WO2013185845A1

WO2013185845A1 - Method for adapting an equalizer to equalize a composite characteristic of an optical communication channel

Info

Publication number: WO2013185845A1
Application number: PCT/EP2012/061515
Authority: WO
Inventors: Fabian Nikolaus Hauske; Fabio PITTALA
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2012-06-15
Filing date: 2012-06-15
Publication date: 2013-12-19

Abstract

The invention relates to a method (100) for adapting an equalizer to equalize a composite characteristic of an optical communication channel comprising a first impulse response characteristic (CD) of a first impulse response length (M) and a second impulse response characteristic (PMD) of a second impulse response length (N), the method (100) comprising: estimating (101) the first characteristic (CD) based on an optical signal (121) transmitted through the optical communication channel to obtain an estimate (123) of the first characteristic (CD); adjusting (105) the equalizer based on the estimate (123) of the first characteristic (CD), the equalizer equalizing the optical signal (121) to provide a first estimate (127) of the optical signal (121) compensated by the first characteristic (CD); estimating (107) the second characteristic (PMD) based on the first estimate (127) of the optical signal (121) to obtain an estimate (129) of the second characteristic (PMD); interpolating (109) the estimate (129) of the second characteristic (PMD) to a filter impulse response length (P) of the equalizer to obtain an interpolated estimate (131) of the second characteristic (PMD); and adjusting (111) the equalizer based on the interpolated estimate (131) of the second characteristic (PMD), the equalizer thereby providing a second estimate (133) of the optical signal (121) compensated by both, the first characteristic (CD) and the second characteristic (PMD).

Description

DESCRIPTION

Method for adapting an equalizer to equalize a composite characteristic of an optical communication channel

BACKGROUND OF THE INVENTION

The present invention relates to a method for adapting an equalizer to equalize a composite characteristic of an optical communication channel and to an optical receiver applying such method. Aspects of the invention relate to digital equalization of a multi- input multi-output (Ml MO) channel in coherent detection receivers.

In coherent optical transmission system, chromatic dispersion (CD), polarization mode dispersion (PMD) and other channel impairments accumulate during fiber transmission and cause severe inter-symbol-interference (ISI) which brings severe degradation to system.

In long-haul optical communication, the length of the equalizer of a transponder is mainly dependent on the inter-symbol interference (ISI) induced by chromatic dispersion (CD). During initialization of the digital coherent receiver, a robust and accurate CD estimation is vital to set the frequency-domain (FD) CD compensation filter. If the CD estimation fails with a large estimation error, none of the subsequent equalization and synchronization stages could work. This would result in a total failure of the transponder. Time-varying effects like polarization rotations and PMD with short memory length require a shorter length of the filter. However, a regular update of the equalizer properties is required to maintain continuous optimum equalization. Typically, a dual stage equalization is considered, where a first static equalization stage 900 as described below with respect to Fig. 9 compensates for the bulk of CD which is used only for initialization, i.e. for initial acquisition and adaptation and a second adaptive stage 2x2 multi-input-multi-output (Ml MO) equalization 1000 as described below with respect to Fig. 10 compensates for residual CD and polarization mode dispersion (PMD) effects which is used for continuous update of filter coefficients. The coefficients of a linear equalizer may be adapted by "blind" non-data-aided (NDA) methods, typically in time domain (TD) or based on a training sequence, which refers to training-aided (TA) channel estimation, typically in frequency domain (FD). TA channel estimation adds a training sequence (TS) Ci, C₂ to the data as described below with respect to Figures 11 and 12, which is repeated at a regular rate fast enough to track time- varying channel distortions. With the aid of the spectra R_Ci, Rc2 of the received training sequence TS and the known transmitted spectra S_Ci, S_C2 of the transmitted training sequence TS, one full and instantaneous channel estimation can be performed. The channel estimation can be employed to calculate the zero-forcing (ZF) or the minimum- mean-square-error (MMSE) solution for FD filters.

Overhead below 2% is sufficient in dual-stage FD equalizer (FDE) receivers 1300 as described below with respect to Fig. 13, where a (NDA) FD CD compensation 1305 is followed by a TA 2><2 multi-input multi-output (Ml MO) FDE 1307.

In the first stage equalization 1305 of a typical coherent transponder 1300 the received signals in the X- and Y-polarization as described below with respect to Fig. 9 are compensated for CD in frequency domain using two fast Fourier transformation (FFT) blocks 901 , 905. CD is efficiently compensated in the FFT blocks 901 and 905. The compensation CD function is:

where λ₀ is the signal wavelength, f_s is the sampling frequency, N is the FFT size, c is the speed of light, n is the tap number, L is fiber length, and D is dispersion coefficient. In links with optical inline CD compensation or in links composed of different fiber types the parameter DL can be replaced by the residual accumulated CD effective at the receiver. Due to complexity reasons, only one FFT block using complex input is applied to each polarization as illustrated by the FFT block 1315 in Fig. 13. The inverse FFT (I FFT) illustrated by the IFFT block 1317 in Fig. 13 is identical to the FFT 1315 although real and imaginary parts are swapped at input and output. From the above equation it becomes clear that the equalization function can be obtained analytical as long as the parameter of the residual CD is known and the equalizer length satisfies the memory requirement. No interpolation operation is necessary. Blind NDA CD estimation algorithms are published in 'R. Andres Soriano, F. N. Hauske, N. Guerrero Gonzalez, Z. Zhang, Y. Ye, I. Tafur Monroy, "Chromatic Dispersion Estimation in Digital Coherent Receivers", Journal of Lightwave Technology, vol.29, no.11 , pp.1627- 1637, June 2011 ' and 'M. Kuschnerov, F.N. Hauske, K. Piyawanno, B. Spinnler, M.S. Alfiad, A. Napoli, B. Lankl, " DSP for Coherent Single-Carrier Receivers", Journal of Lightwave Technology, vol.27, no.16, ρρ.361 3622, Aug.15 2009' and described in the patent applications PCT/CN2009/072624 and PCT/CN2010/070866.

Polarization tracking, PMD compensation and residual CD compensation are done in the second stage equalizer 1307. Such second stage equalizer 1000 is usually implemented in time domain by using finite impulse response (FIR) filters

W_XY, W_YX, Ww arranged in butterfly structure as illustrated in Fig. 10.

The coefficients of the linear equalizer can be adapted by NDA methods based on gradient algorithms like constant-modulus algorithm (CMA) or decision-directed (DD) least mean square (LMS). Unfortunately, filter update by CMA and DD-LMS is strongly dependent on the modulation format, which requires complex implementation with individual cost functions for each modulation and suffers from a relatively slow

convergence with potential sub-optimum acquisition and even failures.

Frequency domain equalization combined with TA channel estimation does not experience convergence problems in terms of speed and singularity. In principle, the modulation of the training sequence and the payload data is independent from each other, which allows flexible switching of the data modulation format. In contrast to CMA/DD-LMS, the FD TA channel estimation can be performed on non-integer numbers of samples per symbols.

Training-based channel estimation is known from wireless communications, where fast channel tracking is required, in particular for mobile communications where each training sequence instantly leads to a full channel estimation, which comes at the cost of additional overhead widening the spectrum of the transmitted signal, usually smaller than 3 percent.

The training sequence TS for the 2x2 Ml MO system can be composed of two orthogonal blocks C1 , C2 as illustrated in Fig. 11 . The length of each block must at least be two times the channel impulse response (CIR) in order to provide four independent equations, one for each element of the 2x2 MIMO channel. With the aid of the received spectra Rc-i , R_C2 and the known transmitted spectra S_Ci , S_C2 of the TS as illustrated in Fig. 12, the receiver estimates the channel as

This equation assumes training sequences with constant amplitude, zero auto-correlation (CAZAC). Many alternatives are known from the literature using sequences with different properties such that the channel estimation is modified accordingly. From the channel estimation, the FD filter taps can be calculated as

W_ZF(f) = H W_MMSE(f) = H'

where and (-)^H denote the complex-conjugate (Hermitian) transpose and the inverse, respectively. o_n ² and o_s ² are the noise and signal powers which should be estimated at the receiver.

The ZF filter function requires much less complexity for the computation of the filter solution and does not require an estimation of o_n ² and o_s ², whereas the MMSE filter function requires more complexity for the computation of the filter solution, but it typically provides the better performance in presence of noise.

A dual stage equalizer requires two equalization stages, which is moie complex to implement. It requires a first stage CD compensation 900 preferably implemented in the frequency domain and a subsequent second stage 2x2 MIMO equalizer 1000 typically implemented in time domain. Apart from initialization, the first stage is static, while the second stage is adaptive. As the ISI is largely reduced after the first stage, the requirement for training aided channel estimation is strongly reduced. Therefore, only low overhead for TA-based channel estimation and adaptive filtering is required.

For a dual stage equalizer framing synchronization is required to detect the training block prior to the channel estimation. Several methods based on correlation in the time-domain or frequency-domain are known. Fig. 13 illustrates a dual stage equalizer 1300 with both stages 1301 , 1303 implemented in the frequency domain. An optical signal 1302 passes a serial-to-parallel converter 1313, the both equalization stages 1301 , 1303, a parallel-to- serial converter 1323 and further DSP processing stages 1325. The first equalization stage 1301 contains FFT processing 1315, 1317 of size M and a CD compensator 1305 of size M for compensating the chromatic dispersion of length M. The second equalization stage 1303 contains FFT processing 1319, 1321 of size N and an equalizer 1307 of size N for compensating the polarization mode dispersion of size N. The composite length of the dual stage equalizer with the two compensation units 1305 and 1307 thus

corresponds to the sum of the chromatic dispersion length M and the polarization mode dispersion length N.

The FFT size for FD TA channel estimation of the second impulse response determines the length of one training sequence (or vice versa) while the repetition rate of the training sequence is determined by the speed of change in the channel. Rate and length of the training sequence define the total overhead. Employing a second stage FD equalizer 1307 the same length N of the FFT size for FD TA channel estimation and for the equalization can be used in an implementation efficient realization. Otherwise, interpolation between the estimated second impulse response and the equalization function is required.

Large size FFTs are more computationally efficient. For low overhead, only the size N of the FFT, i.e. the length of the training sequence can be adjusted, because the rate requirement is fixed due to the SOP rotation specification. To satisfy the ASIC processing speed requirements, a certain degree of parallelization, e.g. 128 is required. With FFTs shorter than 128, several parallel FFTs need to be implemented. However, shorter FFTs are desired to keep the overhead low.

A single-stage equalizer requires much less complexity as shown in 'B. Spinnler, "Equalizer Design and Complexity for Digital Coherent Receivers," IEEE Journal of Selected Topics in Quantum Electronics, vol.16, no.5, pp.1 180-1 192, Sept.-Oct. 2010'. Only one FD 2x2 MIMO structure is required, which requires much less operations. However, if the channel parameters change, e.g. an SOP rotation happens, all FD coefficients need to be updated. As this FD filter has many taps following the requirement of CD compensation, e.g. 1024 taps, it has many degrees of freedom, which makes a stable and fast NDA filter acquisition almost impossible. A classical training aided channel estimation is more practical in this case but as the length of the training sequence follows the total channel impulse length, the overhead is tremendous. This results from the fact that the training sequence should not only cover the PMD but also the CD. If the CD requires an FFT-size of N samples, e.g. N=1024, then also the training sequence should cover N samples. SUMMARY OF THE INVENTION

It is the object of the invention to provide a concept for a fast, memory efficient and accurate dispersion compensation technique in a coherent optical receiver that is suitable for both, initial channel estimation and tracking time varying channel impairments for compensating chromatic dispersion and polarization mode dispersion effects.

This object is achieved by the features of the independent claims. Further implementation forms are apparent from the dependent claims, the description and the figures. The invention is based on the finding that a reduction of the total complexity of the equalization process is achieved by incorporating a single-stage equalization for both, the FD CD compensation and the training aided 2x2 MIMO frequency domain equalizer, where the total overhead is kept low for training aided channel estimation. As the filter length requirement is governed by the bulk of CD to be compensated, an equalizer with length P=M+N, with M»N, nearly equal to that of a FD CD compensator is used, which is initially adapted by blind CD estimation. Short training sequences are included between the payload data with sufficient repetition rate to track time-varying distortions. The length of the training sequence only covers residual CD after FD CD compensation resulting from estimation error of blind CD estimation, PMD and all other impairments with memory as amplitude filtering, electrical receiver bandwidth limitation and other effects. After CD compensation, the channel is estimated with a resolution equal to the training sequence length N based on the received known training sequences. The adaptation requires only one compensation filter but two estimations are used for that compensation filter. The estimated channel elements of length N are interpolated to the length P of the filter stage. The P-size transfer function of the interpolated TA channel estimation and the CD compensation is combined in a single-stage FD equalization function. Continuous update is performed by incremental channel estimation of the equalized signal after the single- stage FD 2x2 MIMO equalizer. By applying such equalization method in the coherent optical receiver, the compensation is significantly improved with respect to accuracy, robustness and speed as will be presented in the following. In order to describe the invention in detail, the following terms, abbreviations and notations will be used:

CD: chromatic dispersion, PMD: polarization mode dispersion,

FD: frequency domain,

TD: time domain,

IS I : inter-symbol-interference,

PDM: polarization division multiplexing, (D)QPSK: (differential) quaternary phase shift keying

quadrature phase shift keying,

FFT: fast Fourier transform, IFFT: inverse fast Fourier transform,

DFT: discrete Fourier transform,

DSP: digital signal processing,

ASIC: application specific integrated circuit,

ADC: analog/digital converter, LO: local oscillator, DA: data aided,

TA: training aided NDA: non-data-aided,

WDM: wavelength division multiplex,

POLMUX- QPSK: polarization-multiplexed quadrature phase shift keying,

BER: bit error rate,

OSNR: optical signal-to-noise ratio,

FIR: finite impulse response,

M R: infinite impulse response, EQ: equalizer,

FO: frequency offset,

TR: timing recovery, sps: samples per symbol,

FFW: feed forward, FB: feed-back,

SOP: state of polarization,

PDL: polarization dependent loss, DGD: differential group delay,

FEC: forward error correction, CPE: carrier phase estimation,

I: in-phase, Q: quadrature,

CAZAC: constant amplitude zero auto-correlation, PN: pseudo noise, ZF: zero forcing,

MMSE: minimum mean square error, MIMO: multi input multi output,

DAC: digital analogue converter,

TS: training sequence, CMA: constant-modulus algorithm,

DD: decision-directed, LMS: least mean squares.

In the following, the term "coupled" is used. A first functional unit coupled to a second functional unit means that an output of the first functional unit is connected by a physical connection to an input of the second functional unit or that the output of the first functional unit is connected via one or more further functional units to the input of the second functional unit. The physical connection may be a wired or wireless electrical or optical connection, e.g. by using an electrical or optical cable or by using a radio interface.

According to a first aspect, the invention relates to a method for adapting an equalizer to equalize a composite characteristic of an optical communication channel, the composite characteristic comprising a first impulse response characteristic of a first impulse response length and a second impulse response characteristic of a second impulse response length, the method comprising: estimating the first impulse response

characteristic based on an optical signal transmitted through the optical communication channel to obtain an estimate of the first impulse response characteristic; adjusting the equalizer based on the estimate of the first impulse response characteristic, the equalizer equalizing the optical signal to provide a first estimate of the optical signal compensated by the first impulse response characteristic; estimating the second impulse response characteristic based on the first estimate of the optical signal to obtain an estimate of the second impulse response characteristic; interpolating the estimate of the second impulse response characteristic to a filter impulse response length of the equalizer to obtain an interpolated estimate of the second impulse response characteristic; and adjusting the equalizer based on the interpolated estimate of the second impulse response

characteristic, the equalizer thereby providing a second estimate of the optical signal compensated by both, the first characteristic and the second characteristic.

The dispersion compensation is thus fast and implementation efficient as the equalization is adjusted based on the estimate of the first impulse response characteristic and thereafter based on the interpolated estimate of the second impulse response

characteristic. So only one equalization stage is required, which results in less complexity and less processing latency. The size of the equalizer is set to the size of the sum of the first impulse response characteristic, e.g. the size of CD, and the size of the second impulse response, e.g. the size of the PMD. The equalizer length is sufficient to provide an accurate compensation for both, first and second impulse response characteristics, e.g. CD and PMD.

In a first possible implementation form of the method according to the first aspect, the method further comprises: interpolating the estimate of the first impulse response characteristic to the filter impulse response length of the equalizer to obtain an

interpolated estimate of the first impulse response characteristic, wherein the adjusting the equalizer based on the estimate of the first impulse response characteristic is based on the interpolated estimate of the first impulse response characteristic.

The adjusting the equalizer is based on the interpolated estimate of the first impulse response characteristic which means that the filter impulse response length P of the equalizer is greater than the first impulse response length M.

In a second possible implementation form of the method according to the first aspect as such or according to the first implementation form of the first aspect, the first impulse response characteristic is a chromatic dispersion. Estimating the value of residual chromatic dispersion, adjusting the filter impulse response to the first impulse response characteristic can be achieved analytically without using interpolation.

The method can be used for equalization of optical signals transmitted over an optical communication channel where the optical signals are influenced by chromatic dispersion.

In a third possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the second impulse response characteristic is one of a polarization mode dispersion, a residual chromatic dispersion, a phase distortion, an amplitude filtering distortion and a receiver bandwidth limitation distortion.

The method can be used for equalization of optical signals transmitted over an optical communication channel where the optical signals are distorted by polarization mode dispersion, residual chromatic dispersion, phase distortion, amplitude filtering distortion, receiver bandwidth limitation distortion or other distortion effects.

In a fourth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the filter impulse response length of the equalizer is greater or equal than a sum of the first impulse response length and the second impulse response length.

Two different estimation functions, one for each of the first impulse response and one for the second impulse response can be applied, e.g. estimation of accumulated CD from the optical channel, which is a static parameter with a long impulse response, and estimation of PMD from the optical channel, which is a time-varying parameter with only a short impulse response.

In a fifth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the first impulse response length is greater than the second impulse response length.

The method can be used for adapting an equalizer for compensation of an optical channel distorted by CD and distorted by PMD. Usually the CD length is greater than the PMD length. However, the method can also be used for adapting an equalizer for compensation of an optical channel not distorted by CD, e.g. an optical channel with CD pre- compensation at the transmitter or with optical in-line CD compensation.

In a sixth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the equalizer comprises a 2x2 MIMO frequency domain equalizer comprising two direct filter paths and two cross filter paths.

In a seventh possible implementation form of the method according to the sixth

implementation form of the first aspect, the adjusting the equalizer based on the estimate of the first impulse response characteristic comprises switching-off the cross filter paths of the 2x2 MIMO frequency domain equalizer; and the adjusting the equalizer based on the interpolated estimate of the second impulse response characteristic comprises switching- on the cross filter paths of the 2x2 MIMO frequency domain equalizer.

In an eighth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the estimating the second impulse response characteristic comprises: evaluating a known training sequence within the optical signal, wherein a length of the known training sequence is shorter than the filter impulse response length of the equalizer, in particular shorter than the first length of the first impulse response characteristic, in particular equal to the second length of the second impulse response characteristic.

In a ninth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the estimating the first characteristic is based on non-data aided channel estimation.

In a tenth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the estimating the second characteristic is based on training-aided channel estimation.

In an eleventh possible implementation form of the method according to the eighth implementation form of the first aspect, the length of the known training sequence corresponds to the second length of the second impulse response characteristic of the optical communication channel.

In a twelfth possible implementation form of the method according to the eighth implementation form of the first aspect, the method further comprises: frame

synchronizing the first estimate of the optical signal to extract the known training sequence from the first estimate of the optical signal.

In a thirteenth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the interpolating the estimate of the second impulse response characteristic comprises: linearly interpolating frequency bins of a frequency domain version of the estimate of the second impulse response characteristic to obtain the interpolated estimate of the second impulse response characteristic in frequency domain.

In a fourteenth possible implementation form of the method according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the interpolating the estimate of the second impulse response characteristic comprises: frequency transforming a zero-padded time domain version of the estimate of the second impulse response characteristic to obtain the interpolated estimate of the second impulse response characteristic in frequency domain. In a fifteenth possible implementation form of the method according to any of the preceding implementation forms of the first aspect, the interpolating the estimate of the first impulse response characteristic comprises: linearly interpolating frequency bins of a frequency domain version of the estimate of the first impulse response characteristic to obtain the interpolated estimate of the first impulse response characteristic in frequency domain.

In a sixteenth possible implementation form of the method according to any of the preceding implementation forms of the first aspect, the interpolating the estimate of the first impulse response characteristic comprises: frequency transforming a zero-padded time domain version of the estimate of the first impulse response characteristic to obtain the interpolated estimate of the first impulse response characteristic in frequency domain. According to a second aspect, the invention relates to an optical receiver for receiving an optical signal, the optical receiver comprising: an equalizer coupled to an input of the optical receiver, the equalizer being configured to equalize a composite characteristic of an optical communication channel, the composite characteristic comprising a first impulse response characteristic of a first impulse response length and a second impulse response characteristic of a second impulse response length, wherein the equalizer is configured to provide an equalized optical signal based on the optical signal; a first estimator coupled to the input of the optical receiver, the first estimator being configured to estimate the first impulse response characteristic providing an estimate of the first impulse response characteristic; a second estimator coupled to an output of the equalizer, the second estimator being configured to estimate the second impulse response characteristic providing an estimate of the second impulse response characteristic; an interpolator and filter synthesizer coupled to an output of the first estimator and coupled to an output of the second estimator, the interpolator and filter synthesizer being configured to synthesize a filter function based on the estimate of the first impulse response characteristic and/or based on the estimate of the second impulse response characteristic and configured to adapt the equalizer based on the filter function.

In a first possible implementation form of the optical receiver according to the second aspect, the interpolator and filter synthesizer comprises: an interpolator configured to interpolate the estimate of the second impulse response characteristic to a filter impulse response length of the equalizer providing an interpolated estimate of the second impulse response characteristic; a filter synthesizer configured to synthesize the filter functbn based on the estimate of the first impulse response characteristic and/or based on the interpolated estimate of the second impulse response characteristic. In a second possible implementation form of the optical receiver according to the second implementation form of the second aspect, the interpolator is configured to interpolate the estimate of the first impulse response characteristic to the filter impulse response length of the equalizer providing an interpolated estimate of the first impulse response

characteristic and the filter synthesizer is configured to synthesize the filter tinction based on the interpolated estimate of the first impulse response characteristic and/or based on the interpolated estimate of the second impulse response characteristic.

In a third possible implementation form of the optical receiver according to the second aspect as such or according to any of the preceding implementation forms of the second aspect, the optical receiver further comprises a frame synchronizer coupled to the output of the equalizer, the frame synchronizer being configured to extract a known training sequence from the equalized optical signal and to provide the known training sequence to the second estimator.

In a fourth possible implementation form of the optical receiver according to the second aspect as such or according to any of the preceding implementation forms of the second aspect, the equalizer comprises a 2x2 Ml MO frequency domain equalizer comprising two direct filter paths and two cross filter paths.

In a fifth possible implementation form of the optical receiver according to the second aspect as such or according to any of the preceding implementation forms of the second aspect, the optical receiver further comprises: a frequency transformer coupled to the input of the optical receiver to transform the optical signal into frequency domain and to provide a frequency domain version of the optical signal to the first estimator and to the equalizer; and an inverse frequency transformer coupled to an output of the equalizer to transform the equalized optical signal into time domain and to provide a time domain version of the equalized optical signal to the second estimator. In a sixth possible implementation form of the optical receiver according to the second aspect as such or according to any of the preceding implementation forms of the second aspect, the first impulse response length is greater than the second impulse response length. In a seventh possible implementation form of the optical receiver according to the second aspect as such or according to any of the preceding implementation forms of the second aspect, the first impulse response characteristic is a chromatic dispersion. In an eighth possible implementation form of the optical receiver according to the second aspect as such or according to any of the preceding implementation forms of the second aspect, the second impulse response characteristic is one of a polarization mode dispersion, a residual chromatic dispersion, a phase distortion, an amplitude filtering distortion and a receiver bandwidth limitation distortion.

In a ninth possible implementation form of the optical receiver according to the third implementation form of the second aspect, the length of the known training sequence corresponds to the second length of the second characteristic of the optical

communication channel.

According to a third aspect, the invention relates to a coherent optical receiver comprising an equalizer an a processor configured to perform one of the methods according to the first aspect as such or according of any of the implementation forms of the first aspect for adjusting the equalizer.

In a first possible implementation form of the coherent optical receiver according to the third aspect, the equalizer comprises a 2x2 Ml MO frequency domain equalizer.

The coherent optical receiver comprises a single-stage Frequency Domain equalization for large values of CD, e.g. 30.000 ps/nm and fast tracking of polarization effects, with low implementation complexity. The coherent optical receiver is implemented with bw training overhead, i.e. the training sequence is shorter than the length of the FFT. The coherent optical receiver is implemented with fast SOP tracking, i.e. with incremental TA channel estimation. The coherent optical receiver offers large CD tolerance as the FFT-size is larger than the training sequence length. The coherent optical receiver requires a low implementation complexity due to the single stage FD filtering, which induces only low- processing latency, and offers high stability and reliability, i.e., robust CD estimation and reliable TA channel estimation. According to a fourth aspect, the invention relates to a computer program having a program code for performing one of the methods according to the first aspect as such or according of any of the implementation forms of the first aspect when run on a computer. The methods described here are applicable in particular for long-haul transmission using 100-Gb/s polarization-multiplexed quadrature phase shift keying (POLMUX-QPSK) modulation, which is widely applied in products for long-haul optical transmission systems. POLMUX-QPSK modulation is often also referred to as CP-QPSK, PDM-QPSK, 2P-QPSK or DP-QPSK. Similarly, the method applies for other digital modulation formats being single polarization modulation, binary phase shift keying (BPSK) or higher-order quadrature amplitude modulation (QAM).

The methods described herein may be implemented as software in a Digital Signal Processor (DSP), in a micro-controller or in any other side-processor or as hardware circuit within an application specific integrated circuit (ASIC).

The invention can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations thereof. BRIEF DESCRIPTION OF THE DRAWINGS

Further embodiments of the invention will be described with respect to the following figures, in which: Fig. 1 shows a schematic diagram of a method for adapting an equalizer to equalize a composite characteristic of an optical communication channel according to an

implementation form;

Fig. 2 shows a schematic diagram of a composite characteristic of an optical

communication channel comprising a first impulse response characteristic of a first impulse response length M and a second impulse response characteristic of a second impulse response length N;

Fig. 3 shows a block diagram of an optical receiver according to an implementation form; Fig. 4 shows a block diagram of an optical receiver according to an implementation form;

Fig. 5 shows a block diagram of an optical receiver according to an implementation form; Fig. 6 shows a block diagram of an optical receiver according to an implementation form;

Fig. 7 shows four eye diagrams illustrating the performance of an optical receiver according to an implementation form; Fig. 8 shows a block diagram of a coherent optical transmission system comprising a coherent receiver applying the method as described with respect to Fig. 1 ;

Fig. 9 shows a block diagram of a conventional chromatic dispersion compensation unit; Fig. 10 shows a block diagram of a conventional polarization mode dispersion

compensation unit;

Fig. 1 1 shows a schematic diagram of a conventional training sequence for training-based channel estimation;

Fig. 12 shows a schematic diagram of a conventional data aided channel estimation; and

Fig. 13 shows a block diagram of a conventional dual-stage equalizer. DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Fig. 1 shows a schematic diagram of a method 100 for adapting an equalizer to equalize a composite characteristic of an optical communication channel according to an

implementation form.

As illustrated in Fig. 2, the composite characteristic 200 comprises a first impulse response characteristic 201 , e.g. a chromatic dispersion CD of a first impulse response length M and a second impulse response characteristic 202, e.g., a polarization mode dispersion PMD of a second impulse response length N. Both impulse response characteristics 201 , 202 are superimposed as depicted by the arrows in Fig. 2 to foim the composite characteristic 200 of length P of the optical communication channel.

The method 100 illustrated in Fig. 1 comprises estimating 101 the first impulse response characteristic CD of the optical communication channel based on an optical signal 121 transmitted through the optical communication channel to obtain an estimate 123 of the first impulse response characteristic CD of the optical communication channel.

The method 100 further comprises adjusting 105 the equalizer based on the estimate 123 of the first impulse response characteristic CD of the optical communication channel, the equalizer equalizing the optical signal 121 to provide a first estimate 127 of the optical signal 121 compensated by the first impulse response characteristic CD f the optical communication channel.

The method 100 further comprises estimating 107 the second impulse response characteristic PMD of the optical communication channel based on the first estimate 127 of the optical signal 121 to obtain an estimate 129 of the second impulse response characteristic PMD of the optical communication channel.

The method 100 further comprises interpolating 109 the estimate 129 of the second impulse response characteristic PMD of the optical communication channel to the filter impulse response length P of the equalizer to obtain an interpolated estimate 131 of the second impulse response characteristic PMD of the optical communication channel.

The method 100 further comprises adjusting 1 1 1 the equalizer based on the interpolated estimate 131 of the second impulse response characteristic PMD of the optical communication channel, the equalizer thereby providing a second estimate 133 of the optical signal 121 compensated by both, the first characteristic CD and the second characteristic PMD of the optical communication channel. In an implementation form of the method 100, the method 100 further comprises interpolating 103 the estimate 123 of the first impulse response characteristic CD of the optical communication channel to the filter impulse response length P of the equalizer to obtain an interpolated estimate 125 of the first impulse response characteristic CD of the optical communication channel, wherein the adjusting 105 the equalizer based on the estimate 123 of the first impulse response characteristic CD is based on the interpolated estimate 125 of the first impulse response characteristic.

In an implementation form of the method 100, the first impulse response characteristic CD of the optical communication channel is a chromatic dispersion.

In an implementation form of the method 100, the second impulse response characteristic PMD of the optical communication channel is one of a polarization mode dispersion, a residual chromatic dispersion, a phase distortion, an amplitudefiltering distortion and a receiver bandwidth limitation distortion.

In an implementation form of the method 100, the filter impulse response length P of the equalizer is greater or equal than the first impulse response length M. To obtain a high precision, the equalizer should have a filter impulse response length P greater than the first impulse response length M. As this first impulse response length M may not be exactly known, a longer filter impulse response length P can be applied such that the first impulse response can be estimated within a wide range of parameters, which makes the equalizer fully compensating the first impulse response characteristicfor many different channel scenarios.

In an implementation form, the filter impulse response length P of the equalizer is smaller than the first impulse response length M. In such an implementation form, the equalizer is not able to fully compensate the first impulse response characteristic, e.g. the chromatic dispersion. However, the equalizer is configured to partly compensate the first impulse response characteristic.

In an implementation form of the method 100, the filter impulse response length P of the equalizer is greater or equal than a sum of the first impulse response length M and the second impulse response length N. Thus, a single filter impulse response length P of the equalizer is sufficient to compensate the total channel impulse response in contrast to a dual-stage equalizer comprising a first stage of length M for compensating the first impulse response characteristic and a second stage of length N for compensating the second impulse response characteristic. The dual stage equalizer might apply additional block overlap, additional serial-to-parallel conversion and an additional FFT/IFFT pair. In an implementation form, the first impulse response length M, for example the impulse response of the chromatic dispersion is greater than the second impulse response length N, for example the impulse response of the polarization mode dispersion.

In an implementation form, the first impulse response characteristic 201 , e.g. the chromatic dispersion CD is zero and the second impulse response characteristic 202, e.g. the polarization mode dispersion PMD is unequal to zero.

The method 100 is suitable for both, compensating an optical channel characterized by chromatic dispersion and other dispersions such as polarization mode dispersion and for compensating an optical channel not characterized by chromatic dispersion, for example an optical channel pre-compensated by a CD compensator.

In an implementation form of the method 100, the estimating 101 the first impulse response characteristic CD of the optical communication channel is based on a time- domain version of the optical signal 121 . In an implementation form of the method 100, the estimating 101 the first impulse response characteristic CD of the optical

communication channel is based on a frequency-domain version of the optical signal 121.

In an implementation form of the method 100, the interpolating 103 the estimate 123 of the first impulse response characteristic CD is performed by zero-padding a time-domain version of the estimate 123 of the first impulse response characteristic CD and

transforming an obtained zero-padded estimate 123 of the first impulse response characteristic CD into frequency-domain. In an implementation form of the method 100, the interpolating 103 the estimate 123 of the first impulse response characteristic CD is performed by linear interpolating intermediate frequency values of a frequency-domain version of the estimate 123 of the first impulse response characteristic CD.

In an implementation form of the method 100, the estimating 107 the second impulse response characteristic PMD of the optical communication channel is based on a time- domain version of the equalized optical signal 127. In an implementation form of the method 100, the estimating 107 the second impulse response characteristic PMD of the optical communication channel is based on a frequency-domain version of the equalized optical signal 127. In an implementation form of the method 100, the interpolating 109 the estimate 129 of the second impulse response characteristic PMD is performed by zero-padding a time- domain version of the estimate 129 of the second impulse response characteristic PMD and transforming an obtained zero-padded estimate 129 of the second impulse response characteristic PMD into frequency-domain. In an implementation form of the method 100, the interpolating 109 the estimate 129 of the second impulse response characteristic PMD is performed by linear interpolating intermediate frequency values of a frequency-domain version of the estimate 129 of the second impulse response characteristic PMD. In an implementation form of the method 100, the equalizer is a frequency domain equalizer and the method 100 further comprises overlap-discarding, in particular overlap- discarding with 50 percent overlap. A number of filter coefficients of the frequency domain equalizer corresponds to two times the required total impulse response length P of the optical communication channel.

In an implementation form of the method 100, the equalizer is a frequency domain equalizer and the method 100 further comprises oversampling, in particular oversampling with two samples per symbol. In an implementation form of the method 100, the equalizer comprises a 2x2 MIMO frequency domain equalizer 601 comprising two direct filter paths (Cn , C22) and two cross filter paths (C_i2, C₂i).

In an implementation form of the method 100, the adjusting 103 the equalizer based on the estimate 123 of the first impulse response characteristic CD of the optical

communication channel comprises switching-off the cross filter paths C12, C21 of the 2x2 MIMO frequency domain equalizer 601.

In an implementation form of the method 100, the adjusting 109 the equalizer based on the interpolated estimate 129 of the second impulse response characteristic PMD of the optical communication channel comprises switching-on the cross filter paths C12, C21 of the 2x2 MIMO frequency domain equalizer 601.

In an implementation form of the method 100, the estimating 105 the second impulse response characteristic PMD of the optical communication channel comprises evaluating a known training sequence TS within the optical signal 121 , wherein a length of the known training sequence TS is shorter than the filter impulse response length P of the equalizer.

In an implementation form of the method 100, the estimating 105 the second impulse response characteristic PMD of the optical communication channel comprises evaluating a known training sequence TS within the optical signal 121 , wherein a length of the known training sequence TS is shorter than the first length M of the first impulse response characteristic CD of the optical communication channel. In an implementation form of the method 100, the estimating 105 the second impulse response characteristic PMD of the optical communication channel comprises evaluating a known training sequence TS within the optical signal 121 , wherein a length of the known training sequence TS is longer or equal to the second length N of the second impulse response characteristic PMD of the optical communication channel.

In an implementation form of the method 100, the equalizer is a time domain equalizer.

Fig. 2 shows a schematic diagram of a composite characteristic of an optical

communication channel comprising a first impulse response characteristic of a first impulse response length M and a second impulse response characteristic of a second impulse response length N as described above.

Fig. 3 shows a block diagram of an optical receiver 300 according to an implementation form. The optical receiver 300 comprises an input 31 1 for receiving an optical signal 302. The optical receiver 300 comprises an equalizer 301 and a first estimator 303 both coupled to the input 31 1 of the optical receiver 300. The optical receiver 300 further comprises a second estimator 305 coupled to an output 313 of the equalizer 301 and an interpolator and filter synthesizer 307 coupled to an output 315 of the first estimator 303 and to an output 317 of the second estimator 305.

The equalizer 301 is configured to equalize a composite characteristic 200 of an optical communication channel comprising a first impulse response characteristic 201 of a first impulse response length M and a second impulse response characteristic 202 of a second impulse response length N as described with respect to Fig. 2. The equalizer 301 provides an equalized optical signal 304 at his output 313 by equalizing the optical signal 302 received at his input 323.

The first estimator 303 is configured to estimate the first impulse response characteristic 201 and to provide an estimate 306 of the first impulse response characteristic 201 at his output 315. The second estimator 305 is configured to estimate the second impulse response characteristic 202 and to provide an estimate 308 of the second impulse response characteristic 202 at his output 317. The interpolator and filter synthesizer 307 is configured to synthesize a filter function 340 based on the estimate 306 of the first impulse response characteristic 201 and/or based on the estimate 308 of the second impulse response characteristic 202. The equalizer 301 is adapted based on the filter function 340. In an implementation form, the filter function W_ZF(f) is an inverse channel impulse response function

W_ZF (f) = H ^l

processed by using a zero forcing (ZF) algorithm as described above with respect to Fig. 12.

In an implementation form, the filter function W_MMSE(f) is an adaptation function

W_MMSE (f) = H

processed by using a minimum mean square error (MMSE) algorithm.

In an implementation form, the filter function is an inverse chromatic dispersion function

( 2imf, Y DL

CD ^_1 (DL) = exp

N J 4TTC as described above with respect to Fig. 9.

In an implementation form, the filter function is an inverse polarization mode dispersion function. In an implementation form, the first impulse response characteristic CD of the optical communication channel is a chromatic dispersion.

In an implementation form, the second impulse response characteristic 202 of the optical communication channel is one of a polarization mode dispersion, a residual chromatic dispersion, a phase distortion, an amplitude filtering distortion and a receiver bandwidth limitation distortion.

In an implementation form, the filter impulse response length P of the equalizer is greater or equal than the first impulse response length M. To obtain a high precision, the equalizer should have a filter impulse response length P greater than the first impulse response length M. As this first impulse response length M may be not exactly known, a longer filter impulse response length P can be applied such that the first impulse response can be estimated within a wide range of parameters, which makes the equalizer fully

compensating the first impulse response characteristic for many different channel scenarios.

In an implementation form, the filter impulse response length P of the equalizer is greater or equal than a sum of the first impulse response length M and the second impulse response length N. Thus, a single filter impulse response length P of the equalizer is sufficient to compensate the total channel impulse response in contrast to a dual-stage equalizer comprising a first stage of length M for compensating the first impulse response characteristic and a second stage of length N for compensating the second impulse response characteristic. The dual stage equalizer might apply additional block overlap, additional serial-to-parallel conversion and an additional FFT/IFFT pair.

In an implementation form, the first impulse response length M, for example the impulse response of the chromatic dispersion is greater than the second impulse response length N, for example the impulse response of the polarization mode dispersion.

In an implementation form, the interpolator and filter synthesizer 307 is configured to first synthesize the filter function 340 based on the estimate 306 of the first impulse response characteristic 201 , e.g. the chromatic dispersion, and thereafter to synthesize the filter function 340 based on the estimate 308 of the second impulse response characteristic 202, e.g. the polarization mode dispersion. The equalizer 301 is first adapted based on the filter function 340 processed with respect to the first impulse response characteristic 201 , e.g. CD, and then adapted based on the filter function 340 processed with respect to the second impulse response characteristic 202, e.g. PMD. That means, the equalizer 301 is initially equalizing the first impulse response characteristic of length M providing a first equalized signal 304 compensated by the first impulse response characteristic, e.g. CD compensated. Afterwards, the equalizer 301 is equalizing the second impulse response characteristic of length N providing a second equalized signal 304 compensated by the second impulse response characteristic, e.g. CD. The equalization of the second impulse response characteristic of length N is processed with the second estimate 308 of the optical signal which is already compensated by the first impulse response characteristic 201.

In an implementation form, the first estimator 303 receives a time-domain version of the optical signal 302. In an implementation form, the equalizer 301 receives a time-domain version of the optical signal 302. In an implementation form, the first estimator 303 receives a frequency-domain version of the optical signal 302. In an implementation form, the equalizer 301 receives a frequency-domain version of the optical signal 302. In an implementation form, the second estimator 305 receives a time-domain version of the equalized optical signal 304. In an implementation form, the second estimator 305 receives a frequency-domain version of the equalized optical signal 304.

In an implementation form, the interpolator and filter synthesizer 307 processes a time- domain version of the estimate 306 of the first impulse response characteristic 201 by zero-padding and subsequent frequency transformation to provide an interpolated estimate of the first impulse response characteristic 201 in frequency domain. In an implementation form, the interpolator and filter synthesizer 307 processes a time-domain version of the estimate 308 of the second impulse response characteristic by zero- padding and subsequent frequency transformation to provide an interpolated estimate of the second impulse response characteristic 202 in frequency domain.

In an implementation form, the interpolator and filter synthesizer 307 processes a frequency-domain version of the estimate 306 of the first impulse response characteristic 201 by linear interpolation of intermediate frequency values to provide an interpolated estimate of the first impulse response characteristic 201 in frequency domain. In an implementation form, the interpolator and filter synthesizer 307 processes a frequency- domain version of the estimate 308 of the second impulse response characteristic 202 by linear interpolation of intermediate frequency values to provide an interpolated estimate of the second impulse response characteristic 202 in frequency domain.

Fig. 4 shows a block diagram of an optical receiver 400 according to an implementation form. The optical receiver 400 comprises an input 31 1 for receiving an optical signal 302. The optical receiver 400 comprises a frequency transformer 431 configured to transform a time-domain version of the optical signal 302 into frequency-domain providing a frequency-domain version 412 of the optical signal 302. The optical receiver 400 comprises an equalizer 301 and a first estimator 303 both coupled to an output of the frequency transformer 431 . The equalizer 301 is configured to equalize thefrequency- domain version 412 of the optical signal 302 and to provide an equalized optical signal 304. The optical receiver 400 comprises an inverse frequency transformer 433 coupled to an output 313 of the equalizer 301 and configured to transform the equalized optical signal 304 into frequency-domain providing a frequency-domain version 414 of the equalized optical signal 304. The optical receiver 400 further comprises a second estimator 305 coupled to an output 313 of the inverse frequency transformer 433 and an interpolator and filter synthesizer 307 coupled to an output 315 of the first estimator 303 and to an output 317 of the second estimator 305. In an implementation form, the frequency transformer 431 and the inverse frequency transformer 433 are processing a fast Fourier transform (FFT) to perform the frequency and time transforms.

The equalizer 301 , the first and second estimators 303, 305 and the interpolator and filter synthesizer 307 may correspond to the respective units described above with respect to Fig. 3.

The interpolator and filter synthesizer 307 comprises an interpolator 401 and a filter synthesizer 403. The interpolator 401 is configured to interpolate the estimate 306 of the first impulse response characteristic 201 to a filter impulse response length P of the equalizer 301 providing an interpolated estimate 402 of the first impulse response characteristic 201. The interpolator 401 is further configured to interpolate the estimate 308 of the second impulse response characteristic 202 to the filter impulse response length P of the equalizer 301 providing an interpolated estimate 404 of the second impulse response characteristic 202. The filter synthesizer 403 is configured to synthesize the filter function 340 based on the interpolated estimate 402 of the first impulse response characteristic 201 and/or based on the interpolated estimate 404 of the second impulse response characteristic 202.

Fig. 5 shows a block diagram of an optical receiver 500 according to an implementation form. The optical receiver 500 is configured to receive an optical signal 502. The optical receiver 500 comprises a serial-to-parallel converter 551 to convert a serial sequence of the optical signal 502 into parallel sequences 562. The optical receiver 500 comprises a frequency transformer 531 configured to transform the parallel sequences 562 of the optical signal 502 from time-domain into frequency-domain providing a frequency-domain version 512 of the optical signal 502. The optical receiver 500 comprises an equalizer 501 and a first estimator 503 both coupled to an output of the frequency transformer 531. The equalizer 501 is configured to equalize the frequency-domain version 512 of the optical signal 502 and to provide an equalized optical signal 504. The optical receiver 500 comprises an inverse frequency transformer 533 coupled to an output of the equalizer 501 and configured to transform the equalized optical signal 504 from frequency-domain into time-domain providing a time-domain version 514 of the equalized optical signal 504. The optical receiver 500 comprises a second estimator 505 coupled via a switch 559 to an output of the inverse frequency transformer 533 and an interpolator and filter synthesizer 507 coupled to an output of the first estimator 503 and to an output of the second estimator 505. The optical receiver 500 comprises a frame synchronizer 509 coupled to the output of the equalizer 501 and to an output of the inverse frequency transformer 533 for providing a synchronization signal controlling the switch 559. The optical receiver 500 comprises a serial-to-parallel converter 555 to convert the time-domain version 514 of the equalized optical signal 504 from parallel sequences to a serial sequence. The optical receiver 500 comprises further digital signal processing 557 for further processing of the serial converted time-domain version 514 of the equalized optical signal 504. The equalizer 501 , the frequency transformer 531 , the inverse frequency transformer 533, the first and second estimators 503, 505 and the interpolator and filter synthesizer 507 may correspond to the respective units described above with respect to Fig. 3.

In an implementation form, the frame synchronizer 509 is configured to detect a known training sequence TS as illustrated with respect to Fig. 12 from the time-domain version 514 of the equalized optical signal 504 and to synchronize the switch 559 by the synchronization signal 554 to provide the known training sequence TS to the second estimator 505. The frame synchronizer 509 uses both, the frequency-domain version 504 and the time-domain version 514 of the equalized optical signal 504 and a clock signal 552 to synchronize the equalized optical signal 504.

In an implementation form, the equalizer 501 comprises a 2x2 MIMO frequency domain equalizer 501 comprising two direct filter paths C , C22 and two cross filter paths C12, C21 as described below with respect to Fig. 6.

In an implementation form, the first estimator 503 performs CD estimation only during initialization. As shown in Fig. 5 the serial data of the optical signal 502 are parallelized in blocks 562 of length M which is equal to the FFT size of the frequency transformer 531. FD CD estimation is applied to the data 512 according to the method described in

' . Andres Soriano, F. N. Hauske, N. Guerrero Gonzalez, Z. Zhang, Y. Ye, I. Tafur Monroy, "Chromatic Dispersion Estimation in Digital Coherent Receivers", Journal of Lightwave Technology, vol.29, no.1 1 , pp.1627-1637, June 201 1 '. The C_i2 and the C21 component of the equalizer 501 are switched off (C12 = C21 = 0) and CD compensation is performed by Cn and C22, which can be described by the equation system

where W_CD corresponds to the first impulse response characteristic of length M

interpolated to a filter length P, here corresponding to the chromatic dispersion and W_xyMiMo, W_yxMiMo, W_XXMIMO, WyyMiMo correspond to the second impulse response

characteristic of length N, here corresponding to the polarization mode dispersion and further dispersion effects.

During initialization, the second estimator 505 performs DA channel estimation and the interpolator and filter synthesizer 507 generates a 2x2 MIMO filter function. The frame synchronizer 509 extracts the training sequences of length N«M. Channel estimation of length N is performed by the interpolator and filter synthesizer 507. The estimated channel elements W_XXMIMO, W_xyMiMo, W_yxMiMo and W_yyMiMo of length N are interpolated leading to vectors of length P. The elements CH

are calculated in a channel synthesis block of the interpolator and filter synthesizer 507. Finally, the chromatic dispersion and the polarization effects are fully equalized.

Any incremental change in the channel will appear as residual ISI after the filter, i.e. the equalizer 501. During a tracking phase after the initialization, the following steps are repeated: Estimating the residual channel transfer function H_MIMO_NEW- If there is an incremental change in the channel transferfunction, the total channel matrix is updated according to the following equation system:

HXX = HcD ^X (ΗχχΜΙΜΟ ^X H_XXMIMO_NEW ⁺ H_XYMIMO ^X H_yxMIMO_NEw),

Hxy = HcD ^X (ΗχχΜΙΜΟ ^X H_xyMIMO_NEW ⁺ H_xyMIMO ^X HyyMIMOJMEw),

HyX = HcD ^X (HyxMIMO ^X H_XXMIMO_NEW ⁺ HyyMIMO ^X H_yxMIMO_NEw),

Hyy = HcD ^X (HyxMIMO ^X H_xyMIMO_NEW ⁺ HyyMIMO ^X HyyMIMOJMEw), where H_CD corresponds to the first impulse response characteristic of length M, here corresponding to the chromatic dispersion and H_xyMi_Mo, H_yxMi_Mo, H_XXMIMO, H_yyMi_Mo correspond to the second impulse response characteristic of length N, here corresponding to the polarization mode dispersion and further dispersion effects.

Zero forcing filter solution can be implemented for CD compensation and MMSE for MIMO.

In an implementation form, the serial-to-parallel (S/P) converter 551 applies overlap- discarding for partitioning the time-domain digital version of the optical signal 502 into overlapping sub-sequences 562. The overlap-discard method (OD, OLD) is an efficient way to evaluate the discrete convolution of a very long signal x[n] with a finite impulse response (FIR) filter h[n]:

where h[n] = O for m outside the region [1,M]. The concept is to divide the problem into multiple convolutions of h[n] with short segments of x[n]:

where L is an arbitrar segment length. Then:

and y[n] can be written as a sum of short convolutions:

where

- x_k[n\ * h[n\

is zero outside the region [1, L + M - 1]. And for any parameter N≥ L+M-1, it is equivalent to the N-point circular convolution of x_k[n] with h[n] in the region [1,N]. The advantage is that the circular convolution can be computed very efficiently as follows, according to the circular convolution theorem: y_k[n] = IFFT( FFT(x_k[n])^■ FFT(h[n])), where FFT and IFFT refer to the fast Fourier transform 531 and inverse fast Fourier transform 533, respectively, evaluated over N discrete points.

In an implementation form, the same overlap-discarding procedure is applied for reconstructing the overlapping sub-sequences 564 corresponding to the serialized equalized optical signal in time domain from the equalized sub-sequences 514

corresponding to the parallelized equalized optical signal in time domain.

Fig. 6 shows a block diagram of an optical receiver 600 according to an implementation form. An optical signal in discrete representation with the two polarizations Xi[k] and x₂[k] is transmitted over an optical channel Q. The two polarizations yi[k] and y₂[k] of the received optical signal are passing an overlap alignment (OLA) block 619 for overlap aligning the received optical signal, e.g. for performing overlap adding or overlap discarding and an equalizer 601 for equalizing the received optical signal to obtain an equalized optical signal with the two polarizations z-i[k] and z₂[k] in discrete representation. A slicer 61 1 and a de-mapping stage 613 are remapping the two polarizations z-i[k] and z₂[k] of the equalized optical signal in continuous representation z-i and z₂. The equalizer 601 comprises a single-stage FDE equalizer with a 2x2 MIMO FDE structure corresponding to the 2x2 MIMO structure 1000 depicted in Fig. 10. The equalizer 601 comprises a Fast Fourier Transformer 607 for transforming the two polarizations y-i[k] and y₂[k] of the optical signal from time-domain into frequency-domain. For each frequency bin "n" of the obtained two sequences yi[n] and y₂[n] a 2x2 MIMO structure with two direct paths for weighting the first and second polarizations yi[n] and y₂[n] with direct path components Cn and C₂₂ and two cross paths for weighting the first and second polarizations yi[n] and y₂[n] with cross path components Ci₂ and C₂i. The 2x2 MIMO structure further comprises an adding device 615 for each polarization to add the first polarization y-i[n] weighted by the first direct path component C and the second polarization y₂[n] weighted by the first cross path component C|₂ obtaining an equalized sequence z-i[n] of the first polarization and to add the second polarization y₂[n] weighted by the second direct path component C₂₂ and the first polarization y-i[n] weighted by the second cross path component C₂₁ obtaining an equalized sequence z₂[n] of the second polarization. The equalizer 601 comprises an Inverse Fast Fourier Transformer 609 for transforming the equalized sequence of the first polarization from frequency-domain into time-domain obtaining the first polarization zi[k] of the equalized optical signal and the second polarization z₂[k] of the equalized optical signal. Both, direct path components Cn and C₂₂ and cross path components Ci₂ and C₂₁ are implemented as complex

multiplications because the two polarization sequences yi[n] and y₂[n] are complex-valued signals.

The optical receiver 600 further comprises a processor 603 for controlling the equalizer 601 . The processor 603 is configured to process a filter function based on the four non- equalized and equalized sequences of both polarizations yi[n], y₂[n], zi[n], z₂[n] and configured to adjust the equalizer 601 by the filter function 610.

In an implementation form, the processor 603 implements the method 100 as described with respect to Fig. 1. In an implementation form, the processor 603 comprises

functionalities of the first estimator 303, the second estimator 305 and the interpolator and filter synthesizer 307 as described with respect to Fig. 3. In an implementation form, the processor 603 comprises functionalities of the first estimator 303, the second estimator 305 and the interpolator and filter synthesizer 307 as described with respect to Fig. 4. In an implementation form, the processor 603 comprises functionalities of the first estimator 503, the second estimator 505 and the interpolator and filter synthesizer 507 as described with respect to Fig. 5. In an implementation form, the processor 603 comprises

functionalities of the first estimator 503, the second estimator 505, the interpolator and filter synthesizer 507 and the frame synchronizer 509 as described with respect to Fig. 5.

Fig. 7 shows four signal constellation plots a), b), c) and d) illustrating the performance of an optical receiver according to an implementation form. The modulation format is QPSK, the input chromatic dispersion is 20000 ps/nm, the input applies a polarization of theta=0.35 and phi=0.00. The received OSNR is 14 dB.

The first diagram a) depicts the initialization. The bit error rate for the QPSK (MMSE) signal is as follows:

BER QPSK (MMSE): 9.10e-004,

or in logarithmic representation:

-logl O(BER) QPSK (MMSE): 3.04 The second diagram b) depicts a phase of updating the MIMO functbn with no channel changes. The bit error rate for the QPSK (MMSE) signal is as follows:

BER QPSK (MMSE): 1 .28e-003,

or in logarithmic representation:

-logl O(BER) QPSK (MMSE): 2.89

The third diagram c) depicts a phase of no updating the MIMO function where the channel changes according to the SOP rotation with polarization parameters theta=0.70 and phi=0.00. The bit error rate for the QPSK (MMSE) signal is as follows:

BER QPSK (MMSE): 1 .54e-002,

or in logarithmic representation:

-logl O(BER) QPSK (MMSE): 1 .81

The fourth diagram d) depicts a phase of updating the MIMO function where the channel changes according to the same SOP rotation as used in diagram c), i.e., with polarization parameters theta=0.70 and phi=0.00. The bit error rate for the QPSK (MMSE) signal is as follows:

BE QPSK (MMSE): 1 .35e-003,

or in logarithmic representation:

-logl O(BER) QPSK (MMSE): 2.87

The SOP step-response is tracked without visible performance degradation. A minor OSNR penalty is observed by updating the filter coefficients, which results from insufficient averaging. Similar results have been performed for PMD changes.

In an implementation form, the updating procedure is more sophisticated by using ZF and MMSE update with optimized averaging.

Fig. 8 shows a block diagram of a coherent optical transmission system 802 comprising a coherent receiver 800 applying the method as described with respect to Fig. 1. The coherent optical transmission system 802 comprises an optical sender 801 for providing an optical signal 850, an optical channel 809 for transmitting the optical signal 850 and a coherent receiver 800 for receiving a received optical signal 852 which corresponds to the optical signal 850 transmitted over the optical channel 809 and influenced by the optical channel 809.

The optical sender 801 comprises a laser diode 803 for providing an optical carrier signal with a center frequency f_T and a given laser line-width 804. The optical sender 801 further comprises a QPSK modulator 805 for modulating the optical carrier signal with a user data signal to provide a modulated optical data signal. The optical sender 801 further comprises a multiplexer for multiplexing the modulated optical data signal with other modulated optical data signals to provide a multiplexed optical data signal. The multiplexed optical signal may be multiplexed according to a Wavelength Division Multiplex (WDM) transmission system. The multiplexed optical signal corresponds to the optical signal 850 to be transmitted.

The optical channel 809 comprises a plurality of amplifier stages and optical fibers for transmitting the optical signal 850. An output of the optical channel 809 is coupled to an input of the coherent receiver 800, such that the coherent receiver 800 receives the received optical signal 852 which corresponds to the optical signal 850 transmitted over the optical channel 809 at its input. The coherent receiver 800 comprises a de-multiplexer 823, a polarization beam splitter (PBS) 825, two 6-port 90-degree optical hybrids 827, 829, two sets of balanced detectors 833, two sets of trans-impedance amplifiers (TIA) 835, four analog-digital converters (ADC) 837 and a digital signal processing device (DSP) 839, for example a digital signal processor or a micro-processor or any other processor which is able to perform digital signal processing.

The de-multiplexer 823 is coupled to the input port of the coherent receiver 800 and receives the received optical signal 852 at its input. The de-multiplexer 823 demultiplexes the received optical signal 852 into a plurality of demultiplexed optical signals following a plurality of receiving paths in the coherent receiver 800. Fig. 8 depicts only one of the plurality of receiving paths. In the following, one of these receiving paths is illustrated. The demultiplexed optical signal following one receiving path is provided to the polarization beam splitter 825 which splits the signal into its X-polarized and its Y-polarized signal components. The X-polarized signal component is provided to a first input, which is a signal input, of the first 6-port 90-degree optical hybrid 827 and the Y-polarized signal component is provided to a first input, which is a signal input, of the second 6-port 90- degree optical hybrids 829. A second input, which is a LO input, of the first 6-port 90- degree optical hybrid 827 receives a Local Oscillator signal from a laser diode 831 providing the Local Oscillator signal having a center frequency f_B. The same Local

Oscillator signal is provided to a second input, which is a LO input, of the 6-port 90-degree optical hybrid 829.

The 90° Optical Hybrids 827, 829 comprise two inputs for signal and LO and four outputs mixing signal and LO. The 90° Optical Hybrids 827, 829 deliver both amplitude and phase of signal, amplify signal linearly and are suitable for both homodyne and heterodyne detection.

The six-port 90° Optical Hybrids 827, 829 comprise linear dividers and combiners interconnected in such a way that four different vectorial additions of a reference signal (LO) and the signal to be detected are obtained. The levels of the four output signals are detected by balanced receivers 833. By applying suitable baseband signal processing algorithms, the amplitude and phase of the un-known signal can be determined. For optical coherent detection, each of the six-port 90° optical hybrids 827, 829 mixes the incoming signal with the four quadrature states associated with the reference signal in the complex-field space. Each of the optical hybrids 827, 829 then delivers the four light signals to two pairs of balanced detectors 833 which detect a respective optical signal and provide a corresponding electrical signal to the succeeding set of trans-impedance amplifiers 835, one trans-impedance amplifier for each pair of balanced detectors 833. The electrical signals amplified by the trans-impedance amplifiers 835 are analog-digitally converted by the set of A/D converters 837 and then provided as digital signals 854 to a digital signal processing 839. The digital signal processing may be implemented as software on a Digital Signal Processor (DSP) or on a micro-controller or as hardware circuit within an application specific integrated circuit (ASIC). In addition, to limit the power consumption associated with inter-chip communication, both the ADCs 837 and digital signal processing 839 may be preferably integrated on a single-chip.

The digital signal processing 839 implements the method 100 as described with respect to Fig. 1 .

For an improved operation of the optical receiver 800, the DSP part 839 comprises the equalizer having a filter impulse response of length P to equalize a composite

characteristic of the optical communication channel 809, the composite characteristic comprising a first impulse response characteristic of a first impulse response length M, e.g. chromatic dispersion and a second impulse response characteristic of a second impulse response length N, e.g. polarization mode dispersion. The DSP part 839 further comprises a processor implementing the method 100 as described with respect to Fig. 1 . This results in a less complex implementation of the optical receiver 800 compared to an optical receiver that does not apply such an equalizer and such an adaptation method. A coherent optical receiver 800 implementing the method as described with respect to Fig. 1 offers the following advantages:

The coherent optical receiver 800 comprises a single-stage Frequency Domain equalization for large values of CD, e.g. 30.000 ps/nm and fast tracking of polarization effects, with low implementation complexity. The coherent optical receiver 800 is implemented with low training overhead, i.e. the training sequence is shorter than the length of the FFT. The coherent optical receiver 800 is implemented with fast SOP tracking, i.e. with incremental TA channel estimation. The coherent optical receiver 800 offers large CD tolerance as the FFT-size is larger than the training sequence length. The coherent optical receiver 800 requires a low implementation complexity due to the single stage FD filtering, inducing only a low processing latency and offers high stability and reliability, i.e., robust CD estimation and reliable TA channel estimation.

According to an implementation form, a reliable initial CD estimation is known, as the CD is static without need for update. No mechanism to separate polarizations and for identification of PolMUX signals is required. Note that this mechanism is required in NDA filter update but is not required with TA acquisition. All benefits from training can be exploited including more stability, polarization/phase identification, support by TA timing/carrier recovery etc. The channel estimation comprising CD estimation and 2x2 TA channel estimation is independent from over-sampling and thus can also be used for 1 , 1 .3 or 2 samples/symbol.

The coherent optical receiver 800 offers fast optical performance monitoring based on TA channel estimation. An interpolation of estimated channel to larger filter length has better performance as the inversion of finite estimated channel leads to infinite impulse response.

For short-haul transmission, the coherent optical receiver 800 offers further benefits as the relation of ASIC processing speed and sampling rate defines the required parallelization factor. In a preferred implementation form, an FFT-size is used that is exactly matching the parallelization requirement. An FFT-size smaller than the parallelization factor requires to use parallel FFTs. An FFT-size greater than the parallelization factor requires a large chip area without optimum pipeline structure and allows several processing steps within one frame capture.

For long-haul transmission an optimized FFT-size results according to the channel memory requirement where CD length is greater than the parallelization factor. For short- haul transmission an optimized FFT-size results according to the parallelization requirement where the parallelization factor is greater than CD length. In each case, the training repetition rate is optimized according to the polarization change requirement.

From the foregoing, it will be apparent to those skilled in the art that a variety of methods, systems, computer programs on recording media, and the like, are provided. The present disclosure also supports a computer program product including computer executable code or computer executable instructions that, when executed, causes at least one computer to execute the performing and computing steps described herein. The present disclosure also supports a system configured to execute the performing and computing steps described herein.

Many alternatives, modifications, and variations will be apparent to those skilled in the art in light of the above teachings. Of course, those skilled in the art readily recognize that there are numerous applications of the invention beyond those described herein. While the present inventions has been described with reference to one or more particular embodiments, those skilled in the art recognize that many changes may be made thereto without departing from the spirit and scope of the present invention. It is therefore to be understood that within the scope of the appended claims and their equivalents, the inventions may be practiced otherwise than as specifically described herein.

Claims

CLAIMS:

1 . Method (100) for adapting an equalizer to equalize a composite characteristic (200) of an optical communication channel, the composite characteristic (200) comprising a first impulse response characteristic (201 , CD) of a first impulse response length (M) and a second impulse response characteristic (202, PMD) of a second impulse response length (N), the method (100) comprising: estimating (101 ) the first impulse response characteristic (201 , CD) based on an optical signal (121 ) transmitted through the optical communication channel to obtain an estimate (123) of the first impulse response characteristic (201 , CD); adjusting (105) the equalizer based on the estimate (123) of the first impulse response characteristic (201 , CD), the equalizer equalizing the optical signal (121) to provide a first estimate (127) of the optical signal (121 ) compensated by the first impulse response characteristic (201 , CD); estimating (107) the second impulse response characteristic (202, PMD) based on the first estimate (127) of the optical signal (121 ) to obtain an estimate (129) of the second impulse response characteristic (202, PMD); interpolating (109) the estimate (129) of the second impulse response

characteristic (202, PMD) to a filter impulse response length (P) of the equalizer to obtain an interpolated estimate (131 ) of the second impulse response characteristic (202, PMD); and adjusting (1 1 1 ) the equalizer based on the interpolated estimate (131 ) of the second impulse response characteristic (202, PMD), the equalizer thereby providing a second estimate (133) of the optical signal (121 ) compensated by both, the first characteristic (201 , CD) and the second characteristic (202, PMD).

2. The method of claim 1 , further comprising: interpolating (103) the estimate (123) of the first impulse response characteristic (201 , CD) to the filter impulse response length (P) of the equalizer to obtain an interpolated estimate (125) of the first impulse response characteristic (201 , CD), wherein the adjusting (105) the equalizer based on the estimate (123) of the first impulse response characteristic (201 , CD) is based on the interpolated estimate (125) of the first impulse response characteristic.

3. The method (100) of claim 1 or claim 2, wherein the first impulse response characteristic (201 , CD) is a chromatic dispersion.

4. The method (100) of one of the preceding claims, wherein the second impulse response characteristic (202, PMD) is one of a polarization mode dispersion, a residual chromatic dispersion, a phase distortion, an amplitude filtering distortion and a receiver bandwidth limitation distortion.

5. The method (100) of one of the preceding claims, wherein the filter impulse response length (P) of the equalizer is greater or equal than a sum of the first impulse response length (M) and the second impulse response length (N).

6. The method (100) of one of the preceding claims, wherein the first impulse response length (M) is greater than the second impulse response length (N).

7. The method (100) of one of the preceding claims, wherein the equalizer comprises a 2x2 MIMO frequency domain equalizer (301 ) comprising two direct filter paths (Cn, C₂₂) and two cross filter paths (C12, C21).

8. The method (100) of claim 6, wherein the adjusting (103) the equalizer based on the estimate (123) of the first impulse response characteristic (201 , CD) comprises switching-off the cross filter paths (C|₂, C₂₁) of the 2x2 MIMO frequency domain equalizer (301 ); and wherein the adjusting (109) the equalizer based on the interpolated estimate (129) of the second impulse response characteristic (202, PMD) comprises switching-on the cross filter paths (C₁₂, C₂₁) of the 2x2 MIMO frequency domain equalizer (301 ).

9. The method (100) of one of the preceding claims, wherein the estimating (105) the second impulse response characteristic (202, PMD) comprises: evaluating a known training sequence (TS) within the optical signal (121 ), wherein a length of the known training sequence (TS) is shorter than the filter impulse response length (P) of the equalizer, in particular shorter than the first length (M) of the first impulse response characteristic (201 , CD), in particular equal to the second length (N) of the second impulse response characteristic (202, PMD).

10. Optical receiver (300, 400) for receiving an optical signal (302), the optical receiver (300) comprising: an equalizer (301 ) coupled to an input (31 1 ) of the optical receiver (300, 400), the equalizer (301 ) being configured to equalize a composite characteristic (200) of an optical communication channel, the composite characteristic (200) comprising a first impulse response characteristic (201 , CD) of a first impulse response length (M) and a second impulse response characteristic (202, PMD) of a second impulse response length (N), wherein the equalizer (301 ) is configured to provide an equalized optical signal (304) based on the optical signal (302); a first estimator (303) coupled to the input (31 1 ) of the optical receiver (300), the first estimator (303) being configured to estimate the first impulse response characteristic (201 , CD) providing an estimate (306) of the first impulse response characteristic (201 , CD); a second estimator (305) coupled to an output (313) of the equalizer (301 ), the second estimator (305) being configured to estimate the second impulse response characteristic (202, PMD) providing an estimate (308) of the second impulse response characteristic (202, PMD); an interpolator and filter synthesizer (307) coupled to an output (315) of the first estimator (303) and coupled to an output (317) of the second estimator (305), the interpolator and filter synthesizer (307) being configured to synthesize a filter function (340) based on the estimate (306) of the first impulse response characteristic (201 , CD) and/or based on the estimate (308) of the second impulse response characteristic (202, PMD) and configured to adapt the equalizer (301 ) based on the filter function (340).

1 1 . The optical receiver (300, 400) of claim 10, wherein the interpolator and filter synthesizer (307) comprises: an interpolator (401 ) configured to interpolate the estimate (308) of the second impulse response characteristic (202, PMD) to a filter impulse response length (P) of the equalizer (301 ) providing an interpolated estimate (404) of the second impulse response characteristic (PMD); a filter synthesizer (403) configured to synthesize the filter function (340) based on the estimate (402) of the first impulse response characteristic (201 , CD) and/or based on the interpolated estimate (404) of the second impulse response characteristic (202, PMD).

12. The optical receiver (300, 400) of claim 1 1 , wherein the interpolator (401 ) is configured to interpolate the estimate (306) of the first impulse response characteristic (201 , CD) to the filter impulse response length (P) of the equalizer (301 ) providing an interpolated estimate (402) of the first impulse response characteristic (201 , CD); and wherein the filter synthesizer (403) is configured to synthesize the filter function (340) based on the interpolated estimate (402) of the first impulse response characteristic (201 , CD) and/or based on the interpolated estimate (404) of the second impulse response characteristic (202, PMD).

13. The optical receiver (300, 400, 500) of one of claims 10 to 12, further comprising: a frame synchronizer (509) coupled to the output of the equalizer (501 ), the frame synchronizer (509) being configured to extract a known training sequence (TS) from the equalized optical signal (504) and to provide the known training sequence (TS) to the second estimator (505).

14. The optical receiver (500) of one of claims 10 to 13, wherein the equalizer (501 ) comprises a 2x2 MIMO frequency domain equalizer (501 ) comprising two direct filter paths (Cii, C22) and two cross filter paths (C12, C21).

15. The optical receiver (500) of one of claims 10 to 14, further comprising: a frequency transformer (531 ) coupled to the input of the optical receiver (500) to transform the optical signal (502) into frequency domain and to provide a frequency domain version (512) of the optical signal (502) to the first estimator (503) and to the equalizer (501 ); and an inverse frequency transformer (533) coupled to an output of the equalizer (501 ) to transform the equalized optical signal (504) into time domain and to provide a time domain version (514) of the equalized optical signal (504) to the second estimator (505).