The present document relates to optical transmission networks. In particular, the present document relates to the demultiplexing of polarization division multiplexed optical signals.

Optical transmission networks may make use of polarization division multiplexing for increasing (notably for doubling) the transmission capacity of a transmission link. For this purpose, information (e.g. a bitstream) may be transmitted on two (typically orthogonal) polarizations of an optical carrier. An optical transmission link comprises an optical transmitter configured to generate a modulated optical signal carrying information on two different polarizations. Furthermore, the optical transmission link comprises an optical receiver (e.g. a coherent optical receiver) configured to recover the information (e.g. the bitstream) from the received optical signal.

An optical signal which has been sent over an optical transmission link by an optical transmitter may incur distortions, e.g. due to chromatic dispersion (CD) and/or polarization mode dispersion (PMD) of the transmission medium of the transmission link, such that the received optical signal typically corresponds to a distorted version of the transmitted optical signal. The optical receiver may be configured to perform digital processing in order to recover the transmitted information from the received optical signal. In particular, the optical receiver may be configured to perform digital processing for demultiplexing the polarization division multiplexed signal. This type of digital processing is often referred to as polarization demultiplexing.

Polarization demultiplexing may constitute a significant part of the digital processing which is performed at the optical receiver. A butterfly filter comprising a plurality of FIR (Finite Impulse Response) subfilters may be used to perform polarization demultiplexing. Each FIR subfilter of the butterfly filter may comprise a substantial number of filter coefficients (e.g. 10 to 15 filter coefficients and more). A CMA (Constant Modulus Algorithm) and/or a MMA (Multi Modulus Algorithm) may be used to determine the filter coefficients in a blind adaptation mode. Alternatively or in addition, training assisted approaches may be used to determine the filter coefficients, using training data comprised within the received optical signal. However, such training assisted approaches typically suffer from an additional transmission overhead and from a limited temporal validity of the determined filter coefficients.

In view of the disadvantages of training assisted approaches, blind adaptation schemes using e.g. CMA or MMA are usually preferred. However, as a result of using a butterfly filter comprising subfilters with relatively high numbers of filter coefficients, the adaptation procedure may be computationally intensive. Furthermore, a misalignment of the subfilters may cause a degradation of the demultiplexing result. In addition, degradation due to a limited length of the subfilters of the butterfly filter may cause degradations. An increase of the filter length typically enables an improved performance in case of optimal adjustment of the filter coefficients, however, an increase of the filter length also tends to decrease the speed of the adaptation algorithms. In addition, the significant computational complexity of CMA or MMA usually causes high power consumption in ASICs (Application specific integrated circuits) which are used for implementing polarization demultiplexing.

The present document addresses the above mentioned technical problems. In particular, the present document describes a method and a corresponding system for performing polarization demultiplexing at reduced computational complexity. The method and system which are described in the present document are particularly well suited for performing polarization demultiplexing of received optical signals which have been transmitted over a transmission medium (e.g. an optical fiber) which exhibits PMD and/or Polarization dependent losses (PDL).

According to an aspect a polarization demultiplexing unit configured to determine a first and a second polarization demultiplexed signal from a first and a second polarization signal is described. The polarization demultiplexing unit may be implemented using a digital signal processor. The polarization demultiplexing unit may be used within an optical receiver of an optical transmission system. The first and the second polarization demultiplexed signals may correspond to signals which have been transmitted using two different polarization planes of an optical signal. The different polarization planes are typically orthogonal with respect to one another. The first and the second polarization signals may have been derived from a received optical signal using a coherent frontend comprising analog-to-digital converters (ADC), to yield the first and the second digital and complex valued polarization signals.

The polarization demultiplexing unit comprises a delay unit configured to delay a signal derived from the first polarization signal relative to a signal derived from the second polarization signal by a delay parameter, to yield a first delayed signal. The first and the second polarization signals may be processed prior to being submitted to the delay unit, thereby yielding a signal derived from the first polarization signal and a signal derived from the second polarization signal. In an example, the delay unit is arranged to delay the first polarization signal relative to the second polarization signal by the delay parameter. The delay parameter may be or may be indicative of a fixed delay or a (time-) variable delay.

The polarization demultiplexing unit further comprises a spatial rotation entity configured to perform a spatial rotation of the first delayed signal and of the signal derived from the second polarization signal using a phase shift parameter and a rotation angle parameter. The spatial rotation entity may comprise a phase shift unit and a rotation unit. The phase shift unit may be configured to apply a phase shift in accordance to the phase shift parameter to the signal derived from the second polarization signal, to yield a second phase shifted signal. Alternatively, the phase shift may be applied to the first delayed signal. In general terms, the phase shift unit may be configured to perform a phase shift in accordance to the phase shift parameter to the signal derived from the second polarization signal or to the first delayed signal. The rotation unit may be configured to rotate the first delayed signal and the second phase shifted signal (or the first delayed and phase shifted signal and the signal derived from the second polarization signal) in accordance to the rotation angle parameter, to yield the first and second polarization demultiplexed signals. For this purpose, the rotation unit may be configured to apply a rotation matrix in accordance to the rotation angle parameter to the two signals at the input of the rotation unit.

The spatial rotation entity may provide the first and/or the second polarization demultiplexed signals at its output (subsequent to phase shifting and rotation).

The polarization demultiplexing unit may further comprise a parameter determination unit configured to determine the phase shift parameter and the rotation angle parameter using a cost function depending on a property of the first and second polarization demultiplexed signals. As indicated above, the delay parameter may be variable (along the sequence of samples of the first and second polarization signals). In such cases, the parameter determination unit may be configured to also determine the delay parameter using the cost function.

As such, the polarization demultiplexing unit may make use of a limited number of parameters, notably a delay parameter, a phase shift parameter and a rotation angle parameter, for performing polarization demultiplexing. The limited number of parameters allows for a resource efficient and high speed implementation of the polarization demultiplexing unit. Furthermore, the use of a delay parameter in combination with a phase shift parameter and a rotation angle parameter allows for the compensation of polarization mode dispersion (PMD) at an optical receiver comprising the polarization demultiplexing unit.

The cost function may depend on an (e.g. average) absolute value of the amplitudes or on a quality factor of the first and the second polarization demultiplexed signals. In particular, the cost function may depend on the sum of the (e.g. averaged) absolute value of the amplitudes or on the quality factors of the first and the second polarization demultiplexed signals.

The parameter determination unit may be configured to determine the phase shift parameter and the rotation angle parameter (as well as the delay parameter) iteratively on a sample-by-sample basis, such that the cost function is increased (e.g. maximized) or decreased (e.g. minimized). For this purpose, a gradient decent scheme may be applied. In particular, the parameter determination unit may be configured to determine the phase shift parameter and the rotation angle parameter (as well as the delay parameter) using e.g. a steepest decent method. As indicated above, the first and second polarization signals may each comprise temporal sequences of samples. Each sample may cover a pre-determined temporal sample period (in accordance to the sampling rate). The delay parameter may correspond to an integer multiple of the temporal sample period. As such, the delay unit may be implemented in a computationally efficient manner using one or more latches.

The delay unit may comprise an interpolation filter comprising a plurality of filter coefficients. The plurality of filter coefficients may be dependent on the delay parameter, such that the interpolation filter is configured to delay the signal derived from the first polarization signal by the delay parameter. As such, an interpolation filter may be used to apply a particular delay (in accordance to the delay parameter) to the signal derived from the first polarization signal. The interpolation filter may be used for delays which correspond to fractions of one or more sample periods.

The delay unit may comprise a look-up table providing a mapping between different delay parameters and different pluralities of filter coefficients for different interpolation filters. The delay unit may be configured to determine the interpolation filter for a particular delay parameter, using the look-up table. As such, the interpolation filter may be determined in a computationally efficient manner.

The polarization demultiplexing unit may further comprise an initial spatial rotation entity configured to perform a spatial rotation of the first and second polarization signals using an initial phase shift parameter and an initial rotation angle parameter, to yield the signals derived from the first and second polarization signals. The initial rotation entity may comprise a phase shift unit and a rotation unit, as outlined above. The use of an initial spatial rotation entity followed by a delay unit and followed by a further spatial rotation unit may be beneficial, as it allows the use of a fixed delay parameter. The parameter determination unit may be configured to also determine the initial phase shift parameter and the initial rotation angle parameter using the cost function.

The polarization demultiplexing unit may comprise a first processing path for determining the first polarization demultiplexed signal, and a second processing path for determining the second polarization demultiplexed signal. The first and second processing paths may each comprise a dedicated delay unit and a dedicated spatial rotation entity using dedicated delay parameters, phase shift parameters and rotation angle parameters. In other words, the first and second polarization demultiplexed signals may be determined using dedicated polarization demultiplexing processing paths. This may be beneficial in situations where the polarization planes of the first and second polarization signals are not fully orthogonal with respect to one another. Such a situation may occur in case of a transmission medium causing polarization dependent losses. The parameter determination unit may then be configured to also determine the dedicated phase shift parameters and rotation angle parameters.

According to a further aspect, an optical receiver configured to recover data from a received optical signal is described. The optical receiver may comprise a coherent frontend configured to determine a first polarization signal and a second polarization signal from the received optical signal. The first and second polarization signals may be digital signals. Furthermore, the first and second polarization signals may be indicative of different polarization planes of the received optical signal. The different polarization planes may be orthogonal with respect to one another.

Furthermore, the optical receiver may comprise a polarization demultiplexing unit to determine a first and a second polarization demultiplexed signal from the first and second polarization signals. The polarization demultiplexing unit may comprise any of the features described in the present document. In addition, the optical receiver may comprise a decision unit configured to determine the data from the first and second polarization demultiplexed signals.

The optical receiver may further comprise first and second shaping filters for filtering signals derived from the first and second polarization signals, respectively. The first and second shaping filters may be dependent on an optical transmitter of the received optical signal.

According to a further aspect, a method for determining a first and a second polarization demultiplexed signal from a first and a second polarization signal is described. The method comprises delaying a signal derived from the first polarization signal relative to a signal derived from the second polarization signal by a delay parameter, to yield a first delayed signal. Furthermore, the method comprises performing a spatial rotation of the first delayed signal and of the signal derived from the second polarization signal using a phase shift parameter and a rotation angle parameter. In addition, the method may comprise determining the phase shift parameter and the rotation angle parameter using a cost function depending on a property of the first and second polarization demultiplexed signals. The property may e.g. relate to an absolute value of an amplitude of the first and second polarization demultiplexed signals.

According to a further aspect, a software program is described. The software program may be adapted for execution on a processor and for performing the method steps outlined in the present document when carried out on the processor.

According to another aspect, a storage medium is described. The storage medium may comprise a software program adapted for execution on a processor and for performing the method steps outlined in the present document when carried out on the processor.

According to a further aspect, a computer program product is described. The computer program may comprise executable instructions for performing the method steps outlined in the present document when executed on a computer.

It should be noted that the methods and systems including its preferred embodiments as outlined in the present patent application may be used stand-alone or in combination with the other methods and systems disclosed in this document. Furthermore, all aspects of the methods and systems outlined in the present patent application may be arbitrarily combined. In particular, the features of the claims may be combined with one another in an arbitrary manner.

The invention is explained below in an exemplary manner with reference to the accompanying drawings, wherein

• Fig. 1 shows a block diagram of an example polarization demultiplexing unit;
• Fig. 2a shows a block diagram of an example frontend of a coherent optical receiver;
• Fig. 2b shows a block diagram of an example polarization demultiplexing unit for an optical signal having incurred PMD;
• Fig. 3 shows a block diagram of another example polarization demultiplexing unit for an optical signal having incurred PMD; and
• Fig. 4 shows a block diagram of an example polarization demultiplexing unit for an optical signal having incurred polarization dependent losses (PDL).

Fig. 2a shows a block diagram of an example frontend of a coherent optical receiver. The received optical signal 211 may be superimposed with a local oscillator signal within a hybrid unit 231 to yield two signals, a first analog polarization signal 221 and a second analog polarization signal 222, which are typically indicative of two orthogonal polarizations of the received optical signal 211. The first analog polarization signal 221 and the second analog polarization signal 222 may be converted into the digital domain using analog-to-digital converters 232 to yield a first (digital) polarization signal 111 and a second (digital) polarization signal 112.

The polarization signals 111, 112 are typically indicative of complex field amplitudes E_x and E_y, respectively, for two different polarization planes x and y. The two polarization planes x and y may be orthogonal with respect to one another. Each polarization signal 111, 112 comprises an in-phase component and a quadrature phase component. The polarization planes of the optical transmitter and of the optical receiver are usually not aligned. Hence, the first and second polarization signals 111, 112 may be viewed as projections of the originally transmitted first and second polarization signals onto the polarization planes x and y of the optical receiver. It is a task of polarization demultiplexing to recover the originally transmitted first and second polarization signals from the first and second polarization signals 111, 112. This may be achieved by performing a rotation of the first and second polarization signals 111, 112 within the socalled Strokes space.

Fig. 1 shows a block diagram of an example polarization demultiplexing unit 100 configured to convert the first and second polarization signals 111, 112, referred to as E_x and E_y, into first and second polarization demultiplexed signals 121, 122, referred to as E'_x and E'_y. The polarization demultiplexing unit 100 comprises a phase retardation or a phase shift unit 101 configured to apply a relative phase shift ϕ to one of the polarization signals 111, 112. In the illustrated example, the phase shift is applied to the second polarization signal 112. Furthermore, the polarization demultiplexing unit 100 comprises a rotation unit 102 configured to apply a rotation to the first and the second polarization signals by the rotation angle α. The phase shift unit 101 and the rotation unit 102 may be referred to as a spatial rotation element. The spatial rotation element may be configured to perform a spatial rotation of the first and second polarization signals 111, 112.

In addition, the polarization demultiplexing unit 100 comprises a parameter determination unit 103 which is configured to determine the phase shift ϕ and the rotation angle α using a cost function J. The cost function typically depends on a property of the polarization demultiplexed signals 121, 122. By way of example, the cost function J may be indicative of the signal power and/or of the signal amplitude of the polarization demultiplexed signals 121, 122. The phase shift ϕ and the rotation angle α may be determined in an iterative and/or a recursive manner by maximizing or minimizing the cost function J on a sample-by-sample basis. The recursive determination of the phase shift ϕ and of the rotation angle α may make use of a gradient method (e.g. a steepest decent method).

The polarization demultiplexing unit 100 of Fig. 1 is beneficial, as it requires the determination of only two parameters (the phase shift ϕ and the rotation angle α) instead of the determination of a butterfly filter comprising FIR subfilters with a relatively high number of filter coefficients (e.g. 10-15 filter coefficients per FIR subfilter). However, the performance of the polarization demultiplexing unit 100 of Fig. 1 typically decreases substantially if the received optical signal 211 has been submitted to PMD. Hence, it may be beneficial to adapt the polarization demultiplexing unit 100 of Fig. 1, in order to increase its performance in case of PMD distorted optical signals.

Polarization Mode Dispersion (PMD) is typically caused by random imperfections and asymmetries of an optical transmission medium (e.g. an optical fiber) which leads to different propagation speeds for the different polarizations of an optical signal. PMD may be modeled using a delay τ. In particular, PMD may be taken into account at the optical receiver by delaying the first polarization signal 111 with respect to the second polarization signal 112 (or vice versa) by a delay τ.

Fig. 3 shows an example polarization demultiplexing unit 300 comprising a phase shift unit 101 and a rotation unit 102. Furthermore, the polarization demultiplexing unit 300 comprises a delay unit 303 configured to apply a delay τ to the first or the second polarization signal 111, 112. In the illustrated example, the delay τ is applied to the first polarization signal. The parameter determination unit 103 (not shown) may be configured to determine the parameters of the polarization demultiplexing unit 300, i.e. the phase shift ϕ₁, the rotation angle ρ₁ and the delay τ_i. As outlined above, the parameters may be determined by reducing (e.g. minimizing) or by increasing (e.g. maximizing) a pre-determined cost function in an iterative and/or recursive manner. The cost function may be dependent on the first and second polarization demultiplexed signals 121, 122. Due to the reduced number of parameters (three parameters, instead of 40-60 parameters), the computational complexity of this iterative process is substantially decreased.

It should be noted that the delay τ_i may be variable and/or may take on fractional sample values. In other words, the delay τ_i may correspond to a fraction of a sample. Such fractional delays may be implemented using an interpolation filter, e.g. an FIR filter, comprising a plurality of filter coefficients. The filter coefficients of the interpolation filter for a particular delay τ_i may be pre-determined. By way of example, the polarization demultiplexing unit 300 may comprise a look-up table for mapping a particular delay τ_i to a corresponding interpolation filter. Hence, the interpolation filter can be determined in a computationally efficient manner. The interpolation filter which generates the delay τ_i may comprise a programmed setting which depends on the available channel adjustment. For adaptation of the interpolation filter a correlation method may be applied.

Fig. 2b shows a block diagram of another polarization demultiplexing unit 200 which is configured to process PMD distorted optical signals. The polarization demultiplexing unit 200 makes use of two spatial rotation entities comprising a phase shift unit 101, 201 and a rotation unit 102, 202 each. The two spatial rotation entities may be separated by a delay unit 203 which is configured to apply a delay τ to one of the polarization signals. The first spatial rotation entity 102 may be directed at changing the orientation of (i.e. rotating) the first and second polarization signals 111, 112 with respect to the delay τ. The second spatial rotation entity 202 may be directed at changing the orientation of (i.e. rotating) the first and second polarization signals 111, 112 with respect to the decision unit of the receiver. The delay τ may be a fixed or a variable delay. In order to reduce the computational complexity, the delay τ may be limited to an integer multiple of a sample period. In this case, the fixed or variable delay may be implemented without using an interpolation filter. The delay may then be implemented e.g. using a latch. Notably when using first and second spatial rotation entities 102, 202, as illustrated in Fig. 2b, the delay τ may be a fixed delay.

It should be noted that the ADCs 232 may be configured to oversample the analog polarization signals 221, 222 (e.g. by a factor of two with respect to the symbol rate). This oversampling may be beneficial for timing recovery at the optical receiver. As such, a delay which is limited to an integer multiple of a sample period may correspond to a fraction (e.g. to ½) of the symbol period.

For the polarization demultiplexing unit 200 of Fig. 2b, the parameters of the first and second spatial rotation entities (i.e. the phase shifts and the rotation angles), as well as a possible variable delay, may be determined using a feedback signal derived from the first and second polarization demultiplexed signals 121, 122 (as outlined above). For this purpose, the polarization demultiplexing unit 200 may comprise a parameter determination unit 103 configured to determine the parameters based on a property and/or a cost function of the first and second polarization demultiplexed signals 121, 122.

In case of significant PDL (polarization dependent loss) a parallelization of the polarization demultiplexing structure as shown in Fig. 4 may be used to determine the polarization demultiplexed signals 121, 122. In case of PDL, it may occur that the polarization components of the received optical signal are not orthogonal with respect to each other. The polarization demultiplexing unit 400 of Fig. 4 takes this into account by performing a separate polarization demultiplexing for the first and for the second polarization demultiplexed signals 121, 122. For this purpose, the polarization demultiplexing unit 400 comprises a first arm or a first path (comprising e.g. the polarization demultiplexing unit 200 or the polarization demultiplexing unit 300) for determining the first polarization demultiplexed signal 121, and a second arm or a second path (comprising e.g. the polarization demultiplexing unit 200 or the polarization demultiplexing unit 300) for determining the second polarization demultiplexed signal 122. The outputs 421, 422 of the first and second processing arm may be used for feedback purposes, i.e. for determining the parameters of the first and second arms (using a parameter determination unit 103).

Such separate processing for the two polarization demultiplexed signals 121, 122 may be beneficial as the optimum parameter values for the two processing arms may not necessarily be the same for the two polarization demultiplexed signals 121, 122.

In the illustrated example, the second processing arm comprises a first spatial rotation entity comprising a phase shift unit 401 and a rotation unit 402, a delay unit 403 and a second spatial rotation entity comprising a phase shift unit 411 and a rotation unit 412.

Subsequent to or downstream of polarization demultiplexing further digital processing stages, such as timing recovery, frequency estimation and/or phase estimation, may be applied to recover the transmitted information comprised within the received optical signal 211.

Furthermore, a signal shaping filter may be applied to individually filter the polarization demultiplexed TE and TM channels (i.e. the first and second polarization demultiplexed signals 121, 122 or signals derived therefrom) separately. These shaping filters may comprise a fixed filter which may depend on the optical transmitter, on the transmission link and/or on the optical receiver (e.g. a RRC, root-raised cosine, filter suitable to the transmitter). Furthermore, the shaping filters may comprise variable filters.

Finally, decision directed feedback may be used to recover the transmitted information from the processed signals. Decision directed feedback may be beneficial due to a fast and high accuracy feedback.

In the present document, polarization demultiplexing units (and corresponding methods) have been described which make use of a reduced number of parameters. As a result of this, the computational complexity and the power consumption of polarization demultiplexing may be reduced, and the adaptation speed may be increased. The polarization demultiplexing units make use of simple mathematical operations such as phase rotations and attenuation, thereby leading to a substantial decrease of computational complexity (e.g. by a factor of two). Subsequent to polarization demultiplexing a shaping filter may be used for channel compensation. Such a shaping filter may be used within each polarization (TE and TM) path individually.

It should be noted that the description and drawings merely illustrate the principles of the proposed methods and systems. It will thus be appreciated that those skilled in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the invention and are included within its spirit and scope. Furthermore, all examples recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the proposed methods and systems and the concepts contributed by the inventors to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the invention, as well as specific examples thereof, are intended to encompass equivalents thereof.

Furthermore, it should be noted that steps of various above-described methods and components of described systems can be performed by programmed computers. Herein, some embodiments are also intended to cover program storage devices, e.g., digital data storage media, which are machine or computer readable and encode machine-executable or computer-executable programs of instructions, wherein said instructions perform some or all of the steps of said above-described methods. The program storage devices may be, e.g., digital memories, magnetic storage media such as a magnetic disks and magnetic tapes, hard drives, or optically readable digital data storage media. The embodiments are also intended to cover computers programmed to perform said steps of the above-described methods.

In addition, it should be noted that the functions of the various elements described in the present patent document may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared. Moreover, explicit use of the term "processor" or "controller" should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASIC), field programmable gate array (FPGA), read only memory (ROM) for storing software, random access memory (RAM), and non volatile storage. Other hardware, conventional and/or custom, may also be included.

Finally, it should be noted that any block diagrams herein represent conceptual views of illustrative circuitry embodying the principles of the invention. Similarly, it will be appreciated that any flow charts, flow diagrams, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.