Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for clock synchronizing an optical system and multiple leaf systems. In some implementations, a method includes: first data is received from an optical system. The first data is detected using a local oscillator signal provided by a local oscillator laser. The first data is processed using a first sampling rate. A frequency of a clock signal supplied by a reference clock is adjusted based on the processed first data. Second data is transmitted to the optical system at a rate based on the clock signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for clock synchronizing an optical system and multiple leaf systems. In some implementations, an apparatus includes a receiver comprising: a local oscillator laser providing a local oscillator signal, a detector circuit operable to receive a first optical signal and detect first data carried by the first optical signal based on the local oscillator signal, a reference clock circuit supplying a clock signal, a digital signal processor (DSP) operable to receive the first data and supply a control signal to the reference clock circuit based on the first data, the reference clock circuit being operable to adjust the clock signal based on the control signal; and a transmitter operable to output a second optical signal carrying second data, the second data having an associated rate that is based on the clock signal.

Abstract: Methods, systems, transceivers, and apparatus are included for clock synchronizing an optical system and multiple leaf systems. In some implementations, a transceiver includes a receiver and a transmitter. The receiver includes an optical hybrid circuit operable to receive a first modulated optical signal and local oscillator light and to supply optical mixing products based on the first modulated optical signal and the local oscillator light. A photodiode circuit operable to supply an electrical signal based on the optical mixing products. An analog-to-digital conversion circuitry operable to supply digital signals based on the electrical signal. A digital signal processor operable to generate a supply signal based on the digital signals and provide the supply signal to a reference clock circuit for generating a clock signal. The transmitter is operable to output a second modulated optical signal that includes a timing of data based on the clock signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for clock synchronizing an optical system and multiple leaf systems. In some implementations, a method includes: first data is received from an optical system. The first data is detected using a local oscillator signal provided by a local oscillator laser. The first data is processed using a first sampling rate. A frequency of a clock signal supplied by a reference clock is adjusted based on the processed first data. Second data is transmitted to the optical system at a rate based on the clock signal.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for clock synchronizing an optical system and multiple leaf systems. In some implementations, an apparatus includes a receiver comprising: a local oscillator laser providing a local oscillator signal, a detector circuit operable to receive a first optical signal and detect first data carried by the first optical signal based on the local oscillator signal, a reference clock circuit supplying a clock signal, a digital signal processor (DSP) operable to receive the first data and supply a control signal to the reference clock circuit based on the first data, the reference clock circuit being operable to adjust the clock signal based on the control signal; and a transmitter operable to output a second optical signal carrying second data, the second data having an associated rate that is based on the clock signal.

Abstract: Methods, systems, transceivers, and apparatus are included for clock synchronizing an optical system and multiple leaf systems. In some implementations, a transceiver includes a receiver and a transmitter. The receiver includes an optical hybrid circuit operable to receive a first modulated optical signal and local oscillator light and to supply optical mixing products based on the first modulated optical signal and the local oscillator light. A photodiode circuit operable to supply an electrical signal based on the optical mixing products. An analog-to-digital conversion circuitry operable to supply digital signals based on the electrical signal. A digital signal processor operable to generate a supply signal based on the digital signals and provide the supply signal to a reference clock circuit for generating a clock signal. The transmitter is operable to output a second modulated optical signal that includes a timing of data based on the clock signal.

Abstract: A system may include an optical transmitter and an optical receiver. The optical transmitter may generate optical signals associated with sub-carriers, and may provide the optical signals via an optical link. The optical receiver may receive the optical signals via the optical link, and may generate samples based on the optical signals. The samples may be associated with the sub-carriers. The optical receiver may combine the samples to form a time domain sample vector having a particular size, and may generate a frequency domain sample vector, having the particular size, based on the time domain sample vector. The optical receiver may demultiplex the frequency domain sample vector to generate domain sample vectors corresponding to the sub-carriers. The optical receiver may process the frequency domain sample vectors to generate equalized frequency domain sample vectors, and may output the equalized frequency domain sample vectors.

Abstract: An optical system includes an optical transmitter configured to modulate an optical signal to carry data, associated with an optical channel, via multiple sub-carriers in a quantity greater than four. The optical system further includes an optical receiver configured to demodulate the optical signal to recover the data from the multiple sub-carriers.

Abstract: An optical system may include optical transmitters to provide respective optical signals. Each of the respective optical signals may provide one or more carriers in an optical channel. The optical channel may include multiple carriers associated with the respective optical signals. First and second carriers, of the multiple carriers, may have a particular carrier space width. The particular carrier space width may include a frequency error associated with one or more optical signals of the respective optical signals. The optical system may include a control system to determine the frequency error and cause one or more of the optical transmitters to adjust the particular carrier space width based on the adjusted frequency error.

Abstract: An optical system includes an optical transmitter configured to modulate an optical signal to carry data, associated with an optical channel, via multiple sub-carriers in a quantity greater than four. The optical system further includes an optical receiver configured to demodulate the optical signal to recover the data from the multiple sub-carriers.

Abstract: An optical receiver may receive input signals carried by sub-carriers, and may apply test phases to each input signal. The optical receiver may determine error values, associated with test phases, for each input signal. The optical receiver may calculate updated metric values, associated with the test phases, for a particular input signal, based on a first error value and a second error value. The first error value may be associated with a first sub-carrier, and the second error value may be associated with a second sub-carrier. The optical receiver may compare the updated metric values associated with the particular input signal, and may determine a test phase that represents an estimated phase, associated with the particular input signal, based on the comparison. The optical receiver may determine a phase estimate value based on the test phase, and may provide the phase estimate value to modify the particular input signal.

Abstract: An optical receiver may receive input signals carried by respective sub-carriers. The optical receiver may determine, based on the input signals, a compensation value to be used to modify an input signal. The optical receiver may use the compensation value to adjust the input signal to form a modified input signal. The compensation value may be used to modify a frequency or a phase of the input signal. The optical receiver may determine, based on the modified input signal, a phase estimate value that represents an estimated phase associated with the input signal. The optical receiver may combine the compensation value and the phase estimate value to form a phase adjustment signal, may combine the input signal and the phase adjustment signal to form an output signal, and may output the output signal.

Abstract: An optical system may include an optical transmitter or an optical receiver. The optical transmitter may include a laser to provide an input signal, a first digital signal processor (DSP) to receive a data signal, provide non-rotated and rotated symbols corresponding to the data signal, and provide digital signals corresponding to the non-rotated and the rotated symbols to cause one or more digital to analog converts to convert the digital signals to analog signals. The optical transmitter may further provide a modified 5 quadrature amplitude modulation (5QAM) signal based on the analog signals and the input signal. A constellation map of the modified 5QAM signal may include all constellation points of a 16QAM signal. The optical receiver may include a second DSP to receive components associated with the 5QAM signal, filter the components, reduce phase noise of the 5QAM signal, and provide data associated with the 5QAM signal.

Abstract: An optical receiver receives an optical signal with a phase error and pilot symbols, and converts the optical signal into an electrical signal. The optical receiver identifies, based on the pilot symbols, a cycle slip due to the phase error and associated with a transition time. The optical receiver determines, based on the pilot symbols, a direction and a center of the cycle slip, and generates a rotation value based on the direction and the center. The optical receiver applies the rotation value to minimize the phase error in the electrical signal except for phase error associated with the transition time and to generate a modified electrical signal. The optical receiver generates an erase signal based on the transition time and the center of the cycle slip, and uses the erase signal to minimize an effect of the phase error associated with the transition time of the cycle slip.

Abstract: A digital signal processor (DSP) may receive a signal that has an x-polarization (x-pol) and a y-polarization (y-pol). The DSP may equalize the x-pol of the signal and the y-pol of the signal based on filter coefficients determined using a constant modulus algorithm (CMA). The DSP may perform phase correction on the equalized x-pol signal and the equalized y-pol signal. The DSP may identify a first frame header pattern within the phase-corrected x-pol signal, and may identify a second frame header pattern within the phase-corrected y-pol signal. The DSP may determine, based on the first frame header pattern and the second frame header pattern, a quantity of lock-in differential group delay (DGD). The device may adjust one or more of the filter coefficients to remove the quantity of lock-in DGD and to permit an amount of polarization mode dispersion to be determined based on the filter coefficients.

Abstract: An optical system may include a digital signal processor (DSP) to receive first samples of a digital signal. The first samples may be Hamming encoded. The DSP may correlate the first samples to multiple groups of second samples to determine multiple correlation values. Each of the multiple groups of second samples may correspond to respective code words. Each of the multiple correlation values may correspond to a correlation measurement between the first samples and each of the multiple groups of second samples. The DSP may determine a particular code word, of the multiple code words, corresponding to one of the correlation values of the multiple correlation values; determine output bits based on bits of the particular code word and the one of the correlation values; and provide the output bits. The output bits may include data associated with the digital signal.

Abstract: A digital signal processor (DSP) may receive samples of a signal from an analog-to-digital converter (ADC); convert the samples from a time domain to a frequency domain; determine a clock phase error of the samples while in the frequency domain; and provide a voltage corresponding to the clock phase error. The voltage may be provided to reduce timing errors associated with the samples.

Abstract: An optical receiver may receive input signals carried by respective sub-carriers. The optical receiver may determine, based on the input signals, a compensation value to be used to modify an input signal. The optical receiver may use the compensation value to adjust the input signal to form a modified input signal. The compensation value may be used to modify a frequency or a phase of the input signal. The optical receiver may determine, based on the modified input signal, a phase estimate value that represents an estimated phase associated with the input signal. The optical receiver may combine the compensation value and the phase estimate value to form a phase adjustment signal, may combine the input signal and the phase adjustment signal to form an output signal, and may output the output signal.

Abstract: An optical receiver may receive input signals carried by sub-carriers, and may apply test phases to each input signal. The optical receiver may determine error values, associated with test phases, for each input signal. The optical receiver may calculate updated metric values, associated with the test phases, for a particular input signal, based on a first error value and a second error value. The first error value may be associated with a first sub-carrier, and the second error value may be associated with a second sub-carrier. The optical receiver may compare the updated metric values associated with the particular input signal, and may determine a test phase that represents an estimated phase, associated with the particular input signal, based on the comparison. The optical receiver may determine a phase estimate value based on the test phase, and may provide the phase estimate value to modify the particular input signal.

Abstract: A digital signal processor (DSP) may receive a signal that has an x-polarization (x-pol) and a y-polarization (y-pol). The DSP may equalize the x-pol of the signal and the y-pol of the signal based on filter coefficients determined using a constant modulus algorithm (CMA). The DSP may perform phase correction on the equalized x-pol signal and the equalized y-pol signal. The DSP may identify a first frame header pattern within the phase-corrected x-pol signal, and may identify a second frame header pattern within the phase-corrected y-pol signal. The DSP may determine, based on the first frame header pattern and the second frame header pattern, a quantity of lock-in differential group delay (DGD). The device may adjust one or more of the filter coefficients to remove the quantity of lock-in DGD and to permit an amount of polarization mode dispersion to be determined based on the filter coefficients.