WO2013020272A1

WO2013020272A1 - Apparatus and method for estimating an optical communication channel at discrete frequencies

Info

Publication number: WO2013020272A1
Application number: PCT/CN2011/078164
Authority: WO
Inventors: Fabian Nikolaus Hauske; Fabio PITTALA; Amine MEZGHANI
Original assignee: Huawei Technologies Co., Ltd.
Priority date: 2011-08-09
Filing date: 2011-08-09
Publication date: 2013-02-14

Abstract

The invention relates to an apparatus (100) for processing a first input signal (112) and a second input signal (114) representing a first polarization component and a second polarization component of an optical signal influenced by an optical communication channel (110), the apparatus (100) comprising: a Fourier transformer (102) for transforming the first input signal (112) into a first transformed signal (122) and the second input signal (114) into a second transformed signal (124) in frequency domain; a first set of channel estimators (104) for estimating a set of frequency components (H(f₁ ),..., H(f_N)) of the optical communication channel (110) according to a first channel estimation scheme; a second set of channel estimators (106) for estimating a set of frequency components (H(f₁ ),..., H(_N)) of the optical communication channel (1 10) according to a second channel estimation scheme; and a selector (108) for selecting for each discrete frequency (f,) either a channel estimator (E₁) from the first set of channel estimators (104) or a channel estimator (E₂) from the second set of channel estimators (106) for estimating the frequency component (Η(ί,)) of the optical communication channel (110) at a discrete frequency (f₁).

Description

DESCRIPTION

Apparatus and method for estimating an optical communication channel at discrete frequencies

BACKGROUND OF THE INVENTION

The present invention relates to an apparatus and a method for estimating an optical communication channel at discrete frequencies.

In a transponder with digital equalization, the equalizer has to be initially converged to provide the optimum equalization performance. To track time-varying effects, e.g. polarization rotations of optical signals or changes in the transmission channel, a regular update of the equalizer properties is required to maintain continuous optimum equalization. The coefficients of a linear equalizer may be adapted by "blind" non-data-aided (NDA) methods or based on a training sequence (TS), which refers to data-aided (DA) channel estimation. Non-data- aided methods are based on gradient algorithms like Constant Modulus Algorithm (CMA) or Least Mean Squares (LMS) and require a long convergence time with a relatively large implementation complexity. Data-aided channel estimation adds a training sequence (TS) to the data, which is repeated at a regular rate fast enough to track time-varying channel distortions. With the aid of the received training sequence and the known transmitted training sequence, the channel can be estimated. The data-aided channel estimation provides the discrete transfer function of the estimated channel.

Two filter solutions or estimation schemes are commonly used for estimating the channel transfer function: A first one is the Zero Forcing (ZF) solution, which simply inverts the estimated channel transfer function. In this case, only inter- symbol-interference (ISI) is compensated neglecting the influence of noise. This can lead to noise enhancement degrading the performance, in particular in systems with narrow-band amplitude filtering. A second one is the Minimum Mean Square Error (MMSE) solution which jointly minimizes the impact of inter-symbol- interference and noise. However, computation is more elaborate, which requires more complexity and more processing latency. Furthermore, the value of the signal power and the noise power needs to be known for an optimum MMSE solution. During initialization, those values are not known. They have to be estimated during the initialization process.

SUMMARY OF THE INVENTION

It is the object of the invention to provide a concept for estimating the channel transfer function of a communication channel which concept provides fast convergence at reduced complexity. 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 for linear communication channels, the channel transfer function represented in Frequency-Domain comprises frequency bins which are independent from each other because the communication channel has an influence on the phase and the amplitude of a transmitted signal but not on its frequency. Consequently, each frequency bin may be separately equalized by using different channel estimation schemes in the Frequency-Domain. Adaptively selecting either solution allows to optimize the performance during different stages of operation. At the same time, the processing complexity can be adjusted for low power consumption or low processing latency.

By use of a training sequence, the channel transfer function can be estimated from a first filter solution, e.g. a Zero Forcing (ZF) filter solution, or a second filter solution, e.g. a Minimum Mean Square Error (MMSE) filter solution, can be calculated. Selecting the ZF solution allows to reduce the processing complexity and the processing latency, in particular for fast convergence during the

initialization phase, when the SNR is not yet known. After convergence dedicated taps can be switched to the more complex MMSE solution, which provides a better performance under steady-state channel conditions. This requires that the SNR has already been estimated. The selection between ZF and MMSE solution is individual to each tap. For each tap, the selection criterion can be based on the received signal power, on the eigenvalue spread, or on other pre-determined parameters. Thus, by the selection between the first (e.g. ZF) and the second (e.g. MMSE) estimation scheme the channel transfer function is estimated fast at reduced computational complexity.

In order to describe the invention in detail, the following terms, abbreviations and notations will be used:

PDM: Polarization Division Multiplexing

(D)QPSK: (Differential) Quaternary Phase Shift Keying, (Differential)

Quadrature Phase Shift Keying

CD: Chromatic Dispersion

PMD: Polarization Mode Dispersion PLL: Phase Locked Loop

FD: Frequency Domain

TD: Time Domain

FFT: Fast Fourier Transform Inverse Fast Fourier Transform Discrete Fourier Transform Digital Signal Processing Analogue-digital converter Finite Impulse Response Local Oscillator

Frequency Offset

Timing Recovery

Polarization-Mode Dispersion Samples per symbol

Feed Forward

Feed Back

State of Polarization

Polarization-dependent Loss Differential Group Delay FEC: Forward Error Correction

BER: Bit-Error Rate

CPE: Carrier-phase estimation

I: Inphase

Q: Quadrature

DA: Data-aided

NDA: Non-data-aided

CAZAC: Constant-amplitude zero auto-correlation

PN: Pseudo noise

DAC: Digital-analogue converter

ZF: Zero Forcing

MMSE: Minimum mean square error

MIMO: Multi input multi output

AGC: Automatic Gain Control

pre-FEC BER: pre Forward-Error-Correction Bit Error Rate According to a first aspect, the invention relates to an apparatus for processing a first input signal and a second input signal, the first input signal representing a first polarization component of an optical signal, the second input signal representing a second polarization component of the optical signal, the optical signal comprising an influence of an optical communication channel, the apparatus comprising: a Fourier transformer for transforming the first input signal into a first transformed signal in frequency domain, and for transforming the second input signal into a second transformed signal in frequency domain, the first transformed signal and the second transformed signal respectively having a number of frequency components at discrete frequencies; a first set of channel estimators for estimating a set of frequency components of the optical communication channel according to a first channel estimation scheme based on the first and/or the second

transformed signals, each channel estimator in the first set of channel estimators being configured to estimate a frequency component of the optical communication channel at a single discrete frequency; a second set of channel estimators for estimating a set of frequency components of the optical communication channel according to a second channel estimation scheme based on the first and/or the second transformed signals, each channel estimator in the second set of channel estimators being configured to estimate a frequency component of the optical communication channel at a single discrete frequency; and a selector for selecting for each discrete frequency from the number of discrete frequencies either a channel estimator from the first set of channel estimators or a channel estimator from the second set of channel estimators for estimating the frequency component of the optical communication channel at a discrete frequency.

By using two different channel estimation schemes, a first one can provide fast initialization at low complexity while a second one can provide accurate and noise- robust convergence at a slightly higher complexity. Thus, the total complexity of filter update is reduced and the initialization procedure is speed up during convergence. In a steady-state operation, the complexity of the channel estimation can be reduced to the minimum requirement without performance degradation, which reduces the power consumption and heat dissipation. The first channel estimation scheme can be a ZF solution and the second one can be a MMSE solution. The best BER performance is reached when a full MMSE filter solution is used, while the ZF solution leads to a slightly degraded but still acceptable performance. Therefore, for a fast initialization, the low-complexity and fast ZF filter solution can be used and later the apparatus can switch to the MMSE solution.

During operation, the optimum BER performance can still be obtained when the MMSE solution is applied only to the most relevant filter taps. Not relevant filter taps can use the low complexity ZF, which leads to a mixed MMSE/ZF filter solution. Relevant filter taps may be identified by analysis of the received spectrum, by Eigenvalue analysis or by signal quality analysis.

In a first possible implementation form of the apparatus according to the first aspect, the selector is configured to select either a channel estimator from the first set of channel estimators or a channel estimator from the second set of channel estimators at a discrete frequency upon a basis of a comparison of a magnitude of a frequency component of the first transformed signal with a magnitude threshold at the discrete frequency, or upon a basis of a comparison of a magnitude of a frequency component of the second transformed signal with a magnitude threshold at the discrete frequency, or upon a basis of a comparison of a magnitude of a frequency component of a combined frequency component comprising the frequency component of the first transformed signal and the second transformed signal with a magnitude threshold.

When comparing the power of the frequency component with a threshold, important frequency components with high power can be precisely estimated by using a noise-robust estimation scheme like MMSE while less important frequency components with low power can be estimated very fast and with low complexity by using a fast initialization estimation scheme like ZF. In a second possible implementation form of the apparatus according to the first aspect as such or according to the first implementation form of the first aspect, the selector is configured to select either a channel estimator from the first set of channel estimators or a channel estimator from the second set of channel estimators at a discrete frequency upon a basis of at least one of: a distribution of eigenvalues of an estimate of a channel matrix, the channel matrix comprising estimates of the frequency components of the optical communication channel. When using an eigenvalue criterion for deciding whether to use the first or the second estimation scheme, the apparatus can detect whether the frequency component is based on a regular channel matrix, in this case the eigenvalue spread is close to 1 , or whether the frequency component is based on a degenerate channel matrix, in this case the eigenvalue spread is far away from 1.

In a third possible implementation form of the apparatus according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the selector is configured to select either a channel estimator from the first set of channel estimators or a channel estimator from the second set of channel estimators at a discrete frequency upon a basis of a comparison of a magnitude of a frequency component of the first transformed signal at the discrete frequency with a magnitude of a frequency component of the first transformed signal at another discrete frequency, or upon a comparison of a magnitude of a frequency component of the second transformed signal at the discrete frequency with a magnitude of a frequency component of the second transformed signal at another discrete frequency, or upon a basis of a comparison of a magnitude of a frequency component of a combined frequency component comprising the frequency component of the first transformed signal and the second transformed signal with a combined frequency component at another discrete frequency. In a fourth possible implementation form of the apparatus according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the selector is configured to select either a channel estimator from the first set of channel estimators or a channel estimator from the second set of channel estimators at a discrete frequency upon a basis of a feed -forward criterion, in particular a power spectral density or an eigenvalue distribution of at least one of the input signals, or upon a basis of a feedback-criterion, in particular a reception error magnitude. The power spectral density or the eigenvalue distribution can be used as feedforward criterion. Thus, the selection parameters are available prior to selection by the selector. For such a feed-forward criterion, each frequency component can be selected by the selector based on its own selection threshold. This improves the selection process and thus the channel estimation.

The selector can be implemented on basis of a feed-back criterion, in particular a reception error magnitude. An error-vector magnitude or a pre-FEC BER quality criterion can be chosen by which specific frequency components may be assigned to a specific estimation scheme. They can be bundled to a single quality criterion for the overall filter estimation. This process can be optimized off-line, i.e. for each filter component all possible estimation schemes are performed and the best estimation scheme for that filter component is chosen. Symmetry properties can be used for reducing the effort of off-line processing. In a fifth possible implementation form of the apparatus according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the selector is configured to select a channel estimator from the first set of channel estimators for a coarse channel estimation, and to select a channel estimator from the second set of channel estimators for a fine channel estimation after a predetermined period of time. The channel estimation is rapidly performed at initialization at the cost of noise- robustness while after a predetermined period of time, the channel estimation is switched to a more precise and noise-robust estimation scheme. The

compensation of the first set of channel estimators may be used as initial compensation when switching to the second set of channel estimators, thereby no interruption caused by the switching can be detected.

In a sixth possible implementation form of the apparatus according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, each channel estimator from the first set of channel estimators and from the second set of channel estimators is comprising a first input for receiving a frequency component of the first transformed signal, a second input for receiving a frequency component of the second transformed signal, a first output for providing a real value of a frequency component of the optical communication channel, and a second output for providing an imaginary value of the frequency component of the optical communication channel.

For an optical signal comprising two polarization components each channel estimator receives both polarization components, thus the channel estimation depends on both polarization components and is thus highly accurate.

In a seventh possible implementation form of the apparatus according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, each channel estimator from the first set of channel estimators or from the second set of channel estimators is configured to estimate a first channel component associated with the first polarization, a second channel component associated with the second polarization, a third channel component representing a crosstalk from the first polarization towards the second polarization and a fourth channel component representing a crosstalk from the second polarization towards the first polarization, each channel estimator is further configured to superimpose the first and the fourth channel component to obtain a real value of the frequency component of the optical communication channel, and to superimpose the second and the third channel component to obtain an imaginary value of the optical communication channel. By estimating the first, second, third and fourth channel components, both, self- talk, represented by the first and second channel components, and cross-talk, represented by the third and fourth channel components, between the two polarization modes are considered. Therefore, the estimation has a higher precision compared to an estimation which only considers the self-talk

components. By superimposing the first and the fourth channel component and superimposing the second and the third channel component, a real value and an imaginary value of the frequency component are obtained which allow to apply the IFFT. Thus, processing results in a real-valued data stream in the time-domain for further processing of timing and carrier recovery.

In an eighth possible implementation form of the apparatus according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the Fourier transformer is comprising the number of output taps for providing the number of frequency components of the first transformed signal, and the number of output taps for providing the number of frequency components of the second transformed signal, wherein each channel estimator comprises two inputs, and wherein the selector is configured to couple two output taps of the Fourier transformer associated with the same discrete frequency to two inputs of a channel estimator from the first set of channel estimators or of a channel estimator from the second set of channel estimators.

The Fourier transformer has such a number of output taps that it can represent a desired number of frequency components for both, the first and the second transformed signal. A size of a Fourier transform which the Fourier transformer performs is configurable. The size can be adjusted in integer numbers or in powers of two. The Fourier transform can use zero-padding or can use cyclic pre- fixing in order to improve a resolution. The Fourier transform can comprise a Fast Fourier Transform in order to reduce the computational complexity. By coupling two output taps of the Fourier transformer associated with the same discrete frequency to two inputs of a channel estimator, the selector is configured to perform a MIMO estimation using both polarization components for each frequency bin. This improves a precision of the apparatus.

In a ninth possible implementation form of the apparatus according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the first channel estimation scheme and the second channel estimation scheme are different channel estimation schemes.

When using different estimation schemes, one of both schemes can be fast converging without considering noise while the second one can use the results of the first scheme and improve the convergence by additionally considering noise performance. Thus, the overall performance is better than for a convergence- optimized scheme in terms of complexity and is better than for a complexity- optimized scheme in terms of convergence. In a tenth possible implementation form of the apparatus according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the first channel estimation scheme and the second channel estimation scheme are one of the following channel estimation schemes: zero forcing estimation, minimum mean least squares estimation, least mean squares estimation, decision-directed estimation.

When the first scheme uses a ZF solution and the second scheme uses an MMSE solution, fast convergence at initialization is reached and improved convergence in the presence of noise is guaranteed by the MMSE solution. The overall performance is better than for solely MMSE in terms of complexity and processing latency and is better than for solely ZF in terms of performance. The same holds for least mean squares and decision-directed estimation.

In an eleventh possible implementation form of the apparatus according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, each channel estimator from the set of first channel estimators or from the set of second channel estimators is configured to perform a data aided frequency domain channel estimation. Data-aided FD channel estimation has a higher precision than blind channel estimation. In a lot of standards for fixed and mobile transmission, the training sequence is available and can be used for frequency equalization. For frequency- domain (FD) filters, efficient NDA methods are not known, only DA methods may be applied.

In a twelfth possible implementation form of the apparatus according to the first aspect as such or according to any of the preceding implementation forms of the first aspect, the apparatus further comprises an inverse Fourier transformer for inversely transforming the outputs of the channel estimators to obtain an estimate of an impulse response of the optical communication channel in time domain.

The frequency transform by FFT and re-transform in time domain by IFFT can be very efficiently performed. There are standard hardware implementations available for both transforms.

According to a second aspect, the invention relates to an optical receiver, comprising: a coherent front end for receiving the optical signal in a transmission band and for providing a first analog signal and a second analog signal in a base band or in an intermediate frequency band, the first analog signal representing a first polarization component of the optical signal, the second analog signal representing a second polarization component of the optical signal; an analog- digital converter for quantizing and discretizing the first analog signal to provide the first input signal and for quantizing and discretizing the second analog signal to provide the second input signal; and an apparatus for channel estimation according to the first aspect as such or according to any of the preceding implementation forms of the first aspect.

The equalization in frequency domain implemented by the optical receiver according to the second aspect has a significant lower complexity than an equalization in time domain. Additionally the complexity of channel estimation and the complexity of filter adaptation of the optical receiver according to the second aspect is reduced compared to a common optical receiver estimating the channel in time domain.

According to a third aspect, the invention relates to a method for processing a first input signal and a second input signal, the first input signal representing a first polarization component of an optical signal, the second input signal representing a second polarization component of the optical signal, the optical receive signal comprising an influence of an optical communication channel, the apparatus comprising: Fourier transforming the first input signal into a first transformed signal in frequency domain, and Fourier transforming the second input signal into a second transformed signal in frequency domain, the first transformed signal and the second transformed signal respectively having a number of frequency components at discrete frequencies; for each discrete frequency, selecting either a first channel estimation scheme for estimating a frequency component of the optical communication channel at a discrete frequency based on the first and/or the second transformed signals, or selecting a second channel estimation scheme for estimating the frequency component of the optical communication channel at the discrete frequency based on the first and the second transformed signals. By using two different channel estimation schemes, a first one can provide fast initialization at low complexity while a second one can provide accurate and noise- robust convergence at a slightly higher complexity. Thus, the total complexity of filter update is reduced and the initialization procedure is speed up during convergence. The first channel estimation scheme can be a ZF solution and the second one can be a MMSE solution. The best BER performance is reached when a full MMSE filter solution is used, while the ZF solution leads to a slightly degraded but still acceptable performance. Therefore, for a fast initialization, the low-complexity and fast ZF filter solution can be used and later the apparatus can switch to the MMSE solution. During operation, the optimum BER performance can still be obtained when the MMSE solution is applied only to the most relevant filter taps. Not relevant filter taps can use the low complexity ZF, which leads to a mixed MMSE/ZF filter solution. Relevant filter taps may be identified by analysis of the received spectrum, by Eigenvalue analysis or by signal quality analysis.

According to a fourth aspect, the invention relates to a computer program with a program code for performing the method according to the third aspect when run on a computer. The method can be performed on any computer. The method can be updated on the computer. The FFT number, the number of estimation schemes and the type of estimation algorithm can be changed when new hardware with higher or lower processing power is available. The method can be updated online in the field without replacing the whole system. The solution is flexible according to the customer's requirements.

According to a fifth aspect, the invention relates to a communication system comprising a coherent receiver according to the second aspect and an apparatus according to the first aspect or one of its implementation forms. In a first possible implementation form of the communication system according to the fifth aspect the communication system is an optical communication system.

In a second possible implementation form of the communication system according to the fifth aspect as such or according to the first implementation form of the fifth aspect, the apparatus is implemented as a program, i.e. software, on a Digital Signal Processor (DSP).

In a third possible implementation form of the communication system according to the fifth aspect as such or according to any preceding implementation form of the fifth aspect, the apparatus is implemented as a hardware circuit on an Application Specific Integrated Circuit (ASIC).

In a fourth possible implementation form of the communication system according to the fifth aspect as such or according to any preceding implementation form of the fifth aspect, the apparatus is a frequency domain (FD) equalizer.

In a fifth possible implementation form of the communication system according to the fifth aspect as such or according to any preceding implementation form of the fifth aspect, the apparatus comprises an adaptive selection unit for selecting between a ZF and an MMSE estimation scheme for estimating a frequency component of a transmission channel of the communication system for each filter tap. The default can be an estimation according to the ZF estimation scheme as the low-complexity ZF filter update is suitable for fast initialization. An update to MMSE estimation can be performed if required; the update of the filter coefficients can start from the found ZF based filter coefficients.

In a sixth possible implementation form of the communication system according to the fifth aspect as such or according to any preceding implementation form of the fifth aspect, the apparatus comprises an optimization unit performing an optimization procedure based on the signal power spectrum or the eigenvalue spread of the received optical signal to optimize each filter tap with respect to the ZF or MMSE estimation scheme..

In a seventh possible implementation form of the communication system according to the sixth implementation form of the fifth aspect, the optimization unit performs an optimization procedure based on an error-vector magnitude (EVM), quality factor (Q-factor) or pre Forward-Error-Correction Bit Error Rate (pre-FEC BER) suitable criteria. Frequency-Domain (FD) filtering provides the same performance as Time-Domain (TD) filtering given the same number of taps, but FD filters have a much less implementation complexity. Consequently, FD filters are likely candidates for highspeed digital coherent receivers with 40G, 100G, 400G, 1T or beyond transmission rates. FD filtering in combination with DA channel estimation makes the system independent from the data modulation format. The same or nearly the same processing can be applied for BPSK, QPSK or 16-QAM, which allows designing transponders with flexible data rates, also called flexi-rate transponders, or re-use of signal processing ASIC design for several product generations. The flexi-rate transponder may be applied in switched networks, where the channel conditions vary for each switched path. Alternatively, the transponder could be provided to customers with a fixed configuration. Still, only one set of hardware devices and only one ASIC design has to be developed, thereby reducing the engineering and manufacturing costs.

The communication system allows selecting an adaptive filter solution which is optimized for

- Low complexity filter update,

- Fast update processing with low latency for fast tracking,

- Best performance. The adaptive selection can be applied during

- Initialization of the digital equalizer as follows: Start with ZF taps for fast acquisition, then estimate the signal and the noise power and switch the relevant taps to MMSE for improved performance.

- Continuous operation of the digital equalizer: As channel conditions change, the filter solution for each filter tap can be optimized by switching between ZF and MMSE for each tap. Furthermore, the communication system allows:

- Instantaneous filter update without any delay, as data may be

buffered during update processing, or gradual convergence phase,

- No mechanism to separate polarizations, i.e. no singularity problem, and for identification of multiplexed polarized (PolMUX) signals is required in contrast to a NDA filter update procedure which requires such identification,

- FD implementation with parallel processing is suitable for high-speed processing with low-complexity FD filter implementation and high degree of parallelization,

- Channel estimation is independent from over-sampling and is also fine for 1 , 1.3 or 2 sample/symbol,

- All benefits from training including more stability, polarization/phase identification, support by DA timing/carrier recovery etc.,

- Fast optical performance monitoring based on DA channel estimation.

According to a sixth aspect, the invention relates to a coherent detection with digital equalization comprising a data-aided filter acquisition. 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 block diagram of an apparatus for processing polarization components of an optical signal according to an implementation form; Fig. 2 shows a block diagram of an apparatus for processing polarization components of an optical signal according to an implementation form;

Fig. 3 shows a schematic diagram of a method for processing polarization components of an optical signal according to an implementation form;

Fig. 4 shows a schematic diagram of an optical signal with two polarization components received at 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 graph illustrating the eigenvalue-spread measured at internal nodes of an apparatus for processing polarization components of an optical signal according to an implementation form;

Fig. 7 shows a graph illustrating signal powers and eigenvalue-spread measured at internal nodes of an apparatus for processing polarization components of an optical signal according to an implementation form; Fig. 8 shows a graph illustrating signal powers and eigenvalue-spread measured at internal nodes of an apparatus for processing polarization components of an optical signal according to an implementation form; Fig. 9 shows a graph illustrating bit error rates of an apparatus for processing polarization components of an optical signal according to an implementation form; and

Fig. 10 shows a schematic diagram of a method for receiving an optical signal with two polarization components according to an implementation form.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Fig. 1 shows a block diagram of an apparatus 100 for processing polarization components of an optical signal according to an implementation form.

The apparatus 100 comprises a Fourier transformer (i.e., a Fourier transforming unit) 102, a first set of channel estimators (i.e., channel estimation units) 104, a second set of channel estimators (i.e., channel estimation units) 106 and a selector (i.e., a selecting unit) 108. The apparatus 100 is used for processing a first input signal 112 representing a first polarization component (X-polarized component) of an optical signal and a second input signal 1 14 representing a second polarization component (Y-polarized component) of the optical signal. The optical signal is received via an optical communication channel 1 10 having a channel frequency response H(f). Thus, the optical signal and its polarization components 1 12, 114 are influenced by the optical communication channel 1 10. In an implementation form, the polarization components 1 12, 1 14 of the optical signal correspond to the polarization components 411 and 413 of the optical signal 403 as described below with respect to Fig. 4. In an implementation form, the optical signal comprises a training signal (TS) 405 as described below with respect to Fig. 4. The Fourier transformer 102 transforms the first input signal 1 12 into a first transformed signal 122 in frequency domain and transforms the second input signal 1 14 into a second transformed signal 124 in frequency domain. The first transformed signal 122 and the second transformed signal 124, respectively, have a number of frequency components at discrete frequencies fi , . . . ,fN, wherein N is the size of the Fourier transformation. In an implementation form, the Fourier transformer 102 comprises a Discrete Fourier Transformation (DFT) of an integer numbered size N. In an implementation form, the Fourier transformer 102 comprises a Fast Fourier Transformation (FFT) of a size N being a power of two. The Fourier transformer 102 provides the first transformed signal 122 and the second transformed signal 124 at two outputs which are connected to two inputs of both the first set of channel estimators 104 and the second set of channel estimators 106.

The first set of channel estimators 104 comprises a plurality of channel estimators Ei for estimating a set of frequency components H_Ei (fi ), . . . , H_Ei (fN) of the optical communication channel 1 10 according to a first channel estimation scheme based on the first 122 and/or the second 124 transformed signals. Each channel estimator Ei in the first set of channel estimators 104 estimates a frequency component Η(ί,) of the optical communication channel 1 10 at a single discrete frequency fi, wherein i=1 ..N. The first set of channel estimators 104 provide the set of frequency components H_Ei (fi ), . . . , H E I (f N ) at N outputs which are connected to N inputs of the selector 108.

In an implementation form, the first set of channel estimators 104 estimate the set of frequency components H_Ei (fi ), . . . , H_Ei(f_N) based on both, the first 122 and the second 124 transformed signals. This implementation form is illustrated in Fig. 1 and an estimation formula is described with respect to Fig. 4.

The second set of channel estimators 106 comprises a plurality of channel estimators E₂ for estimating a set of frequency components H_E2(fi ), . . . , H_E2(fN) of the optical communication channel 1 10 according to a second channel estimation scheme based on the first 122 and the second 124 transformed signals. Each channel estimator E2 in the second set of channel estimators 106 estimates a frequency component Η(ί,) of the optical communication channel 1 10 at a single discrete frequency f,, wherein i=1 ..N. The second set of channel estimators 106 provide the set of frequency components H_E2(fi ), ... ,

at N outputs which are connected to N inputs of the selector 108.

In an implementation form, the second set of channel estimators 106 estimate the set of frequency components H_E2(fi ), ... ,

based on both, the first 122 and the second 124 transformed signals. This implementation form is illustrated in Fig. 1 and an estimation formula is described with respect to Fig. 4.

In an implementation form, the first channel estimation scheme is a Zero Forcing (ZF) channel estimation scheme and the second channel estimation scheme is a Minimum Mean Square Error (MMSE) estimation scheme. In an implementation form, the apparatus comprises a further set of channel estimators for estimating the optical channel according to a third channel estimation scheme. In an implementation form, the third channel estimation scheme comprises a Least Mean Squares (LMS) algorithm. In an implementation form, the apparatus comprises a multiple number of sets of channel estimators for estimating the optical channel according to different channel estimation schemes.

The selector 108 selects for each discrete frequency f, from the number of discrete frequencies f 1 , ... , f _N either a channel estimator Ei from the first set of channel estimators 104 or a channel estimator E2 from the second set of channel estimators 106 for estimating the frequency component H(fj) of the optical communication channel 1 10 at a discrete frequency f,. The selector 108 receives the set of frequency components H_Ei (fi ),■■■ , H_Ei

at N inputs and receives the set of frequency components H_E2(fi ), ... , H_E2(fN ) at N further inputs and provides the frequency components H(fi ), ... , H(fN) of the optical communication channel 1 10 at N outputs which are outputs of the apparatus 100. Fig. 2 shows a block diagram of an apparatus 100 for processing polarization components of an optical signal according to an implementation form. The apparatus 100 corresponds to the apparatus 100 as described with respect to Fig. 1 , wherein Fig. 2 illustrates an implementation form of the Fourier transformer 102, the first set of channel estimators 104, the second set of channel estimators 106 and the selector 108 as described above with respect to Fig. 1 .

The Fourier transformer 102 comprises a first Fourier transformation unit Fi{ } that transforms N time values of the first input signal 1 12 received at N time-referenced inputs ti , . . . , tN of the first Fourier transformation unit Fi{ } into N frequency values of the first transformed signal 122 provided at N frequency-referenced outputs f 1 , . . . , f N of the first Fourier transformation unit Fi{ } which are outputs of the Fourier transformer 102. The Fourier transformer 102 comprises a second Fourier transformation unit F2{ } that transforms N time values of the second input signal 1 14 received at N time-referenced inputs ti , . . . ,†.N of the second Fourier

transformation unit F2{ } into N frequency values of the second transformed signal 124 provided at N frequency-referenced outputs f i , ... , f N of the second Fourier transformation unit F2{ } which are outputs of the Fourier transformer 102. The N frequency-referenced outputs fi , . . . , fN of the first and second Fourier

transformation units Fi{ } and F2{ } provide complex-valued frequency values comprising a real part and an imaginary part.

The first set of channel estimators 104 comprises a plurality of channel estimators Ei for estimating a set of frequency components H_Ei (fi ), . . . , H_Ei (fN) of the optical communication channel 1 10 according to a first channel estimation scheme. Each channel estimator Ei(f,) of the N channel estimators has a first input for receiving a frequency value of the first transformed signal 122 from the first Fourier

transformation unit Fi{ } and a second input for receiving a frequency value of the second transformed signal 124 from the second Fourier transformation unit F2{ } according to the frequency bin f,. Each channel estimator Ei(f,) provides a respective frequency component H_Ei(fi) according to the frequency bin f, at its output. Hence, the first channel estimator Ei(fi) receives the frequency value with respect to the first frequency bin fi of the first transformed signal 122 at its first input and receives the frequency value with respect to the first frequency bin fi of the second transformed signal 124 at its second input and provides the frequency component H_Ei(fi) at its output. The N-th channel estimator

receives the frequency value with respect to the N-th frequency bin fN of the first transformed signal 122 at its first input and receives the frequency value with respect to the N- th frequency bin fN of the second transformed signal 124 at its second input and provides the frequency component H_Ei(fN) at its output.

The second set of channel estimators 106 comprises a plurality of channel estimators E₂ for estimating a set of frequency components H_E2(fi), - -,

of the optical communication channel 1 10 according to a second channel estimation scheme. Each channel estimator E2(f,) of the N channel estimators has a first input for receiving a frequency value of the first transformed signal 122 from the first Fourier transformation unit Fi{ } and a second input for receiving a frequency value of the second transformed signal 124 from the second Fourier transformation unit F2{ } according to the frequency bin f,. Each channel estimator E2(f,) provides a respective frequency component HE2(fi) according to the frequency bin f, at its output. Hence, the first channel estimator E2(fi) receives the frequency value with respect to the first frequency bin fi of the first transformed signal 122 at its first input and receives the frequency value with respect to the first frequency bin fi of the second transformed signal 124 at its second input and provides the frequency component HE2(fi) at its output. The N-th channel estimator

receives the frequency value with respect to the N-th frequency bin fN of the first transformed signal 122 at its first input and receives the frequency value with respect to the N- th frequency bin fN of the second transformed signal 124 at its second input and provides the frequency component at its output. In an implementation form, the first channel estimation scheme is a Zero Forcing (ZF) channel estimation scheme and the second channel estimation scheme is a Minimum Mean Square Error (MMSE) estimation scheme. In an implementation form, the apparatus comprises a further set of channel estimators for estimating the optical channel according to a third channel estimation scheme. In an implementation form, the third channel estimation scheme comprises a Least Mean Squares (LMS) algorithm. In an implementation form, the apparatus comprises a multiple number of sets of channel estimators for estimating the optical channel according to different channel estimation schemes.

The selector 108 comprises for each discrete frequency f, a sub-selection unit for selecting either a channel estimator Ei from the first set of channel estimators 104 or a channel estimator E₂ from the second set of channel estimators 106 according to the discrete frequency f,. In an implementation form, the selector 108 selects the channel estimators Ei and E₂ based on a power of frequency bins of the first 122 and the second 124 transformed signals. In an implementation form, the selector 108 applies a threshold to the spectral power of the first 122 and the second 124 transformed signals and selects a channel estimator Ei from the first set of channel estimators 104 if the power of a respective frequency bin is below the threshold and selects a channel estimator E₂ from the second set of channel estimators 106 if the power of a respective frequency bin is above the threshold. In an implementation form the threshold is 10 μ\Ν according to the illustrations of Figures 7 and 8 as described below. In an implementation form, the selector 108 selects the channel estimators Ei for peripherally located frequency bins of the first 122 and the second 124 transformed signals and selects the channel estimators E₂ for centrally located frequency bins of the first 122 and the second 124 transformed signals. In an implementation form, the selector 108 selects the channel estimators Ei according to an ZF estimation scheme for peripherally located frequency bins of the first 122 and the second 124 transformed signals and selects the channel estimators E₂ according to an MMSE estimation scheme for centrally located frequency bins of the first 122 and the second 124

transformed signals.

In an implementation form, the channel selector 108 selects the channel estimators Ei and/or the channel estimators E₂ based on the power of the received optical signal or/and based on the eigenvalue spread of the received optical signal or/and based on an error-vector magnitude (EVM) or/and based on a quality factor (Q-factor) or/and based on a pre Forward-Error-Correction Bit Error Rate (pre-FEC BER) suitable criteria.

Fig. 3 shows a schematic diagram of a method 300 for processing polarization components of an optical signal according to an implementation form. The method 300 is for processing a first input signal and a second input signal, the first input signal representing a first polarization component of an optical signal, the second input signal representing a second polarization component of the optical signal, the optical signal comprising an influence of an optical communication channel.

The method 300 comprises: Fourier transforming (301 ) the first input signal into a first transformed signal in frequency domain, and Fourier transforming (303) the second input signal into a second transformed signal in frequency domain, the first transformed signal and the second transformed signal respectively having a number of frequency components at discrete frequencies.

The method 300 further comprises: for each discrete frequency, selecting (305) either a first channel estimation scheme for estimating a frequency component of the optical communication channel at a discrete frequency based on the first and the second transformed signals, or selecting a second channel estimation scheme for estimating the frequency component of the optical communication channel at the discrete frequency based on the first and the second transformed signals. Fig. 4 shows a schematic diagram of an optical signal with two polarization components received at an optical receiver according to an implementation form.

An optical signal 401 comprising an X-polarized signal component 407 and a Y- polarized signal component 409 is transmitted by a transmitter through an optical channel H(f), 110 corresponding to the optical channel 110 as described with respect to Figures 1 and 2. An optical receiver receives an optical signal 403 comprising an X-polarized signal component 411 and a Y-polarized signal component 411 , which received optical signal 403 is influenced by the optical channel 110. The received optical signal 403 which is used for equalization is a training sequence section 405 of a data stream. The training sequence comprises pilot symbols which are known to the optical receiver.

Training-based channel estimation is known from wireless communications, where fast channel tracking is required, in particular for mobile communications.

Therefore, training sequences (TS) are preferred, where each training sequence instantly leads to a full channel estimation. In an implementation form, the training sequence (TS) for the 2x2 multi-input multi-output (MIMO) system as depicted in Fig. 4 is composed of four independent blocks C1 , C2, C3 and C4,

where C1 and C2 represent the X-polarized component 420 and C3 and C4 represent the Y-polarized component 422. The length of each block covers at least the channel memory length.

With the aid of the received spectra Rci, Rc2, Rc3, Rc4 and the known transmitted spectra of the training sequence Sci, Sc2, Sc3, Sc4, the receiver estimates the channel according to the Data-Aided (DA) channel estimation as follows:

J Since 1/SciSq for i=1 ..4 and j=1 ..4 is known and pre calculated at the receiver, the ZF channel estimation consists of two complex multiplications and one division per frequency tap. Other training sequences, structures, methods and architectures are also known to provide the estimated channel transfer function. In an

implementation form, training sequences, structures, methods and architectures according to "N. Benvenuto and G. Cherubini, Algorithms for Communications Systems and their Applications. John Wiley & Sons, 2005" are used.

In an implementation form, the training sequence (TS) for the 2x2 multi-input multi- output (Ml MO) system as depicted in Fig. 4 is composed of the two independent blocks C1 and C3. The channel estimation is performed analogously as described above with respect to the four blocks C1 , C2, C3 and C4. The receiver estimates the channel according to the Data-Aided (DA) channel estimation as follows:

By using only the two blocks C1 and C3 a complexity for channel estimation is reduced. Depending on the properties of the training sequences, additional processing steps might be required to obtain the final channel estimation.

Furthermore, alternative methods for data-aided channel estimation might be applied that also provide an estimate of the discrete channel transfer function.

From the channel estimation, the FD filter taps are calculated

W_ZF (f) = H ^l

W_MMSE(f)

where and ( )^H denote the inverse and the complex-conjugate (Hermitian) transpose, respectively. o_n ² and o_s ² are the noise and signal powers which are estimated at the receiver. WzF(f) are the frequency domain (FD) filter taps estimated according to the Zero Forcing (ZF) channel estimation scheme and Wi iMSE(f) are the frequency domain (FD) filter taps estimated according to the Minimum Mean Square Error (MMSE) channel estimation scheme

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. The MMSE filter function requires more complexity for the computation of the filter solution, but it also provides the better performance which will be shown in Figures 6 and 9.

Fig. 5 shows a block diagram of an optical receiver according to an

implementation form. The optical receiver comprises an optical front end 501 , a framing synchronization unit 503, a serial-to-parallel converter and FFT processing unit 505, a frequency domain (FD) equalizer comprising the four multipliers H_xx(f), Hxy(f), Hyx(f), Hyy(f) and the two adders 51 1 , 513, an I FFT processing unit and parallel-to-serial converter 507 and a timing recovery and carrier recovery unit 509.

The optical front end 501 comprises an analog-digital converter (ADC) and an automatic gain control (AGC) unit. The optical front end 501 is adapted to receive an optical signal. In an implementation form, the optical signal is according to the optical signal as described with respect to the Figures 1 and 2 represented by its two polarization components, the X-polarized component 1 12 and the Y-polarized component 1 14. In an implementation form, the optical signal is according to the optical signal as described with respect to the Figure 4 represented by its two polarization components, the X-polarized component 41 1 and the Y-polarized component 413. The received optical signal has passed an optical channel 1 10 according to the representation of Figures 1 , 2 and 4 and is influenced by the optical channel with respect to its phase and amplitude.

The framing synchronization unit 503 is used to synchronize received frames of the optical signal to a phase reference signal and/or a frequency reference signal in order to detect the beginning of each received frame.

The serial-to-parallel converter and FFT processing unit 505 is used to convert time-domain signal samples of the received optical signal, i.e. both, X-polarized and Y-polarized complex-valued signal components XI+JXQ and YI+JYQ of the received optical signal, from a serial representation into a parallel representation. The parallel representation is adequate for the succeeding Fast Fourier

Transformation performed by the unit 505. In an implementation form, a size of the parallel representation is greater or equal than the size of the FFT transformation. In an implementation form, the FFT transformation comprises cyclic prefix processing for which the size of the parallel representation is greater or equal than a sum of the size of the FFT and the size of the cyclic prefix. In an implementation form, instead of cyclic pre-fix, overlapping data from the adjacent signal blocks is used to perform an overlap-add or overlap-discard processing. In an

implementation form, the serial-to-parallel converter and FFT processing unit 505 comprises a memory for storing the parallel representation values of the time- domain optical signal. The serial-to-parallel converter and FFT processing unit 505 further performs a Fast Fourier Transformation of the received time-domain optical signal, i.e. an FFT for each signal component, which are X-polarized and Y- polarized, of the optical signal, and provides the two signal spectra R_x(f) and R_y(f) according to the X-polarized and the Y-polarized signal component which are input to the FD equalizer. In an implementation form, two separate FFTs are

implemented, one for the X-polarized complex-valued signal component XI+JXQ and one for the Y-polarized complex-valued signal component. YI+JYQ. The FD equalizer has a 2x2 MIMO structure for each frequency component. It can be interpreted as a 1-tap 2x2 MIMO filter for each sample. For each frequency bin fi delivered by the serial-to-parallel converter and FFT processing unit 505, the FD equalizer performs a first summation 511 adding the X-polarized signal spectrum R_x(fi) multiplied with the X-polarized autocorrelation component H_xx(fi) of the estimated channel and the Y-polarized signal spectrum R_y(f,) multiplied with the Y- polarized/X-polarized cross-correlation component H_yx(fi) of the estimated channel to provide the X-polarized signal spectrum at an X-polarized output of the FD equalizer. For each frequency bin f, delivered by the serial-to-parallel converter and FFT processing unit 505, the FD equalizer further performs a second summation 513 adding the Y-polarized signal spectrum R_y(f,) multiplied with the Y- polarized autocorrelation component H_yy(fi) of the estimated channel and the X- polarized signal spectrum R_x(f,) multiplied with the X-polarized /Y-polarized cross- correlation component H_xy(fi) of the estimated channel to provide the Y-polarized signal spectrum at an Y-polarized output of the FD equalizer. Although the structure with the four multipliers H_xx(f), H_xy(f), H_yx(f), H_yy(f) and the two adders 51 1 , 513 is only shown once in Fig. 5, this block exists in a multiple number of instances depending on the number of discrete frequency bins to be processed which is at least the size of the FFT.

For each equalized frequency bin, the resulting X-polarized and Y-polarized outputs are input to the IFFT processing unit and parallel-to-serial converter 507 which is configured to retransform the frequency bins into time domain and serialize the received parallel data stream. In an implementation form, two separate IFFTs are implemented, one for the X-polarized frequency bins and one for the Y-polarized frequency bins. In an implementation form, the IFFT processing unit and parallel-to-serial converter 507 comprises a memory for storing the X- polarized and Y-polarized outputs of the FD equalizer. The timing recovery and carrier recovery unit 509 receives the output signal of the IFFT processing unit and parallel-to-serial converter 507 which is the equalized received optical signal and which represents the optical signal as transmitted by the transmitter. By using the results of the framing synchronization unit 503, i.e. the synchronization of the received optical frames to a phase reference signal and/or a frequency reference signal and the detected beginning of each received frame, timing of the equalized optical signal is recovered and a carrier of the equalized optical signal is reconstructed.

As the FD equalizer comprising the four multipliers H_xx(f), H_xy(f), H_yx(f), H_yy(f) and the two adders 51 1 , 513 applies a 2x2 Ml MO structure for each frequency component, a high degree of parallelization is reached by the parallel processing, which is suitable for high-speed processing. The number of filter taps is dependent on the length of the training blocks 405 as depicted in Fig. 4. Each tap can be independently calculated using the most appropriate solution, i.e ZF or MMSE.

The channel matrix H(f) for ZF estimation reads:

J

wherein the four components H_ZF,xx(f), H_ZF,xY(f), H_ZF,Yx(f), HzF,w(f) of the channel matrix H_ZF(f) correspond to the above-mentioned components H_xx(f), H_xy(f), H_yx(f), Hyy(f) when ZF estimation is used.

The channel matrix H(f) for MMSE estimation reads:

MMSE,XX if) ^{1 1} MMSE X if)

H MMSE if)

H MMSE,XY if) H MMSE,YY if) J

wherein the four components H_MMSE,xx(f), H_MMSE,xY(f), H_MMSE,Yx(f), H_MMSE,YY(f) of the channel matrix H_MivisE(f) correspond to the above-mentioned components H_xx(f), H_xy(f), H_yx(f), Hyy(f) when MMSE estimation is used

Analysing the Eigenvalues of the estimated channel matrix H(f) shows that the MMSE solution gives a better channel estimation compared to the ZF solution because the condition number of the central taps is closer to 1 . Fig. 6 shows two graphs illustrating eigenvalue spreads measured at internal nodes of an apparatus for processing polarization components of an optical signal according to an implementation form. The two graphs depicts the eigenvalue spread, also called condition number, over discrete frequency taps for a ZF (Zero Forcing) channel estimation (upper graph) and a MMSE (Minimum Mean Square Error) estimation (lower graph). The internal nodes at which the eigenvalue spreads of the upper graph were measured correspond to the outputs of the first set of channel estimators 104 as depicted in Figures 1 and 2 providing the individual estimated frequency components HEi(fi )...

of the optical channel 1 10 using the first estimation scheme, which is here ZF estimation. The internal nodes at which the eigenvalue spreads of the lower graph were measured correspond to the outputs of the second set of channel estimators 106 as depicted in Figures 1 and 2 providing the individual estimated frequency components HE2(fi )- - - of the optical channel 1 10 using the second estimation scheme, which is here MMSE estimation.

The eigenvalue spread is defined as | _max(f)/ λ,η,ηίί)! , i.e. the absolute value of the relation between the maximum eigenvalue _max(f) and the minimum eigenvalue min(f) at a specified frequency f. The ZF channel estimation is according to the first set of channel estimators 104 as depicted in Figures 1 and 2 for estimating a channel matrix HEi(f) of the optical communication channel 1 10 according to the first channel estimation scheme which is here the Zero Forcing (ZF) estimation scheme. The MMSE channel estimation is according to the second set of channel estimators 106 as depicted in Figures 1 and 2 for estimating a channel matrix

HE2(f) of the optical communication channel 1 10 according to the second channel estimation scheme which is here the Minimum Mean Square Error (MMSE) estimation scheme. Two reference lines 603 and 601 mark condition numbers of 3 and 1 , respectively. While for the ZF estimation condition numbers lie between 1 and 3, for the MMSE estimation condition number lie closely above 1 , in particular for center frequencies around 0 Hz. Therefore, the MMSE estimation scheme performs better than the ZF estimation scheme as an eigenvalue spread of one for all frequencies represents perfect channel estimation.

In an implementation form, the received signal spectrum is measured and based on that spectrum MMSE estimation for estimating the channel matrix HE2(f) is used only in those taps that have power above a certain threshold, for all other taps the low complexity ZF estimation for estimating the channel matrix HEi(f) is used. An optical filtering bandwidth for receiving and measuring the optical received signal spectrum is 35GHz.

Fig. 7 shows a graph illustrating received signal powers and eigenvalue spreads measured at internal nodes of an apparatus for processing polarization

components of an optical signal according to an implementation form. The two graphs depicts the received signal power spectrum in Watts (upper graph) and the eigenvalue spread, i.e. the condition number (lower graph) over discrete frequency taps for a combined ZF channel estimation and MMSE channel estimation. The combination is according to the description with respect to Figures 1 and 2, where a selector 108 selects for each discrete frequency tap (f,) either a channel estimator Ei from the first set of channel estimators 104, which is here ZF estimation, or a channel estimator E₂ from the second set of channel estimators 106, which is here MMSE estimation, for estimating the frequency component Η(ί,) of the optical communication channel 1 10 at a discrete frequency tap f,. The internal nodes at which the spectrum is measured correspond to the outputs of the selector 108 as depicted in Figures 1 and 2 providing the individual estimated frequency components

of the optical channel 1 10.

For centrally positioned frequency taps the MMSE channel estimation is applied while for peripherally positioned frequency taps the ZF channel estimation is applied. From the upper graph it can be seen that centrally located frequency taps have a higher signal power than peripherally located frequency taps. A threshold of 10 μ\Ν forms the border line between centrally located frequency taps being processed by MMSE estimation and peripherally located frequency taps being processed by ZF estimation. The lower graph depicts the eigenvalue spread for these frequency taps. The condition number of the centrally located frequency taps closely approximates the condition number of the centrally located frequency taps as depicted in Fig. 6 (lower graph) where MMSE estimation is applied to all taps. The condition number of the peripherally located frequency taps closely approximates the condition number of the peripherally located frequency taps as depicted in Fig. 6 (upper graph) where ZF estimation is applied to all taps.

Therefore, a combination of MMSE estimation applied to high energy frequency taps with ZF estimation applied to low energy frequency taps improves the channel estimation with respect to precision and computational complexity. The high energy (centrally located) frequency taps are precisely estimated by using the precise MMSE estimation scheme, whereas the low energy (peripherally located) frequency taps are rapidly and efficiently estimated by using the fast ZF estimation scheme.

An optical filtering bandwidth for receiving and measuring the optical received signal spectrum is 35GHz. But the same holds when a more aggressive optical filtering is applied, for example 20 GHz which can be seen in Fig. 8.

Fig. 8 shows a graph illustrating signal powers and eigenvalue spreads measured at internal nodes of an apparatus for processing polarization components of an optical signal according to an implementation form. The behavior is the same as described with respect to Fig. 7. The difference lies in the different optical filtering bandwidth which is here limited to 20 GHz while in Fig. 7 a bandwidth of 35 GHz was applied. As far as the MMSE is used in the estimation of the central taps the condition number and thus the bit error rate (BER) performance is the same as when the full MMSE channel estimation as depicted in the lower graph of Fig. 6 is used. Fig. 9 shows a graph illustrating bit error rates of an apparatus for processing polarization components of an optical signal according to an implementation form. The negative logarithm of the bit error rate -log(BER) is represented over the optical signal-to-noise ratio (OSNR) for different implementation forms of an apparatus 100 as depicted in Figures 1 and 2. The diagram was measured by using a frequency span of 32 discrete frequency taps (f,). In a first implementation form, the selector 108 selects for all discrete frequency taps (f,) the channel estimator Ei from the first set of channel estimators 104 according to ZF estimation. The performance diagram is represented by the first curve 901.

In a second implementation form, the selector 108 selects for the 16 frequency taps (fi) having maximum signal power the channel estimator E₂ from the second set of channel estimators 106 according to MMSE estimation and for the remaining 16 frequency taps (f,) having minimum signal power the channel estimator Ei from the first set of channel estimators 104 according to ZF estimation. The performance diagram is represented by the second curve 902.

In a third implementation form, the selector 108 selects for the 20 frequency taps (fi) having maximum signal power the channel estimator E₂ from the second set of channel estimators 106 according to MMSE estimation and for the remaining 12 frequency taps (f,) having minimum signal power the channel estimator Ei from the first set of channel estimators 104 according to ZF estimation. The performance diagram is represented by the third curve 903. In a fourth implementation form, the selector 108 selects for the 24 frequency taps (fi) having maximum signal power the channel estimator E₂ from the second set of channel estimators 106 according to MMSE estimation and for the remaining 8 frequency taps (f,) having minimum signal power the channel estimator Ei from the first set of channel estimators 104 according to ZF estimation. The performance diagram is represented by the fourth curve 904. In a fifth implementation form, the selector 108 selects for all discrete frequency taps (fi) the channel estimator E2 from the second set of channel estimators 106 according to MMSE estimation. The performance diagram is represented by the fifth curve 905.

According to the diagram, up to 12 filter taps may use the ZF solution without performance degradation, see curves 905, 904 and 903 illustrating nearly the same low bit error rates. Fig. 10 shows a schematic diagram of a method for receiving an optical signal with two polarization components according to an implementation form. A computer program may be used to apply this method. In a first step 1002 of the method or the computer program, a full frame of the optical signal is sampled including the training sequence (TS) and data. The full frame is stored in a buffer. In a second step 1004 of the method or the computer program, framing detection is performed by detecting the received training sequence (TS). In a third step 1006 of the method or the computer program, a Fast Fourier Transformation (FFT) is applied to the training sequence (TS). In an implementation form, the training length, i.e. the length of the training sequence, is optimized for the FFT size. In an

implementation form, any other frequency transformation is used for the FFT. In a fourth step 1008 of the method or the computer program, each of the four channel components H^A(f) = [ H\_x H^A _yx; H\_y H^A _yy ] is estimated.

In a fifth step 1010, for each discrete frequency f, ZF estimation scheme (left path of the diagram) or MMSE estimation scheme (right path of the diagram) is chosen. When the ZF estimation scheme is chosen for a discrete frequency, in a sixth step 1012, the frequency component WzF(f) of the optical channel 1 10 is estimated according to the ZF solution, which is defined as W_ZF(f) = Η^Λ"1. When the MMSE estimation scheme is chosen for a discrete frequency, in a seventh step 1014, the received signal and noise power spectrum is estimated and in an eighth step 1016 the frequency component W_MivisE(f) of the optical channel 1 10 is estimated according to the MMSE solution, which is defined as W_MMSE(f) = Η^ΛΗ (Η^Λ Η^ΛΗ +

For both estimation schemes, in a ninth step 1018, equalization is performed by filtering the received data in a frequency domain (FD) filter implementation, wherein the channel estimation also directly provides a FD filtering function. In a tenth step 1020 an inverse Fast Fourier Transformation (IFFT) is applied to the obtained frequency components WzF(f) and WMMSE(f) which form a combined estimated channel W(f) in frequency domain depending on the frequency taps chosen in step 1010 to be processed by ZF and to be processed by MMSE. The combined channel W(f) is transformed in time domain by the IFFT and the channel impulse response w(t) of the optical channel 110 is obtained. In an eleventh step 1022, synchronization of the timing signal and the carrier with data aided (DA) methods processing from both sides is performed, wherein the synchronization uses the estimated channel impulse response w(t) obtained in step 1020.

For each frequency domain (FD) tap W(f), ZF or MMSE solution may be chosen. During initialization, when σ_η ² and a_s ² are not yet known, in an implementation form only ZF solution is chosen. This is also less complex and faster as there is less processing delay.

In an implementation form, the spectral power density of the received signal is calculated in a side processor which does not need to be a high-speed ASIC. Also the Eigenvalue analysis on basis of the estimated channel may be similarly performed. In an implementation form, spectral components with low magnitude or with high Eigenvalue spread are chosen to remain ZF filter taps. All others are upgraded to MMSE.

Typically, central taps follow the MMSE solution and outer taps may be ZF taps without performance degradation. Therefore, in an implementation form, ZF taps are turned into MMSE taps starting from the center (DC, 0 Hz) to the high frequency components. In an implementation form, the signal quality, i.e. error- vector magnitude (EVM), quality factor (Q-factor), pre Forward-Error-Correction Bit Error Rate (pre-FEC BER) and others and/or combinations thereof are an indicator for the selector 108 how many taps have to be turned from ZF to MMSE.

General purpose computers may implement the foregoing methods and computer programs, in which the computer housing may house a CPU (central processing unit), memory such as DRAM (dynamic random access memory), ROM (read only memory), EPROM (erasable programmable read only memory), EEPROM

(electrically erasable programmable read only memory), SRAM (static random access memory), SDRAM (synchronous dynamic random access memory), and Flash RAM (random access memory), and other special purpose logic devices such as ASICs (application specific integrated circuits) or configurable logic devices such GAL (generic array logic) and reprogrammable FPGAs (field programmable gate arrays).

Each computer may also include plural input devices (for example, keyboard, microphone and mouse), and a display controller for controlling a monitor.

Additionally, the computer may include a floppy disk drive; other removable media magneto optical media); and a hard disk or other fixed high-density media drives, connected using an appropriate device bus such as a SCSI (small computer system interface) bus, and Enhanced IDE (integrated drive electronics) bus, or an Ultra DMA (direct memory access) bus. The computer may also include a compact disk reader, a compact disk reader/writer unit, or a compact disc jukebox, which may be connected to the same device bus or to another device bus.

The invention envisions at least one computer readable medium. Examples of computer readable media include compact discs, hard disks, floppy disks, tape, magneto optical disks, PROMs (for example, EPROM, EEPROM, Flash EPROM), DRAM, SRAM, SDRAM. Stored on any one or on a combination of computer readable media is software for controlling both the hardware of the computer and for enabling the computer to interact with other elements, to perform the functions described above. Such software may include, but is not limited to, user

applications, device drivers, operating systems, development tools, and so forth. Such computer readable media further include a computer program product including computer executable code or computer executable instructions that, when executed, causes a computer to perform the methods disclosed above. The computer code may be any interpreted or executable code, including but not limited to scripts, interpreters, dynamic link libraries, Java classes, complete executable programs, and the like.

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 . Apparatus (100) for processing a first input signal (1 12) and a second input signal (1 14), the first input signal (112) representing a first polarization component of an optical signal, the second input signal (1 14) representing a second polarization component of the optical signal, the optical signal comprising an influence of an optical communication channel (1 10), the apparatus (100) comprising: a Fourier transformer (102) for transforming the first input signal (112) into a first transformed signal (122) in frequency domain, and for transforming the second input signal (1 14) into a second transformed signal (124) in frequency domain, the first transformed signal (122) and the second transformed signal (124) respectively having a number of frequency components at discrete frequencies (fi,

a first set of channel estimators (104) for estimating a set of frequency

components (H(fi ), ... ,

of the optical communication channel (110) according to a first channel estimation scheme based on the first (122) and/or the second (124) transformed signals, each channel estimator (Ei) in the first set of channel estimators (104) being configured to estimate a frequency component (Η(ί,)) of the optical communication channel (1 10) at a single discrete frequency (f,); a second set of channel estimators (106) for estimating a set of frequency components (H(fi ), ... ,

of the optical communication channel (1 10) according to a second channel estimation scheme based on the first (122) and/or the second (124) transformed signals, each channel estimator (E2) in the second set of channel estimators (106) being configured to estimate a frequency component (Η(ί,)) of the optical communication channel (1 10) at a single discrete frequency (f,); and a selector (108) for selecting for each discrete frequency (f,) from the number of discrete frequencies (fi,

either a channel estimator (Ei) from the first set of channel estimators (104) or a channel estimator (E2) from the second set of channel estimators (106) for estimating the frequency component (Η(ί,)) of the optical communication channel (1 10) at a discrete frequency (f,).

2. The apparatus (100) of claim 1 , wherein the selector (108) is configured to select either a channel estimator (Ei ) from the first set of channel estimators (104) or a channel estimator (E2) from the second set of channel estimators (106) at a discrete frequency upon a basis of a comparison of a magnitude of a frequency component of the first transformed signal (122) with a magnitude threshold at the discrete frequency, or upon a basis of a comparison of a magnitude of a frequency component of the second transformed signal (124) with a magnitude threshold at the discrete frequency, or upon a basis of a comparison of a magnitude of a frequency component of a combined frequency component comprising the frequency component of the first transformed signal (122) and the second transformed signal (124) with a magnitude threshold.

3. The apparatus (100) of claim 1 or 2, wherein the selector (108) is configured to select either a channel estimator (Ei ) from the first set of channel estimators (104) or a channel estimator (E2) from the second set of channel estimators (106) at a discrete frequency upon a basis of at least one of: a distribution of eigenvalues of an estimate of a channel matrix, the channel matrix comprising estimates of the frequency components of the optical communication channel.

4. The apparatus (100) of any of the preceding claims, wherein the selector (108) is configured to select either a channel estimator (Ei) from the first set of channel estimators (104) or a channel estimator (E2) from the second set of channel estimators (106) at a discrete frequency upon a basis of a comparison of a magnitude of a frequency component of the first transformed signal (122) at the discrete frequency with a magnitude of a frequency component of the first transformed signal (122) at another discrete frequency, or upon a comparison of a magnitude of a frequency component of the second transformed signal (124) at the discrete frequency with a magnitude of a frequency component of the second transformed signal (124) at another discrete frequency, or upon a basis of a comparison of a magnitude of a frequency component of a combined frequency component comprising the frequency component of the first transformed signal (122) and the second transformed signal (124) with a combined frequency component at another discrete frequency.

5. The apparatus (100) of any of the preceding claims, wherein the selector (108) is configured to select either a channel estimator (Ei) from the first set of channel estimators (104) or a channel estimator (E₂) from the second set of channel estimators (106) at a discrete frequency upon a basis of a feed-forward criterion, in particular a power spectral density or an eigenvalue distribution of at least one of the input signals, or upon a basis of a feedback-criterion, in particular a reception error magnitude.

6. The apparatus (100) of any of the preceding claims, wherein the selector (108) is configured to select a channel estimator (Ei) from the first set of channel estimators (104) for a coarse channel estimation, and to select a channel estimator (E₂)from the second set of channel estimators (106) for a fine channel estimation after a predetermined period of time.

7. The apparatus (100) of any of the preceding claims, each channel estimator (Ei, E₂) from the first set of channel estimators (104) and from the second set of channel estimators (106) comprising a first input for receiving a frequency component of the first transformed signal (122), a second input for receiving a frequency component of the second transformed signal (124), a first output for providing a real value of a frequency component of the optical communication channel (1 10), and a second output for providing an imaginary value of the frequency component of the optical communication channel (1 10).

8. The apparatus (100) of any of the preceding claims, each channel estimator (Ei, E₂) from the first set of channel estimators (104) or from the second set of channel estimators (106) being configured to estimate a first channel component (Hxx(f)) associated with the first polarization (X pol.), a second channel component (Hyy(f)) associated with the second polarization (Y pol.), a third channel component (H_Xy(f)) representing a crosstalk from the first polarization (X pol.) towards the second polarization (Y pol.) and a fourth channel component (H_yx(f)) representing a crosstalk from the second polarization (Y pol.) towards the first polarization (X pol.), each channel estimator (Ei, E₂) being further configured to superimpose the first (Hxx(f)) and the fourth (H_yx(f)) channel component to obtain a real value of the frequency component of the optical communication channel (1 10), and to superimpose the second (H_yy(f)) and the third (H_xy(f)) channel component to obtain an imaginary value of the optical communication channel (1 10).

9. The apparatus (100) of any of the preceding claims, the Fourier transformer (102) comprising the number of output taps for providing the number of frequency components of the first transformed signal (122), and the number of output taps for providing the number of frequency components of the second transformed signal (124), wherein each channel estimator (Ei, E₂) comprises two inputs, and wherein the selector (108) is configured to couple two output taps of the Fourier

transformer (102) associated with the same discrete frequency to two inputs of a channel estimator (Ei) from the first set of channel estimators (104) or of a channel estimator (E₂) from the second set of channel estimators (106).

10. The apparatus (100) of any of the preceding claims, wherein the first channel estimation scheme and the second channel estimation scheme are different channel estimation schemes.

1 1 . The apparatus (100) of any of the preceding claims, wherein the first channel estimation scheme and the second channel estimation scheme are one of the following channel estimation schemes: zero forcing estimation, minimum mean least squares estimation, least mean squares estimation, decision-directed estimation.

12. The apparatus (100) of any of the preceding claims, wherein each channel estimator (Ει, E₂) from the set of first channel estimators (104) or from the set of second channel estimators (106) is configured to perform a data aided frequency domain channel estimation.

13. The apparatus (100) of any of the preceding claims, further comprising an inverse Fourier transformer (507) for inversely transforming the outputs of the channel estimators (Ει, E₂) to obtain an estimate of an impulse response of the optical communication channel (1 10) in time domain.

14. An optical receiver, comprising: a coherent front end (501 ) for receiving an optical signal in a transmission band and for providing a first analog signal and a second analog signalin a base band or in an intermediate frequency band, the first analog signal representing a first polarization component (X pol.) of the optical signal, the second analog signal representing a second polarization component (Y pol.) of the optical signal; an analog-digital converter (501 ) for quantizing and discretizing the first analog signal to provide the first input signal (112) and for quantizing and discretizing the second analog signal to provide the second input signal (1 14); and the apparatus (100) of any of the claims 1 to13 for channel estimation.

15. Method (300) for processing a first input signal (1 12) and a second input signal (1 14), the first input signal (1 12) representing a first polarization component (X pol.) of an optical signal, the second input signal (1 14) representing a second polarization component (Y pol.) of the optical signal, the optical signal comprising an influence of an optical communication channel (1 10), the method comprising: Fourier transforming (301 ) the first input signal (1 12) into a first transformed signal (122) in frequency domain, and Fourier transforming (303) the second input signal (1 14) into a second transformed signal (124) in frequency domain, the first transformed signal (122) and the second transformed signal (124) respectively having a number of frequency components at discrete frequencies; for each discrete frequency, selecting (305) either a first channel estimation scheme for estimating a frequency component of the optical communication channel (110) at a discrete frequency based on the first and/or the second transformed signals (122, 124), or selecting a second channel estimation scheme for estimating the frequency component of the optical communication channel (1 10) at the discrete frequency based on the first and the second transformed signals (122, 124).

16. Computer program with a program code for performing the method of claim 15 when run on a computer.