Kramers-Kronig receiver

A Kramers-Kronig transceiver, comprising a reception path and a transmission path and a local oscillator that is configured to generate a continuous wave (CW) signal;

• wherein the transmission path comprises a complex modulator that is configured to receive the CW signal and is configured to modulate the CW signal to generate a transmitted signal that is transmitted to a communication link;
• wherein the reception path comprises:
• a combiner that is configured to add the CW signal with a received signal from the communication link to provide a combined signal;
• wherein the received signal comprises a first sideband and a second sideband that are spaced apart from each other by a guard band;
• wherein the CW signal has a frequency that is included in the guard hand;
• a first optical filter that is configured to filter the combined signal and output a first intermediate signal that comprises the CW signal and the first sideband;
• a second optical filter that is configured to filter the combined signal and output a second intermediate signal that comprises the CW signal and the second sideband;
• a first photodiode that is configured to receive the first intermediate signal and output a first photocurrent that represents the first intermediate signal;
• a second photodiode that is configured to receive the second intermediate signal and output a second photocurrent that represents the second intermediate signal;
• a first analog to digital converter that is configured to generate a digital representation of the first photocurrent;
• a second analog to digital converter that is configured to generate a digital representation of the second photocurrent;
• and a digital processor that is configured to process the digital representation of the first photocurrent and the digital representation of the second photocurrent to provide a reconstructed received signal, wherein the processing is based on a Kramers-Kronig relationship related to the received signal.

A Kramers-Kronig transceiver, comprising a reception path and a transmission path and a local oscillator that is configured to generate a continuous wave (CW) signal;

• wherein the transmission path comprises a complex modulator that is configured to receive the CW signal and is configured to modulate the CW signal to generate a transmitted signal that is transmitted to a communication link;
• wherein the reception path comprises:
• a polarization demultiplexing circuit that is configured to receive a polarization-multiplexed signal and to output a first polarization component of the polarization-multiplexed signal and a second polarization component of the polarization-multiplexed signal;
• a first optical filter that is configured to filter the first polarization component and output a first sideband of the first polarization component;
• a second optical filter that is configured to filter the first polarization component and output a second sideband of the first polarization component;
• wherein the first and second sidebands of the first polarization component are spaced apart from each other by a guard band;
• a first combiner that is configured to add the CW signal with the first sideband of the first polarization component to provide a first combined signal;
• a second combiner that is configured to add the CW signal with the second sideband of the first polarization component to provide a second combined signal;
• a first photodiode that is configured to receive the first combined signal and output a first photocurrent that represents the first combined signal;
• a second photodiode that is configured to receive the second combined signal and output a second photocurrent that represents the second combined signal;
• a first analog to digital converter that is configured to generate a digital representation of the first photocurrent;
• a second analog to digital converter that is configured to generate a digital representation of the second photocurrent;
• a third optical filter that is configured to filter the second polarization component and output a first sideband of the second polarization component;
• a fourth optical filter that is configured to filter the second polarization component and output a second sideband of the second polarization component;
• wherein the first and second sidebands of the second polarization component are spaced apart from each other by the guard band;
• a third combiner that is configured to add the CW signal with the first sideband of the second polarization component to provide a third combined signal;
• a fourth combiner that is configured to add the CW signal with the second sideband of the second polarization component to provide a fourth combined signal;
• a third photodiode that is configured to receive the third combined signal and output a third photocurrent that represents the third combined signal;
• a fourth photodiode that is configured to receive the fourth combined signal and output a fourth photocurrent that represents the fourth combined signal;
• a third analog to digital converter that is configured to generate a digital representation of the third photocurrent;
• a fourth analog to digital converter that is configured to generate a digital representation of the fourth photocurrent;
• and a digital processor that is configured to process the digital representation of the first photocurrent, the second photocurrent, the third photocurrent and the fourth photocurrent to provide a reconstructed polarization-multiplexed signal, wherein the processing is based on a Kramers-Kronig relationship related to the polarization-multiplexed signal.

A method, comprising:

• receiving, by a Stokes receiver of a reception path of Kramers-Kronig receiver, a polarization-multiplexed signal;
• outputting by the Stokes receiver, a Stokes vector;
• wherein the polarization-multiplexed signal comprises a first modulated signal, a second modulated signal and a continuous wave signal;
• wherein the first modulated signal is of a first polarization;
• wherein the second modulated signal is of a second polarization;
• wherein the continuous wave signal is of the first modulation or of the second modulation;
• performing an analog to digital conversion, by a set of analog to digital converters, of the Stokes vector to provide a digital representation of the Stokes vector;
• and processing, by a digital processor of the reception path of Kramers-Kronig receiver, the digital representation of the Stokes vector to provide a reconstructed polarization-multiplexed signal, wherein the processing is based on a Kramers-Kronig relationship related to the polarization-multiplexed signal.

A method, comprising:

• generating by a local oscillator a continuous wave (CW) signal;
• modulating, by a complex modulator, the CW signal to generate a transmitted signal that is transmitted to a communication link;
• adding, by a combiner of a reception path of Kramers-Kronig receiver, the CW signal with a received signal from the communication link to provide a combined signal;
• wherein the received signal comprises a first sideband and a second sideband that is spaced apart from each other by a guard band;
• wherein the CW signal has a frequency that is included in the guard band;
• filtering, by a first optical filter of the reception path of Kramers-Kronig receiver, the combined signal and output a first intermediate signal that comprises the CW signal and the first sideband;
• filtering, by a second optical filter of the reception path of Kramers-Kronig receiver, the combined signal and output a second intermediate signal that comprises the CW signal and the second sideband;
• receiving by a first photodiode of the reception path of Kramers-Kronig receiver the first intermediate signal and outputting a first photocurrent that represents the first intermediate signal;
• receiving, by a second photodiode of the reception path of Kramers-Kronig receiver, the second intermediate signal and outputting a second photocurrent that represents the second intermediate signal;
• performing an analog to digital conversion of the first photocurrent, by a first analog to digital converter of the reception path, to generate a digital representation of the first photocurrent;
• performing an analog to digital conversion of the second photocurrent, by a second analog to digital converter of the reception path, to generate a digital representation of the second photocurrent;
• and processing, by a digital processor of the reception path of Kramers-Kronig receiver, the digital representation of the first photocurrent and the digital representation of the second photocurrent to provide a reconstructed received signal, wherein the processing is based on a Kramers-Kronig relationship related to the received signal.

A method, comprising:

• generating by a local oscillator a continuous wave (CW) signal;
• modulating, by a complex modulator, the CW signal to generate a transmitted signal that is transmitted to a communication link;
• receiving a polarization-multiplexed signal by a polarization demultiplexing circuit of a reception path of Kramers-Kronig receiver and outputting a first polarization component of the polarization-multiplexed signal and a second polarization component of the polarization-multiplexed signal;
• filtering, by a first optical filter of the reception path of Kramers-Kronig receiver, the first polarization component and outputting a first sideband of the first polarization component;
• filtering, by a second optical filter of the reception path of Kramers-Kronig receiver, the first polarization component and outputting a second sideband of the first polarization component;
• wherein the first and second sidebands of the first polarization component is spaced apart from each other by a guard band;
• combining, by a first combiner of the reception path of Kramers-Kronig receiver, the CW signal with the first sideband of the first polarization component to provide a first combined signal;
• combining, by a second combiner of the reception path of Kramers-Kronig receiver the CW signal with the second sideband of the first polarization component to provide a second combined signal;
• receiving, by a first photodiode of the reception path of Kramers-Kronig receiver, the first combined signal and outputting a first photocurrent that represents the first combined signal;
• receiving, by a second photodiode of the reception path of Kramers-Kronig receiver, the second combined signal and outputting a second photocurrent that represents the second combined signal;
• converting, by a first analog to digital converter of the reception path of Kramers-Kronig receiver, the first photocurrent to provide a digital representation of the first photocurrent;
• converting, by a second analog to digital converter of the reception path of Kramers-Kronig receiver, the second photocurrent to provide a digital representation of the second photocurrent;
• filtering, by a third optical filter of the reception path of Kramers-Kronig receiver, the second polarization component and outputting a first sideband of the second polarization component;
• filtering, by a fourth optical filter of the reception path of Kramers-Kronig receiver, the second polarization component and outputting a second sideband of the second polarization component;
• wherein the first and second sidebands of the second polarization component is spaced apart from each other by a guard band;
• combining, by a third combiner of the reception path of Kramers-Kronig receiver, the CW signal with the first sideband of the second polarization component to provide a third combined signal;
• combining, by a fourth combiner of the reception path of Kramers-Kronig receiver the CW signal with the second sideband of the second polarization component to provide a fourth combined signal;
• receiving, by a third photodiode of the reception path of Kramers-Kronig receiver, the third combined signal and outputting a third photocurrent that represents the third combined signal;
• receiving, by a fourth photodiode of the reception path of Kramers-Kronig receiver, the fourth combined signal and outputting a fourth photocurrent that represents the fourth combined signal;
• converting, by a third analog to digital converter of the reception path of Kramers-Kronig receiver, the third photocurrent to provide a digital representation of the third photocurrent;
• converting, by a fourth analog to digital converter of the reception path of Kramers-Kronig receiver, the fourth photocurrent to provide a digital representation of the fourth photocurrent;
• and processing, by a digital processor of the reception path the digital representation of the first photocurrent, the second photocurrent, the third photocurrent and the fourth photocurrent to provide a reconstructed polarization-multiplexed signal, wherein the processing is based on a Kramers-Kronig relationship related to the polarization-multiplexed signal.