A coherent receiver includes a receive signal path including i) an input configured to connect a receive signal, ii) one or more signal paths connected to the input and to one or more optical hybrids, and iii) a variable optical attenuator (VOA) in each of the one or more signal paths; and a local oscillator (LO) signal path including i) an input configured to connect to an LO and the one or more optical hybrids, and ii) one or more complementary VOAs located between the input and the one or more optical hybrids, wherein the one or more complementary VOAs are configured to cancel any phase changes from the VOA in each of the one or more signal paths. The VOA in each of the one or more signal paths and the one or more complementary VOAs can be p-i-n junctions.

A receiving unit (2020) generates a received frame from a modulated optical signal. The modulated optical signal is generated such that a transmission symbol is generated by mapping an encoded bit string obtained by encoding a transmission bit string to an m-dimensional symbol space, a transmission frame is generated by mapping the transmission symbol to an n-dimensional frame space (n<m), and an optical carrier wave is modulated by using the transmission frame. A converting unit (2040) generates candidate vectors (m-dimensional vectors belonging to a partial symbol space within the symbol space) by using a received frame. A first computing unit (2070) computes a probability of that the transmission symbol belonging to the partial symbol space is transmitted for each partial symbol space. A second computing unit (2080) computes a log-likelihood ratio of each bit of the encoded bit string by using the probability.

Upon receiving a communications signal conveying symbols at a symbol period T, a receiver applies filter coefficients to a digital representation of the communications signal, thereby generating filtered signals characterized by a substantially raised cosine shape in the frequency domain with a roll-off factor α, where components of the filtered signals correspond to angular frequencies $\omega =-\frac{\pi \left(1+\alpha \right)}{T}\text{.Math.}-\frac{\pi \left(1-\alpha \right)}{T},+\frac{\pi \left(1-\alpha \right)}{T}\text{.Math.}+\frac{\pi \left(1+\alpha \right)}{T}.$
The receiver calculates first-order components from a first phase derivative of the components at a first differential distance, second-order components from a second phase derivative of the first-order components at a second differential distance, and composite second-order components from an average of the second-order components over multiple time intervals. Using the composite second-order components, the receiver calculates at least one of (i) an

Consistent with the present disclosure, a local oscillator is provided in a receiver. The local oscillator laser a first and second mirrors and phase section and heaters are provided adjacent each portion of the laser, such that the temperature and thus the frequency of light output from the local oscillator laser may be tuned. Applying electrical power, such as a current or voltage to the phase section may result in rapid frequency tuning of light output from the local oscillator laser but over a limited frequency range. Temperature changes to the mirror sections, however, may afford frequency tuning over a wider range, but frequency tuning the mirror sections requires more time than that required to tune the phase section. Consistent with the present disclosure, a tuning method and apparatus is provided that optimizes laser tuning by selectively tuning the phase and mirror sections.

When a frequency deviation compensation amount is compensated for by use of frequency shift, a phase offset occurs between adjacent input blocks included in a plurality of input blocks as divided, with the result that an error occurs in a reconstructed bit sequence. A frequency deviation compensation system of the invention is characterized by comprising: a frequency deviation compensation means for compensating for a frequency deviation occurring in a signal by use of frequency shift; and a phase offset compensation means for compensating for a phase offset occurring, in the signal, due to the frequency shift.

When a frequency deviation compensation amount is compensated for by use of frequency shift, a phase offset occurs between adjacent input blocks included in a plurality of input blocks as divided, with the result that an error occurs in a reconstructed bit sequence. A frequency deviation compensation system of the invention is characterized by comprising: a frequency deviation compensation means for compensating for a frequency deviation occurring in a signal by use of frequency shift; and a phase offset compensation means for compensating for a phase offset occurring, in the signal, due to the frequency shift.

Optical transmitters and receivers for improving synchronization of data transmitted over an optical network are described. The receiver can perform non-linear filtering as part of framer index estimation operations to improve the synchronization. The receiver can determine estimated positions of framer indices in data frames received from the transmitter. Next, using a non-linear filter, the receiver can remove estimated positions that are likely erroneous or are greater than a threshold away from the median or mode estimated framer index position. By removing the likely erroneous estimated positions, the receiver can then determine the estimated position of a framer index position for multiple frames with greater confidence.

The disclosed systems and methods for processing a subcarrier-multiplexed signal comprising: i) mixing the subcarrier-multiplexed signal with a local oscillator (LO) signal; ii) extracting a respective subcarrier signal from the subcarrier-multiplexed signal; iii) sampling the respective subcarrier signal; iv) extracting timing recovery information from the respective subcarrier signal; and v) processing the respective sampled subcarrier signal to extract data from the respective sampled subcarrier signal.

When a frequency deviation compensation amount is compensated for by use of frequency shift, a phase offset occurs between adjacent input blocks included in a plurality of input blocks as divided, with the result that an error occurs in a reconstructed bit sequence. A frequency deviation compensation system of the invention is characterized by comprising: a frequency deviation compensation means for compensating for a frequency deviation occurring in a signal by use of frequency shift; and a phase offset compensation means for compensating for a phase offset occurring, in the signal, due to the frequency shift.

An electronic device may include clocking circuitry with primary and secondary lasers that generate first and second optical local oscillator (LO) signals. A phase-locked loop (PLL) may tune the secondary laser based to phase lock the first and second optical LO signals. A self-injection locking loop path may couple an output of the secondary laser to its input. The self-injection locking loop path may include a first mixer and a second mixer. The first mixer may generate a beat signal using the first and second optical LO signals. The second mixer may generate a self-injection locking signal based on the first optical LO signal and the beat signal. A delay line or optical resonator may iteratively self-inject the self-injection locking signal onto the secondary laser. This may serve to minimize phase noise and jitter of the optical LO signals.