Patent Publication Number: US-11038598-B1

Title: Method and apparatus for transmit/receive radio frequency crosstalk compensation in a photonic integrated circuit

Description:
TECHNICAL FIELD 
     The present disclosure relates generally to crosstalk compensation with optical elements or apparatus, and in particular embodiments, to crosstalk compensation between transmit and receive signals in a photonic integrated circuit (PIC). 
     BACKGROUND 
     Photonic integrated circuits (PICs) integrate multiple components such as lasers, modulators, and detectors on a single chip. Such devices are popular due to their small size, low cost and added functionality and value. 
     A transceiver implemented on a PIC can include a transmitter and a receiver in close proximity to one another. Due to the small size of PICs, radio frequency (RF) crosstalk can significantly affect performance of the device. The RF components and wires are very close to each other in a PIC, which can significantly increase RF signal crosstalk between transmit and receive pathways causing performance degradation. The smaller the footprint of the PIC, the larger effect the crosstalk may have on the device. 
     A coherent optical transmission system is capable of performing coherent detection, which involves an optical receiver tracking the phase of a signal from the optical transmitter. As phase coherence is maintained between the transmitter and receiver, it is possible to enable multiple channels that are out of phase with one another between the transmitter and receiver. In a coherent optical transceiver, a transmitter driver amplifies signals for four separate channels. The four channels correspond to a real component of a horizontal polarization component of the transmission signal, a real component of a vertical polarization component of the transmission signal, an imaginary component of a horizontal polarization component of the transmission signal, and an imaginary component of a vertical polarization component of the transmission signal. The crosstalk exists amongst all the branches. The strength of crosstalk increases with closer geometric distance on the PIC. 
     In a coherent transceiver implemented on a PIC, a drive signal in a transmitter chain of the transceiver is much larger than a received signal in the receiver chain. This can result in the crosstalk between the transmitter chain and receiver chain being even worse. Therefore, RF crosstalk compensation is important to improve the performance of PICs. 
     Some crosstalk can be decreased by careful RF design. However, in a coherent optical transceiver implemented on a PIC, RF signals in the transmitter have a much larger power than RF signals in the receiver. The RF signal in the transmitter chain may be as much as 20 dB higher than the received signal in the receiver chain. Therefore, higher RF isolation is important for such an implementation. Furthermore, in some implementations the arrangement of the transmitter and the receiver have little room for repositioning with respect to one another because the PIC may be connected with a digital signaling processor application-specific integrated circuit (DSP ASIC) with device pinout that is fixed. 
     Therefore, improved mechanisms for crosstalk compensation for coherent optical transceivers would be beneficial for optical communication systems, especially when trying to further reduce footprint size and costs. 
     SUMMARY 
     Because a photonic integrated circuit (PIC) is typically small, the performance of the PIC can be significantly affected by radio frequency (RF) crosstalk. In the case of a coherent transceiver, the drive signal at the transmitter side is much larger than the received signal at the receiver side, which makes the crosstalk impairment even worse. Therefore, RF crosstalk compensation is critical to the performance of PIC. 
     Embodiments disclosed herein provide a low-cost and efficient solution to compensate transmitter/receiver RF crosstalk that occurs in the analog domain by implementing the solution in a digital signal processor (DSP) in the digital domain. 
     According to some aspects to the present disclosure, there is provided a method involving in the digital domain, compensating crosstalk occurring in the analog domain between transmit and receive radio frequency (RF) signals in a coherent optical transceiver implemented on a photonic integrated circuit. 
     In some embodiments, the compensating involves, in the digital domain, generating a crosstalk compensation element by delaying at least one component of a digital domain version of a RF transmission signal and convolving the at least one delayed component of the digital domain version of the RF transmission signal with a digital domain version of an impulse response, the crosstalk occurring between an analog domain version of the at least one signal component of the RF transmission signal and an analog domain version of at least one component of an analog domain version of a RF receive signal and subtracting the crosstalk compensation element from a digital domain version of the crosstalk affected RF receive signal. 
     In some embodiments, the method further involves upsampling the at least one component of the digital domain version of the RF transmission signal and the digital domain version of the crosstalk affected RF receive signal. 
     In some embodiments, the method further involves converting the at least one component of the digital domain version of the RF transmission signal to an analog domain version of the at least one component of the RF transmission signal. 
     In some embodiments, the method further involves converting the analog domain version of the crosstalk affected RF receive signal to the digital domain version of the crosstalk affected RF receive signal. 
     In some embodiments, in the digital domain, the at least one signal component of the digital domain version of the RF transmission signal is a version of the at least one signal component that has not been pre-compensated for effects of additional processing on a transmit chain in the coherent optical transceiver. 
     In some embodiments, the digital domain version of the RF transmission signal includes one or more of: a) a digital domain version of a real component of a horizontal polarization component of the transmission signal; b) a digital domain version of a real component of a vertical polarization component of the transmission signal; c) a digital domain version of an imaginary component of a horizontal polarization component of the transmission signal; and d) a digital domain version of an imaginary component of a vertical polarization component of the transmission signal. 
     In some embodiments, the analog domain version of the RF receive signal comprises one or more of: a) a real component of a horizontal polarization component of the receive signal; b) a real component of a vertical polarization component of the receive signal; c) an imaginary component of a horizontal polarization component of the receive signal; and d) an imaginary component of a vertical polarization component of the receive signal. 
     In some embodiments, the method further involves, during a calibration period when a receiver chain of the coherent optical transceiver is configured in an open circuit mode such that no receive data is processed, determining a delay used in the delaying of the at least one component of the digital domain version of the RF transmission signal and determining the impulse response used in convolving the at least one delayed component of the digital domain version of the RF transmission signal to generate the crosstalk compensation element. 
     In some embodiments, the method further involves during a calibration period, the receiver chain is receiving data, determining the delay used in the delaying of the at least one component of the digital domain version of the RF transmission signal; and determining the impulse response used in convolving the at least one delayed component of the digital domain version of the RF transmission signal to generate the crosstalk compensation element. 
     In some embodiments, the impulse response is determined using the formula:
 
 =[[ Tx Sig] T ·[ Tx Sig]] −1 ·[ Tx Sig] T · 
 
wherein   is the impulse response, [TxSig] is a matrix representation of a digital domain version of the signal on the at least one channel of the RF transmission signal, [TxSig] T  is the transpose of the matrix representation of the digital domain version of the signal on the at least one channel of the RF transmission signal, and   is the digital domain version of the crosstalk affected RF receive signal.
 
     In some embodiments, the impulse response is determined using a matrix based calculation. 
     According to some aspects to the present disclosure, there is provided a digital signal processor (DSP) configured to: in the digital domain, compensate crosstalk occurring in the analog domain between transmit and receive radio frequency (RF) signals in a coherent optical transceiver implemented on a photonic integrated circuit. 
     In some embodiments, the DSP is configured to, in the digital domain, generate a crosstalk compensation element by delaying at least one component of a digital domain version of a RF transmission signal, and convolving the at least one delayed component of the digital domain version of the RF transmission signal with a digital domain version of an impulse response, the crosstalk occurring between an analog domain version of the at least one signal component of the RF transmission signal and an analog domain version of at least one component of an analog domain version of a RF receive signal, and subtract the crosstalk compensation element from a digital domain version of the crosstalk affected RF receive signal. 
     In some embodiments, the DSP is further configured to upsample the at least one component of the digital domain version of the RF transmission signal and the digital domain version of the crosstalk affected RF received signal. 
     In some embodiments, the DSP is further configured to convert the at least one component of the digital domain version of the RF transmission signal to an analog domain version of the at least one component of the RF transmission signal. 
     In some embodiments, the DSP is further configured to convert the analog domain version of the crosstalk affected RF receive signal to the digital domain version of the crosstalk affected RF received signal. 
     In some embodiments, in the digital domain, the at least one signal component of the digital domain version of the RF transmission signal is a version of the at least one signal component that has not been pre-compensated for effects of additional processing on a transmit chain in the coherent optical transceiver. 
     In some embodiments, wherein the at least one component of a digital domain version of the RF transmission signal comprises one or more of: a) a digital domain version of a real component of a horizontal polarization component of the transmission signal; b) a digital domain version of a real component of a vertical polarization component of the transmission signal; c) a digital domain version of an imaginary component of a horizontal polarization component of the transmission signal; and d) a digital domain version of an imaginary component of a vertical polarization component of the transmission signal. 
     In some embodiments, wherein the at least one component of the analog domain version of the RF receive signal comprises one or more of: a) a real component of a horizontal polarization component of the receive signal; b) a real component of a vertical polarization component of the receive signal; c) an imaginary component of a horizontal polarization component of the receive signal; and d) an imaginary component of a vertical polarization component of the receive signal. 
     In some embodiments, the DSP is further configured to, during a period when a receiver chain of the coherent optical transceiver is configured in an open circuit mode such that no received data is processed: determine a delay used in the delaying the at least one component of the digital domain version of the RF transmission signal; and determine the impulse response used in convolving the at least one delayed component of the digital domain version of the RF transmission signal to generate the crosstalk compensation element. 
     In some embodiments, the DSP is further configured to, during a calibration period when a receiver chain of the coherent optical transceiver is receiving data: determine a delay used in the delaying the at least one component of the digital domain version of the RF transmission signal; and determine the impulse response used in convolving the at least one delayed component of the digital domain version of the RF transmission signal to generate the crosstalk compensation element. 
     In some embodiments, the impulse response is determined using the formula:
 
 =[[ Tx Sig] T ·[ Tx Sig]] −1 ·[ Tx Sig] T · 
 
wherein   is the impulse response, [TxSig] is a matrix representation of a digital domain version of the signal on the at least one channel of the RF transmission signal, [TxSig] T  is the transpose of the matrix representation of the digital domain version of the signal on the at least one channel of the RF transmission signal, and   is the digital domain version of the crosstalk affected RF receive signal.
 
     In some embodiments, the impulse response is determined using a matrix based calculation. 
     According to some aspects to the present disclosure, there is provided a coherent optical transceiver implemented on a photonic integrated circuit comprising a digital signal processor as described in the embodiments above. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present embodiments, and the advantages thereof, reference is now made, by way of example, to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a block diagram of a coherent transceiver demonstrating potential crosstalk between a transmitter chain and a receiver chain in close proximity to one another. 
         FIG. 2  is a block diagram of an example system in which embodiments of the disclosure may occur. 
         FIG. 3  is a block diagram of a coherent transceiver demonstrating potential crosstalk between a transmitter chain and a receiver chain in which crosstalk compensation may occur according to embodiments of the disclosure. 
         FIG. 4  is a block diagram showing further detail of functional blocks of  FIG. 3  according to an aspect of the present disclosure. 
         FIG. 5  is a block diagram of a coherent transceiver demonstrating an example of calibrating a crosstalk compensation element according to an aspect of the present disclosure. 
         FIG. 6  is a flow chart illustrating an example method performed to calibrate a crosstalk compensation element in the digital domain, for crosstalk that occurs in the analog domain, according to an embodiment of the present disclosure. 
         FIG. 7  illustrates a graphical plot resulting from a computer simulation for a crosstalk compensation solution according to an embodiment of the present disclosure. 
         FIG. 8  is a flow chart illustrating an example method performed to compensate crosstalk in the digital domain that occurs in the analog domain according to an embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     For illustrative purposes, specific example embodiments will now be explained in greater detail below in conjunction with the figures. 
     The embodiments set forth herein represent information sufficient to practice the claimed subject matter and illustrate ways of practicing such subject matter. Upon reading the following description in light of the accompanying figures, those of skill in the art will understand the concepts of the claimed subject matter and will recognize applications of these concepts not particularly addressed herein. It should be understood that these concepts and applications fall within the scope of the disclosure and the accompanying claims. 
     Moreover, it will be appreciated that any module, component, or device disclosed herein that executes instructions may include or otherwise have access to a non-transitory computer/processor readable storage medium or media for storage of information, such as computer/processor readable instructions, data structures, program modules, and/or other data. A non-exhaustive list of examples of non-transitory computer/processor readable storage media includes magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, optical disks such as compact disc read-only memory (CD-ROM), digital video discs or digital versatile discs (i.e. DVDs), Blu-ray Disc™, or other optical storage, volatile and non-volatile, removable and non-removable media implemented in any method or technology, random-access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology. Any such non-transitory computer/processor storage media may be part of a device or accessible or connectable thereto. Computer/processor readable/executable instructions to implement an application or module described herein may be stored or otherwise held by such non-transitory computer/processor readable storage media. 
       FIG. 1  shows a block diagram of a coherent optical transceiver  100 . The coherent optical transceiver  100  includes a transmit chain  105  and a receive chain  107  in close proximity. An input to the transmit chain  105  is a digital domain signal that includes a set of bits  110  that corresponds to a pattern to be transmitted. The set of bits  110  are received by a transmitter chain digital signal processor (Tx DSP)  120  which generates four separate digital domain channel signals, i.e. a real component of a horizontal polarization component (TX_XI) of the transmit signal, a real component of a vertical polarization component (TX_YI) of the transmit signal, an imaginary component of a horizontal polarization component (TX_XQ) of the transmit signal, and an imaginary component of a vertical polarization component (TX_YQ) of the transmit signal. For the purposes of discussion, lower-case letters are used when referring to a signal in the analog domain and capital letters are used when referring to a signal in the digital domain. Outputs of the Tx DSP  120  are provided to a digital to analog converter (DAC)  130 . The DAC  130  converts the digital domain signals to analog domain signals., i.e. a real component of a horizontal polarization component (tx_xi) of the transmit signal, a real component of a vertical polarization component (tx_yi) of the transmit signal, an imaginary component of a horizontal polarization component (tx_xq) of the transmit signal, and an imaginary component of a vertical polarization component (tx_yq) of the transmit signal. An output of the DAC  130  is provided to a transmitter chain driver  140 . The driver  140  amplifies the RF signals. Each of the four separate channel signals is provided to a modulator  150 . A laser source  148  is shown as an input to the modulator  150 . An output of the laser source  148  is modulated using the four separate channel signals input to the modulator. It can be considered that the pattern input  110  and processing in the Tx DSP  120  occur in the digital domain and subsequent to the DAC  130 , the signal and any processing occur in the analog domain. 
     A signal that is received by receiver chain  107  of the coherent optical transceiver  100  is an analog domain signal and is input to an integrated coherent receiver (ICR)  160 . Another input to the ICR  160  is a local oscillator  158  used by the ICR in recovering the received signal. The ICR  160 , with the aid of the LO  158 , converts the received signal into four separate signals, of the same type as in the transmitter, i.e. a real component of a horizontal polarization component (rx_xi) of the receive signal, a real component of a vertical polarization component (rx_yi) of the receive signal, an imaginary component of a horizontal polarization component (rx_xq) of the receive signal, and an imaginary component of a vertical polarization component (rx_yq) of the receive signal. Signals on the four separate channels output from the ICR  160  are provided to an analog to digital converter (ADC)  170 . The ADC  170  coverts the analog domain signals on the four channels to digital domain versions of those signals. The four channel outputs of the ADC  170  are provided to a receiver chain DSP  180 , which converts the signals of the four channels into a single set of bits in the digital domain. It can be considered that the received signal at the ICR  160  and crosstalk that happens between the transmitter chain and the receiver chain occur in the analog domain and after the ADC  170  the signal and any processing occur in the digital domain. 
     Crosstalk occurs in the analog domain between the signals in the four separate channels between the driver  140  and the modulator  150  in the transmitter chain  105  and the four separate channels between the ICR  160  and the ADC  170  in the receiver chain  107 . Crosstalk can occur between any of the four transmitter chain signals and any of the four receiver chain signals. For example, the real component of a horizontal polarization component of the transmission signal can cause crosstalk with the real component of a horizontal polarization component of the receive signal, the real component of a vertical polarization component of the receive signal, the imaginary component of a horizontal polarization component of the receive signal, and the imaginary component of a vertical polarization component of the receive signal. Each of the other three RF transmission signals can likewise cause cross talk with the four RF receive signal components. 
     The strength of crosstalk increases with closer geometric distance on the PIC. Therefore, in  FIG. 1 , the most significant crosstalk occurs between tx_yq and tx_xi, as these are the two closest transmit and receive signal paths. 
       FIG. 1  shows a value s_xtalk added to tx_xi as a representative of the crosstalk that is added to tx_xi. The value s_xtalk is representative of the crosstalk from all of the transmission chain channels. While it is not shown explicitly in the other three separate receive channels, they would each have a respective s_xtalk value added representative of the crosstalk affecting the signal on that channel. 
     Aspects of the present disclosure propose a method of crosstalk compensation in the digital domain for crosstalk that occurs in the analog domain. 
       FIG. 2  illustrates a system in which coherent transceivers may be used.  FIG. 2  may be a wavelength division multiplexing optical communication system  200  having a multiple transceivers  210   a ,  210   b  and  210   c  that are connected to one another by an optical conduit, such as optical fiber. Optical fiber  220   a  connects transceivers  210   a  and  210   b , optical fiber  220   b  connects transceivers  210   a  and  210   c , and optical fiber  220   c  connects transceivers  210   b  and  210   c . Each of the transceivers are at a respective location remote from the other transceivers. Each transceiver has a transmitter chain and a receiver chain that includes functional components such as found in  FIG. 1 . The transmit chain in each transceiver is responsible for transmitting a signal to one, or both, of the other two transceivers and the receiver chain in each transceiver is responsible for receiving a signal from one, or both, of the other two transceivers. This is clearly a very rudimentary example of multiple transceivers being connected together to provide a context for the use of the transmitters. It is to be understood that any number of such transceivers would be connected together. 
       FIG. 3  illustrates a block diagram of a coherent optical transceiver  300  including a transmitter chain  305  and a receiver chain  307  similar to that of  FIG. 1 , but which further includes a solution for implementing digital domain crosstalk compensation for crosstalk that occurs in the analog domain.  FIG. 3  is used to illustrate a mathematical model for compensating crosstalk s_xtalk that occurs between channels carrying signals tx_yq to rx_xi. While  FIG. 3  pertains to a specific occurrence of crosstalk between channels carrying signal tx_yq to tx_xi, it is to be understood that a similar mathematical model could be employed for other occurrences of transmitter chain receiver chain crosstalk (tx_[x or y, q or i] to rx_[x or y, q or i]). For the purposes of discussion, lower-case letters are used when referring to a signal in the analog domain and capital letters are used when referring to a signal in the digital domain. 
       FIG. 3  includes a Tx DSP  310 , a DAC  320 , a driver  330  and a modulator  340  (with laser source  338 ) in a transmitter chain  305 . The Tx DSP  310  operates in the digital domain. The DAC  320  converts signals from the digital domain to the analog domain. The driver  330  and the modulator  340  operate in the analog domain. As in  FIG. 1 , there may be signals on any of channels xi, xq, yi, and yq (analog domain) or XI, XQ, YI, and YQ (digital domain) of the coherent transceiver. Again, the convention for describing signals on the respective channels involves RX and TX for receiver and transmitter, respectively, together with the particular channel and lowercase letters are representative of the analog domain and uppercase letters are representative of the digital domain. 
     The receiver chain  307  includes an ICR  350  (with local oscillator  348 ), an ADC  360  and Rx DSP  370 . The ICR  350  operates in the analog domain. The ADC  360  converts signals from the analog domain to the digital domain. The Rx DSP  370  operates in the digital domain. 
       FIG. 3  illustrates in the analog domain crosstalk signal component s_xtalk  335  from the transmitter chain  305 , in particular tx_yq, being added to the signal component tx_xi, which is output from the ICR  350 . However, while only tx_xi is contemplated in  FIG. 3 , it is understood that the crosstalk can also include one or more of the three other transmit channels being combined with the output of the ICR  350 . The adder symbol shown in  FIG. 3  is merely representative of the physical manifestation of the couple that results between the transmit and receive signals. There need not be a physical adder between the transmitter chain  305  and the receiver chain  307 . 
     The combination of rx_xi+s_xtalk is provided to the ADC  360 , which converts the analog signal to a digital signal represented as RX XI +S Xtalk . The digital signal RX XI +S Xtalk  is provided to Rx DSP  370 . Another input to the Rx DSP  370  is a digital domain representation of the input pattern received from the Tx DSP  310  in the transmitter chain. In  FIG. 3 , the digital domain representation of the input pattern is a representation of the signal on the transmit YQ channel, i.e. S YQ , as that is the channel that is being considered physically closest to the receiver XI channel. However, it is understood that the transmit digital domain representation can also include one or more of the other three channels. 
     The signal S YQ  in the digital domain is a digital emulation of the signal component tx_yq output from the driver  330  in the analog domain. Therefore, the crosstalk signal component resulting from the signal on channel tx_yq can substantially be determined from S YQ . 
     The crosstalk component S Xtalk , which is a result of the signal on channel tx_yq, can then be compensated at the Rx DSP  370  by subtracting the determined crosstalk component that is determined based on S YQ . A more detailed example of the processing involved to determine the crosstalk based on S YQ  follows below. 
       FIG. 4  is a block diagram illustrating example operations that may be performed in Tx DSP  310  and Rx DSP  370  of  FIG. 3 . 
     Tx DSP  310  is illustrated in  FIG. 4  including an upsampling and pulse shaping processing block  312  and a pre-compensation block  314 . The pre-compensation block  314  performs pre-compensation in the Tx DSP  310  to compensate for effects that occur in the DAC  320  and driver  330  in the transmitter chain  305  of  FIG. 3 . In some embodiments, the pre-compensation is S 21  pre-compensation. The input bits corresponding to the YQ pattern  308  provided to the Tx DSP  310  are provided to the upsampling and pulse shaping processing block  312 . An output of the upsampling and pulse shaping processing block  312  is provided to the pre-compensation block  314 . In order that the S YQ  value is representative of the tx_yq signal component occurring after the DAC  320  and the driver  330  in the transmitter chain  305 , the value of S YQ  should be representative of a value before the pre-compensation block  314 . Therefore, the S YQ  component that is provided to the RX DSP  370  is an output of the upsampling and pulse shaping processing block  312 . 
     In an alternative form of a Tx DSP, a DAC sample rate may be equivalent to a data symbol rate and so upsampling and pulse shaping may not be used in such a Tx DSP. 
     Rx DSP  370  is illustrated in  FIG. 4  including a Crosstalk Estimator  371  used to determine an estimate of the crosstalk component S′ Xtalk . In the scenario being described in  FIGS. 3 and 4 , S′ Xtalk  is S′ YQ  as the crosstalk component being considered is from tx_yq. The output S′ Xtalk  of the Crosstalk Estimator  371  is provided to a Crosstalk Compensator  373 . The Crosstalk Compensator  373  also receives the output RX XI +S Xtalk  from the ADC  360 . The Crosstalk Compensator  373  subtracts the estimate of the crosstalk component S′ Xtalk  from RX XI +S Xtalk . Since S′ Xtalk  should substantially be equal to S Xtalk , the crosstalk should be substantially compensated. 
     The output of the Crosstalk Compensator  373  can then be provided to DSP  375  for further processing. 
     The value of S Xtalk  that is part of the signal provided to the Rx DSP  370  can be considered a delayed version of S YQ  multiplied by an impulse response H Xtalk (t). The impulse response H Xtalk (t) includes a distributed feedback of crosstalk, crosstalk magnitude and dependence of frequency. 
     A time delay τ (the symbol tau) is used to compensate for the time the RF signal takes to travel from the Tx DSP  310  via the Tx DAC  320  and the driver  330  in the transmitter chain  305  to the Rx DSP  370  via the ADC  360  in the receiver chain  307 . It should be noted that if the RF link from the driver  330  to the modulator  340  in the transmitter chain  305  is long, i.e. the time delay τ is larger than a symbol period, then the time delay r is not a single discrete value but is a small range. In such a case, r indicates the center of the range. 
     In the Crosstalk Estimator  371 , the estimated version of crosstalk S′ Xtalk  is determined based on the time delayed version of S YQ  convolved with the impulse response H Xtalk (t), which is represented by the mathematical relationship S′ Xtalk =S YQ (t−τ)⊗H Xtalk (t). The crosstalk S Xtalk  is then be compensated by subtracting the estimated crosstalk S′ Xtalk  from the input signal to the RX DSP 510, i.e. RX XI +S Xtalk  as shown in  FIG. 4 . 
     In order to properly compensate for the crosstalk generated in the analog domain, a value of the time delay τ and an appropriate impulse response H Xtalk (t) are determined. In some embodiments, the calibration can be performed to determine the crosstalk effect of each transmit channel on each received channel and then the crosstalk effects can be combined to determine an overall cross talk effect for each received channel. A manner of calibrating the value of the time delay r and an appropriate impulse response H Xtalk (t) as performed in the Crosstalk Estimator of  FIG. 4  is shown in  FIG. 5 . The functional blocks in  FIG. 5  are numbered the same as in  FIG. 3 . 
     An open circuit  355  is shown between the ICR  350  and the Rx ADC  360 . The open circuit  355  can be operated to open circuit any of the receive channels individually or in combination to ensure that, as a result, the only signal component being provided to the Rx ADC  360  is the crosstalk component s_xtalk from the transmitter, which in the case of  FIG. 5  is illustrated to be the crosstalk of the yq transmission channel. It should also be understood that the transmitter chain can be controlled such that only a single channel, for example carrying the real or imaginary component of the vertical or horizontal polarization component or a combination of channels, is propagated through the transmitter channel so that crosstalk between particular channels can be determined. The only signal detected at the Rx DSP  370  is S Xtalk , which is the crosstalk, because there is no received signal due to the open circuit. 
     The time delay τ between S YQ  and crosstalk S Xtalk  can be obtained by performing a cross correlation operation of S YQ  and S Xtalk . 
     In some embodiments, up-sampling of the signal prior to performing the cross correlation operation may be used to enable better accuracy. The upsampling of the two signals S YQ  and S Xtalk  may be performed in the Rx DSP  370 . The upsampling for S YQ  may be done prior to the Crosstalk Estimator  371  in  FIG. 4  or may be done as a preliminary step in the Crosstalk Estimator  371 . The upsampling for S Xtalk  may be done prior to the Crosstalk Compensator  373  in  FIG. 4  or may be done as a preliminary step in the Crosstalk Compensator  373 . The accuracy is improved when using a larger number of signal samples. After the cross correlation operation of S YQ  and S Xtalk  to determine the time delay r is completed, an impulse response H Xtalk (t) can be determined. 
     As indicated above, the estimated crosstalk S′ Xtalk  can be determined based on the mathematical relationship S′ Xtalk =S YQ (t−τ)⊗H Xtalk (t). The impulse response H Xtalk (t) can be determined during the calibration process because values for both S′ Xtalk  and S YQ (t−τ) are known. The value of S′ Xtalk  while normally being an estimate value, in this case is the signal S Xtalk , which is the signal on channel tx_yq that is converted by ADC  360  because there is no received signal due to the open circuit. The value of S YQ (t−τ) is known based on the value of S YQ  provided by Tx DSP  310  that is time shifted based on the time delay τ. 
     In some embodiments, the value of impulse response H Xtalk (t) can be obtained based on the following operations, in which the subscript n indicates a number of taps used in the impulse response. The Tx values are representative of transmit values that correspond to a matrix representation of S YQ (t−τ). The Rx values are representative of receive values that correspond to a vector representation of S Xtalk . The h values are representative of the impulse response values that correspond to a vector representation of H Xtalk (t). 
     
       
         
           
             
               
                 
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     Using a matrix representation for the known values, the impulse response can be determined by the Crosstalk Estimator  371  in Rx DSP  370 . 
     For the crosstalk from other transmit channels (tx_xi, tx_xq, and tx_yi) to rx_xi, the same calibration can be done to obtain emulated crosstalk values for S′ Xtalk_txxi , S′ Xtalk_txxq , S′ Xtalk_txyi . 
     Following the calibration process, i.e. once the time delay τ and the impulse response H Xtalk (t) are determined, those values can be used to determine the estimated crosstalk in order to compensate for the crosstalk. For example, the overall crosstalk from all transmit channels to the rx_xi channel can be compensated at the Rx DSP  370  by subtracting the emulated crosstalk values from rx_xi signal as shown in the equation below.
 
 V′   XI   =V   XI   +S   Xtalk_txxi   +S   Xtalk_txxq   +S   Xtalk_txyi   +S   Xtalk_txyq   −S′   Xtalk_txxi   −S′   Xtalk_txxq   −S′   Xtalk_txyi   −S′   Xtalk_txyq  
 
     Crosstalk compensation for the other receive channels can be done in a similar manner. 
       FIG. 6  illustrates an example flow chart  600  of how the crosstalk calibration may be performed for determining the time delay τ and the impulse response H Xtalk (t) with regard to crosstalk occurring in the analog domain from the yq transmit channel and on a receive channel. Crosstalk calibration for the other transmit channels yi, xq and xi on one or more receive channels could be performed in a similar manner. 
     A first optional step  610  involves performing upsampling of both the YQ channel data S YQ  received from the transmit chain and the crosstalk data S Xtalk  in the receive chain that has been converted to the digital domain by the ADC in the receive chain resulting in upsampled versions of both data S YQ_us  and S Xtalk_us . The S Xtalk  and S Xtalk_us  correspond to the crosstalk signal caused by the yq channel on a particular receive channel as the receive channel has been open circuited. 
     Cross correlation is performed at step  620  to determine the time delay τ, based on the relationship of arg t  max(S YQ_us ⊗S Xtalk_us ), i.e. the time delay τ is determined based on an occurrence of a maximum value of the correlation of the two signals indicating when they would overlap in time. 
     At step  630 , the H Xtalk (t) impulse response is determined based in a relationship between S YQ_us (t−τ) and S Xtalk_us . 
     The calibration described above can be performed initially and may then be performed again as needed to ensure a proper calibration factor is maintained. 
     A method similar to that described above could also be based on a dynamic calibration. In the case of the dynamic calibration, the receiver chain is not open circuited, but has a received data input. As the receiver chain is still receiving data, a longer time average may be needed to perform the calibration process and obtain the appropriate time delay τ and the H Xta (t) impulse response. 
       FIG. 7  shows a graphical plot of a simulation result for 100 Gigabit Quadrature Phase Shift Keying (QPSK) modulation (33.675 GBaud). The x-axis is crosstalk in dB and is defined as 20*log 10(rms(s_xtalk)/rms(tx_yq)). The y-axis is illustrating bit error rate (BER) for a particular crosstalk value. 
     In the simulation, for simplicity, it is assumed that the time delay from the driver to the modulator (i.e. driver  330  and modulator  340  in  FIG. 3 ) is less than a symbol period and the crosstalk is not frequency dependent. 
     Without crosstalk compensation, the BER increases greatly from 6.4×10 −4  to 5.2×10 −2  with an increment of crosstalk from −20 dB to −5 dB. 
     However, with crosstalk compensation as described in the present application, the BER is greatly reduced. With an increment of crosstalk from −20 dB to −5 dB, the BER increases from 2.5×10 −4  to 3.2×10 −4 . The small BER increment results from a difference between the estimate crosstalk S′ Xtalk  based on Tx signal and the real crosstalk S Xtalk  on Rx signal. This difference may be in part due to finite effective number of bits (ENOB) of the DAC in the transmitter chain and the ADC in the receiver chain and inaccuracies of the convolution and impulse response calculations. 
     In the simulation the voltage level of tx_yq is similar to rx_xi. However in the integrated device, the voltage level of tx_yq might be much larger (around 20 dB) than rx_xi. In such a scenario the crosstalk induced penalty would be larger than that shown in the  FIG. 7 . 
       FIG. 8  is an example flow diagram  800  that describes a method for, in the digital domain, compensating crosstalk occurring in the analog domain between transmit and receive RF signals in a coherent optical transceiver implemented on a photonic integrated circuit. 
     Step  810  involves, converting at least one component of a digital domain version of a RF transmission signal to an analog domain version of the at least one component of the RF transmission signal. The at least one component of the digital domain version of the RF transmission signal may be, for example, a digital domain version of any of the real and imaginary components of horizontal and vertical polarization components of the RF transmission signal. 
     Step  820  involves, converting at least one component of an analog domain version of a crosstalk affected RF receive signal to a digital domain version of the at least one component of the crosstalk affected RF receive signal. The at least one component of the analog domain version of the crosstalk affected RF transmission signal may be, for example, an analog domain version of any of the real and imaginary components of horizontal and vertical polarization components of the RF receive signal that has been affected by crosstalk resulting from close proximity of at least one component of an analog domain version of any of the real and imaginary components of horizontal and vertical polarization components of the RF transmission signal. 
     Step  830  is an optional step that involves, in the digital domain, upsampling the at least one component of the digital domain version of the RF transmission signal and the at least one component of the digital domain version of the crosstalk affected RF receive signal. The at least one component of the digital domain version of the RF transmission signal is a version of the transmission signal that has not been pre-compensated for effects of additional processing in a transmit chain in the coherent optical transceiver. 
     Step  840  involves determining a time delay and impulse response to be used in a crosstalk compensation element in the digital domain. An example of how this may be performed in shown in the  FIG. 6 . 
     Step  850  involves, generating a crosstalk compensation element. A substep of generating the crosstalk compensation element involves delaying at least one component of the digital domain version of the RF transmission signal. An additional subset of generating the crosstalk compensation element involves convolving the delayed at least one component of the digital domain version of the RF transmission signal with a digital domain version of an impulse response, the crosstalk occurring between an analog domain version of the at least one component of the RF transmission signal and an analog domain version of at least one component of the RF receive signal. 
     Step  860  involves, also in the digital domain, subtracting the crosstalk compensation element from a digital domain version of at least one component of the crosstalk affected RF receive signal. 
     It should be appreciated that one or more steps of the embodiment methods provided herein may be performed by corresponding units or modules. For example, a signal may be transmitted by a transmitting unit or a transmitting module. A signal may be received by a receiving unit or a receiving module. A signal may be processed by a processing unit or a processing module. The respective units/modules may be hardware, software, or a combination thereof. For instance, one or more of the units/modules may be an integrated circuit, such as field programmable gate arrays (FPGAs) or application-specific integrated circuits (ASICs). It will be appreciated that where the modules are software, they may be retrieved by a processor, in whole or part as needed, individually or together for processing, in single or multiple instances as required, and that the modules themselves may include instructions for further deployment and instantiation. 
     In addition, it would be understood that the steps described above and referred to with regard to  FIG. 8  do not necessarily need to be performed in the exact temporal order as indicated. 
     Although a combination of features is shown in the illustrated embodiments, not all of them need to be combined to realize the benefits of various embodiments of this disclosure. In other words, a system or method designed according to an embodiment of this disclosure will not necessarily include all of the features shown in any one of the Figures or all of the portions schematically shown in the Figures. Moreover, selected features of one example embodiment may be combined with selected features of other example embodiments. 
     While this disclosure has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. Various modifications and combinations of the illustrative embodiments, as well as other embodiments of the disclosure, will be apparent to persons skilled in the art upon reference to the description. It is therefore intended that the appended claims encompass any such modifications or embodiments.