-modulated among M different levels.
• the modulation produces a signal constellation, such as exemplified by the constellations 700A, 700B and 700C.
• a constellation control module 1340 is configured to control an amplitude and/or a bias of laser drive signal of the laser 1330, e.g. to provide the amplitude modulation of the optical signal 1315 to produce the signal constellation.
• the transmitter 1305 also includes a feedback module 1350.
• the feedback module 1350 is configured to receive a measure of symbol spacing of the signal constellation of the optical signal 1315 and to regulate the control module 1340 to adjust the laser 1330 drive signal in response to the measure of symbol spacing.
• the feedback module 1350 provides a first electrical signal to the control module 1340 and a second electrical signal to a digital-to- analog converter (DAC) 1360.
• DAC digital-to- analog converter
• An optional amplifier 1370 may scale the output of the DAC 1360 to an appropriate level.
• the first signal may be a bias adjust and/or amplitude signal, e.g. may direct the control module 1340 to change a DC bias and/or signal amplitude applied to the laser 1330 drive signal.
• the second signal may be a peak amplitude spacing adjustment signal, e.g. may direct the DAC 1360 to change one or more peak amplitude spaces between constellation symbols.
• the bias /amplitude adjust signal and the symbol spacing adjustment signal may be applied dynamically, e.g. on the time scale of the individual symbols conveyed by the optical signal 1315, so that a spacing between the amplitude peaks of the signal constellation may be controlled.
• the spacing between amplitude peaks be substantially equal among the adjacent symbols.
• substantially equal means the spacing between peak amplitudes in the symbol constellation differ by less than about 10%. In some cases, it may be preferable that the spacings differ by no greater than about 5%. In still other cases, it may be preferable that the spacings differ by no greater than about 1%.
• the module 1335 may determine any suitable measure of the spacing between the peak amplitude of adjacent pairs of symbols, e.g. an average spacing, or determining the spacing between best-fit geometrical models of the constellation symbols, e.g. ellipses.
• the embodiment of FIG. 13 is described for the nonlimiting example of controlling the laser 1330 to produce the signal 1315 in response to the output of the drive module 1340.
• the signal 1315 may be produced by, e.g. the transmitter 510 (FIG. 5) or the transmitter 610 (FIG. 6) .
• the control module 1340 may control an electro-absorption modulator or an MZM as appropriate to the particular embodiment.
• FIG. 14 presents an embodiment of a method 1400, e.g. for adjusting the amplitude and/or DC bias of the signal 1315 to at least partially equalize differences in amplitude between symbols of a received constellation, e.g. a pulse amplitude modulation constellation.
• the method 1400 may be performed, e.g. by the control module 1340 and DAC 1360.
• the method 1400 is described with reference to the functional entities illustrated in FIG. 13 without limitation to the illustrated embodiment.
• the illustrated method 1400 may include additional steps, or may include different steps, that effect the desired amplitude characteristics while remaining within the scope of the disclosure.
• the laser control signal is set, e.g.
• the laser driving signal could have four levels that are about integer multiples of an initial level V 0 , e.g. V 0 , 2V 0 , 3V 0 , and 4V 0 .
• the initial bias may be any value, e.g. about zero volts DC.
• a step 1420 it is determined whether the amplitude levels of the signal constellation are about equally spaced, e.g. by the module 1335 after detection by the receiver 1320. If the amplitudes are not determined to be about equally spaced then the method advances to a step 1430, in which the amplitude and/or DC bias of the laser control signal is/are adjusted and/or the level spacing of the DAC is adjusted. Such adjustment may include sending by the module 1335 to the feedback module 1350 one or more signals characterizing differences between the received constellation and desired amplitude characteristics, e.g. even spacing between symbol rings. The feedback module 1350 may then operate as previously described to effect a change of the laser control signal.
• the method 1400 then returns to the step 1420 and again tests the symbol amplitudes of the received constellation. If the symbol constellation responded in a desired manner to the change of amplitude and/or DC bias of the laser control signal and the level spacing of the DAC, the module 1335 and the feedback module may operate to incrementally about equalize differences of the constellation symbol spacing. If instead the symbol constellation responded such that the differences in constellation symbol spacing are greater, the module 1335 and the feedback module 1350 may operate to change the amplitude and/or DC bias of the laser control signal in a manner that differences of the constellation symbol spacing.
• the method 1400 may advance to a termination state 1440.
• a threshold value e.g. a level that results in reduced BER of the symbol stream received by the receiver 1320
• the method 1400 may advance to a termination state 1440.
• the module 1335 and the feedback module 1350 may continue to monitor the received symbol constellation and operate to change laser control signal amplitude and/or DC bias and level spacing as needed to maintain a desired level of BER.
• FIG. 15 illustrates BER as a function of OSNR for two cases of a test system transmitting a 32 Gbaud 4-PAM signal generated by an EAM.
• a laser e.g. the laser 1330
• the laser was controlled to equalize the intensities of the constellation symbols, e.g. the rings of the constellation 700A. This case is similar to the BER characteristic shown in FIG. 8.
• the laser was controlled to equalize the spacing between the constellation symbols.
• a comparison between the BER characteristics for these two cases shows about a factor of ten improvement of BER at 30dB OSNR, which is expected to significantly improve transmission fidelity and/or allow for a longer transmission reach.

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