Method for digitally compensating a phase response of an optical channel

BACKGROUND OF THE INVENTION

The present invention relates to a method for digitally compensating the phase response of an optical channel in frequency domain by using filter banks and to a coherent optical receiver applying such method.

In coherent optical transmission system, chromatic dispersion (CD) accumulates during fiber transmission and causes severe inter-symbol-interference (ISI), which brings severe degradation to the system. The characteristics of CD can be described as an all-pass transfer function with parabolic phase behaviour. This results in a linear group delay, wherein the group delay is defined as minus the derivative of the phase response.

Therefore, digital compensation filters can be implemented in frequency domain and in time-domain. Any other channel impairment with a phase response can be compensated.

Current frequency-domain (FD) CD compensation covers the largest part of the whole gate-count in the application specific integrated circuit (ASIC) for digital equalization and synchronization of digital coherent receivers.

For implementing the digital CD compensation stage, currently two processing methods are used: Overlap-discard frequency domain equalization (Overlap-discard FD EQ) and Cyclic-prefix frequency domain equalization (Cyclic pre-fix FD EQ). In Overlap-discard FD CD compensation, the serial data stream is cut into blocks of e.g. 512 samples, and each block is extended by an overlap with the adjacent previous and subsequent block. The total overlap at least equals to the channel ISI spread, which depends on the bandwidth B of the channel. The spread in terms of symbols can be approximated by /V _/S i = R B D _C D 8 ^"6 , where R refers to the Baudrate given in GBaud, D _C D refers to the accumulated CD in the optical transmission given in ps/nm, and B refers to the (full-band) bandwidth of the channel given in GHz. The term 8 ^"6 in ms accounts for scaling terms including the speed of light (3x10 ⁸ m/s) and the carrier wavelength (1150 nm) and results from 8x 10 ^"6 ms= 10 ⁹ /s x 10 ⁹ /s x 10 ^"12 s/(10 ^"9 m) x (1550 x 10 ^"9 m) ² /(3 x 10 ⁸ m/s). At each side of the block half overlap is required as the channel is symmetric. For 512 samples, typically an overlap of 25 % at each side is required which equals a total overlap of 50% corresponding to 512 samples. This provides parallel blocks, where each block size refers to the original block size increased by the overlap, i.e. a total block size of 1024 samples. The block length of 512 samples is optimized for fast Fourier transform (FFT), FD CD compensation and inverse FFT (I FFT) when implementing an FFT-size of 1024. After I FFT, the overlap is removed and the adjacent blocks are serialized to the time-domain (TD) signal stream. Clearly, the overlap leads to an increase in the size of the FFT and accordingly the FD CD filter. Overlap-discard method is also known as overlap-save method.

As an alternative to the overlap discard-method, cyclic prefix can be added to the signal. However as cyclic-prefix has to be added at the transmitter, a different transmitter design is required making cyclic-prefix FD EQ incompatible to overlap-discard FD EQ. In the cyclic prefix case, no overlap of the input blocks at the receiver is required as in the overlap-discard method. However, an overhead is required in the transmitted signal accordingly. The overlap length and the overhead length follow the channel memory requirement. A system with 50% overlap requirement would require 100% overhead, which would double the required bandwidth.

The purpose of cyclic prefix and overlap is the same: In both cases, block interference due to the cyclic convolution implemented via the FFT/IFFT is avoided. Cyclic prefix adds overhead to the transmitted signal but keeps the FFT-size low and the rate in which the FFT is implemented is low. Overlap-discard processing adds overhead to the block-wise processing increasing the FFT size and the rate in which the FFT is implemented and accordingly to the complexity of the processing.

As a typical example, the system requirement for uncompensated (non-dispersion managed) long-haul 112Gbit/s (28 GBaud) optical transmission over 2000 km standard single-mode fiber (SSMF) asks for a CD tolerance up to +/-30.000 ps/nm, which refers to an ISI of about 240 symbols. After Analog-Digital Conversion (ADC) with 2

samples/symbol, for example, an FFT size of 1024 samples is required, which are 256 symbols x 2 samples/symbol x 2 for the overlap-discard implementation.

It is clearly noticed that a 50% overlap is needed for processing with overlap-discard method. In the cyclic-prefix implementation, an FFT size of 512 samples can be used but the required net data rate of 112Gbit/s can not be fulfilled within the same bandwidth.

For the design of next generation optical systems, there is a requirement to go beyond this tolerance, e.g. to extend the long-haul reach to 40.000 ps/nm. This can be done either by employing a larger FFT size of 2048 samples inducing a complexity increase for ASIC implementation or by increasing the overlap factor such that it covers the increased channel memory length, e.g. by an increase in a factor of 4/3. Given the same FFT size, the net amount of equalized data after discarding the overlap is reduced by that factor of 3/4. This would require an increase in the block processing rate by a factor of 4/3.

Furthermore, for uncompensated ultra-long-haul transmission and sub-marine systems, CD tolerance of more than 100.000 ps/nm is required, which cannot be realized with acceptable complexity with the aforementioned two methods.

The large gate-count of the FD CD compensation also relates to large power consumption and heat dissipation. It is desired to reduce the gate count in future generations in order to save operational expenses or in order to spend more complexity in forward error correction or advanced equalization techniques for nonlinearity mitigation. Additionally, there is a mismatch between the processing rate which is about 500MHz and the block-rate, e.g. 56 GSamples/s are arranged in 50%-overlapping blocks of 1024 samples, which yields a block-rate of about 100MHz. In the optimum case, a block-rate of 500 MHz should be achieved in order to keep the used chip-area low, which also relates to lower gate-count and power consumption.

We propose another method for FD CD EQ based on filter banks as a valuable

generalization of the overlap discard method. The Filter Bank (FB) based FD equalizer is composed by an analysis FB (AFB) that decomposes the high rate signal into narrow subbands, the FD per-subband equalizer and the synthesis FB (SFB) that reconstructs the high rate signal. The AFB and SFB are efficiently implemented with the help of the FFT, IFFT and polyphase decomposition. The AFB is realized by a polyphase network and an FFT and the SFB is realized by an IFFT and a polyphase network. The polyphase network is composed by parallel FIR filters, the so called polyphase components of the prototype filter. In the polyphase network of the AFB, the digital serial signal is first converted into 50% overlapping blocks of parallel samples passed into parallel paths which differ by the according sampling phase, where each parallel path represents a down-sampled representation of the serial input signal. The above example with parallelization of factor 1024 refers to a 512-fold down-sampling in each parallel path. As a next step in the AFB, the samples in each parallel path or sub-band are filtered by the polyphase components of the prototype filter, which are static or channel adaptive multi-tap filters individual to each path. The obtained filtered parallel signals are transformed into frequency domain by an FFT of size N _SUB .

Decomposing the signal into different sub-spectra having a (sub-band) bandwidth of AB=B/N _SUB by a N _SUB -point FFT, an ISI of ΔΛ/, _δ/ = R Δβ D _C D 8 ^"6 per sub-band is relevant. For equalization, this would require a linear FIR filter with an impulse response of Δ/V/si in each sub-band, where ΔΛ/ _/δ/ * N _sampies / _S y _mb0 *2l N _sub corresponds to the number of taps per sub-band. For a (subband) bandwidth of ΔΒ = 1/(R D _C D 8 ^"6 ) there is practically no ISI in the sub-band domain, which allows equalization with a single tap filter per sub-band. In the example above (R=28GBaud, D _C D =30.000 ps/nm), ΔΛ/ _/δ/ ≤1 can be achieved separating a 36 GHz bandwidth signal into N _sub =245 sub-bands. In a digital implementation, it is multiplied by the sampling factor, e.g. 2 samples per symbol, and extended by the overhead, e.g. 50%, to yield the requirement for a 1024 FFT. In the synthesis filter bank, the equalized signal is first transformed to the time domain by an inverse FFT of size N _sub . Then, at the input of the polyphase network, the signal, which is still represented by parallel samples, is first filtered with the polyphase components. Finally a TD serialized output is obtained by block overlapping the output blocks.

Implementations of the digital CD compensation stage in coherent optical receivers which are applying FD filtering use a linear transfer function in the frequency domain which is the processing between the FFT and the I FFT. Such implementations use a FD CD

compensation filter with a single complex multiplication per spectral component. This is the preferred FD CD compensation as the complexity of the FFT grows more slowly than the complexity of a time-domain FIR filters. Such implementations do not make use of the fact that CD induces a group delay (or phase) distortion, which could be compensated by according group delay (or phase) equalizers. For this reason, also multi-tap FD equalizers have not been investigated for optical communications so far.

The overlap-discard method can be interpreted as a filter bank structure with a trivial prototype filter in both AFB and SFB with the particularity that in this case the prototypes have different lengths in the AFB and SFB. Namely, the prototype of the SFB has half the length of the prototype of the AFB.

In summary, the existing CD compensation implementations for coherent optical systems require a large FFT-size defined by the ISI-spread and additional amount of overhead or overlap. In typical systems, the overhead is about 50% of the block length being processed such that the FFT-size covers twice the ISI-spread. On the other hand, the bandwidth increase by use of cyclic-prefix with 100% overhead cannot be tolerated in bandwidth limited transmission system. However, by using filter bank architectures, a reduced FFT-size together with a multi-tap FD filtering can be implemented to tolerate high CD values although the non trivial polyphase filters might induce an additional complexity. SUMMARY OF THE INVENTION

It is the objective of the invention to provide a concept for a wide-range and accurate chromatic dispersion compensation technique in a coherent optical receiver. A low- complexity implementation is desired which is able to accurately compensate for dispersion effects arising from group delays between different frequency components.

This objective is achieved by the features of the independent claims. Further

implementation forms are apparent from the dependent claims, the description and the figures.

This objective 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 the overlap of an overlap-discard frequency domain equalization or the overhead of a cyclic-prefix frequency domain equalization guarantees that there is no interference between signal blocks when being processed, which arises due to processing in the frequency domain or to the channel memory and that the signal can be reconstructed. In a filter bank structure, the input signal is first processed in the polyphase network which, together with the FFT, performs a sub-band

decomposition. In each sub-band, the signal is processed at a lower sample rate

(downsampling).

Filter bank processing with modulated prototype filters is known from multi-carrier transmission systems. The principle can be understood by taking the sampled receive signal and decomposing it into N parallel streams. In each parallel path k, each (k+N)th symbol is represented, which appears as a "downsampled" sub-signal stream, where each parallel path refers to a different sampling phase. Downsampling can cause aliasing.

Therefore, the prototype filter has to guarantee that there is a minimal subband interference or aliasing. OFDM systems, however, require a distinct architecture where the transmitter uses an IFFT and the receiver uses an FFT to be compatible with each other. Such an architecture is different for single-carrier transmission in optical networks.

Aspects of the invention combine the properties of a filter bank efficiently implemented with a polyphase network and FFT and IFFT blocks generating parallel sub-bands with a multi- tap FD phase equalizer.

An efficient filter bank structure should still eliminate intra-block interference and aliasing: The AFB of the efficient filter bank structure decomposes the received signal into parallel sub-bands , which can be equalized separately. The equalized FD or sub-bands signals are then combined in the SFB and serialized. This architecture still requires 50% of block overlap. By this new design architecture the same FFT-size including a marginal increase in the overall complexity due to polyphase filters is obtained at a larger channel memory tolerance, e.g. CD tolerance, than comparable designs. Alternatively, a reduced FFT-size is obtained for a given CD compensation requirement.

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,

ISI: inter-symbol-interference,

PDM: Polarization Division Multiplexing,

(D)QPSK: (Differential) Quadrature Phase Shift Keying FFT: Fast Fourier Transform,

IFFT: Inverse Fast Fourier Transform,

DSP: Digital Signal Processing,

ASIC: Application Specific Integrated Circuit,

ADC: Analog/Digital converter,

LO: Local Oscillator,

DA: Data-aided,

NDA: Non-data-aided,

WDM: Wavelength Division Multiplex,

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

BER: Bit error ratio,

OSNR: Optical signal-to-noise ratio,

CSD: Canonical signed digit,

FB: Filter banks

FIR: Finite impulse response,

MR: Infinite impulse response,

PN: polyphase network,

AF: analysis filter of a polyphase network,

SF: synthesis filter of a polyphase network,

AFB: analysis filter bank

SFB synthesis filter bank

EQ: equalizer, TX: transmitter,

RX: receiver, OA, OLA: overlap-add.

According to a first aspect, the invention relates to a method for digitally compensating the phase response of an optical channel in FD or in sub-bands by using filter banks, the method comprising: partitioning a time-domain digital signal representing an optical signal transmitted over the optical channel into overlapping sub-sequences; decomposing the overlapping sub-sequences into polyphase signal components; filtering the decomposed signal components in the polyphase network obtaining the filtered polyphase components; transforming the filtered polyphase components in the FD by using an FFT obtaining sub- band signals; equalizing the sub-band signals by using a multi-tap equalizer obtaining equalized sub-band signals; transforming the equalized frequency sub-band signals back into time domain by using an IFFT obtaining equalized time domain; filtering the equalized time domain in the polyphase network obtaining equalized sub-sequences; and

reconstructing the phase compensated signal by applying a block overlap procedure to the equalized sub-sequences.

In the AFB, the input time domain serial signal is first parallelized and then downsampled with a sampling rate that is double the size of the FFT that is applied after the down- sampled parallel samples have been filtered in the polyphase network. Thus, the signal processing speed can be reduced according to the down-sampling rate. The independent blocks of the sub-bands at the output of the AFB are equalized with a multi-tap equalizer that is realized by an FIR filter, e.g. realizing a group delay filter, within each sub-band path. The filter coefficients can be considered to be static to compensate non-time-varying impairments or adaptive to track time-varying distortions.

The FFT is a standard algorithm. A lot of implementations exist in hardware and software which can be adapted for the application to CD compensation. The FFT is highly computational efficient. A large FFT size provides better robustness against distortions over a wider range.

In a first possible implementation form of the method according to the first aspect, the output of the sub-band equalizer is a function of its input parameterized according to the phase response to be compensated.

In a second possible implementation form of the method according to the first

implementation form of the first aspect, the sub-band equalizer function is a linear FIR filter. An FIR filter structure is easy to implement and is stable due to the absence of recursions.

In a third possible implementation form of the method according to the first implementation form of the first aspect, the function is a linear MR filter. The MR filter structure provides a fast convergence at reduced complexity, only few coefficients are required to implement a filter with specified phase response.

In a fourth possible implementation form of the method according to any of the preceding implementation forms of the first aspect, the sub-band linear filter possesses one of very few non-zero multipliers.

A sub-band filter having only one or a few non-zero coefficients has a low complexity. It provides the desired phase compensation due to the combination of an adjustable delay which is realized by the position of the non-zero coefficients and a phase correction which is realized as the inverse of the phase of the channel.

In a fifth possible implementation form of the method according to the first aspect as such or according to the any of the preceding implementation forms of the first aspect, the polyphase filters of the polyphase network are efficiently realized with lattice structures.

A lattice structure provides robustness to the quantization of the coefficients of the polyphase components, allowing to represent them with very short word-length and, consequently, reducing the implementation complexity and chip area.

According to a second aspect, the invention relates to a coherent optical receiver for receiving a time-domain digital signal representing an optical signal transmitted over an optical channel, the coherent optical receiver comprising: a processor configured for compensating a phase response of the optical channel according to the method according to the first aspect as such or according to the any of the preceding implementation forms of the first aspect.

After polyphase decomposition, polyphase network and FFT, parallel sub-bands are obtained. These sub-band signals can be regarded as down-sampled spectral

representation of the signal, where the FFT-size is related to the down-sampling rate. Thus, the signal processing speed can be reduced according to the down-sampling rate and the size of the FFT can be reduced according to the number of polyphase

components. The multi-tap equalizer can be efficiently realized by a phase compensating filter within each sub-band. The FFT is a standard algorithm. A lot of implementations exist in hardware and software which can be adapted for application for CD compensation. The FFT is highly computational efficient. Still, large FFTs are complex to be implemented for high-speed processing. A larger FFT size provides better robustness against distortions over a wider range.

According to a third 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 112-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.

In an implementation form, the filter bank structure is applied to chromatic dispersion FD equalization. In an implementation form, the filter bank structure is applied to PMD FD equalization. For PMD FD equalization, the filter bank structure requires additional complexity compared to CD FD equalization. In an implementation form which is suitable for both CD and PMD equalization, the filtering stage of the equalizer is realized by a 2x2 multi-input multi-output (MIMO) structure.

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 digitally compensating a phase response of an optical channel according to an implementation form;

Fig. 2 shows a block diagram of a coherent optical transmission system comprising a coherent receiver applying the method illustrated in Fig. 1 ;

Fig. 3 shows a block diagram of a coherent optical receiver according to an

implementation form;

Fig. 4 shows a schematic diagram of a method for digitally compensating a phase response of an optical channel according to an implementation form;

Fig. 5 shows a block diagram of a device for compensating a phase response of an optical channel according to an implementation form;

Fig. 6 shows a block diagram of an FIR lattice structure of a polyphase component according to an implementation form;

Fig. 7 shows a plot comparing performance of prior art with polyphase network and multi- tap FD filter according to an implementation form.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Fig. 1 shows a schematic diagram of a method 100 for digitally compensating a phase response of an optical channel in frequency domain by using filter banks according to an implementation form. The method 100 comprises: partitioning 101 a time-domain digital signal 102 representing an optical signal transmitted over the optical channel into overlapping sub-sequences; decomposing 103 the overlapping sub-sequences into signal components; filtering 105 the decomposed signal components in the polyphase network obtaining polyphase filtered signals; transforming 107 the polyphase filtered signals into frequency domain by using a Fast Fourier Transform obtaining frequency sub-band signals; equalizing 109 the frequency sub-band signals by using a sub-band equalizer obtaining equalized frequency sub-band signals; transforming the equalized frequency sub-band signals back into time domain by using an inverse Fast Fourier Transform obtaining equalized signals; filtering 113 the equalized signals in the polyphase network obtaining equalized filtered sub-sequences; and reconstructing 115 the overlapping subsequences compensated by the inverse of the phase response of the optical channel.

In an implementation form the partitioning 101 of a time-domain digital signal 102 into overlapping sub-sequences is done with a 50 percent overlap factor.

The decomposition 103 of a signal into decomposed signal components is performed by applying the operation of decimation at the input of the analysis filter bank. By filtering 105 the decomposed signal components in the polyphase network, polyphase filtered signals are obtained. By using this decomposition a filter bank structure with M branches, i.e. number of sub-bands, can be defined. Lower sampling rates as can be seen in branches of the filter bank. The processing in the lower sampling rate is achieved by means of the efficient implementation of the complex modulated filter bank. In the case of complex modulated filter banks, the efficient implementation is obtained with the use of the polyphase decomposition of the prototype filter and FFT/IFFT.

In an implementation form, an overlapping sequence for reconstructing 115 from the equalized sub-sequences is done with a 50 percent overlap factor. In an implementation form the polyphase components in the polyphase network can be implemented by lattice structures.

In an implementation form the prototype filter forming the polyphase components can be optimized according to the channel.

The lattice structure allows an implementation of the polyphase components that has very low sensitivity to the quantization of the coefficients, allowing the use of very short word- length for the representation of the multipliers.

Fig. 6 illustrates a lattice filter in FIR structure. The values ko, ki , ... k _n represent filter coefficients by which the respective branches are multiplied and the blocks designated by „T" are delay elements delaying the signal by the time interval T corresponding to the sampling period.

Thus, using the lattice filter for implementing the polyphase components of the polyphase network as described above is computational effective and low sensitive solution.

In an implementation form, the equalizing 109 the frequency sub-band signals by using a sub-band equalizer is performed by using an FIR filter. In an implementation form, the equalizing 109 the frequency sub-band signals by using a sub-band equalizer is performed by using an MR filter.

Fig. 2 shows a block diagram of a coherent optical transmission system 202 comprising a coherent receiver 200 applying the method as described with respect to Fig. 1 . The coherent optical transmission system 202 comprises an optical sender 201 for providing an optical signal 250, an optical channel 209 for transmitting the optical signal 250 and a coherent receiver 200 for receiving a received optical signal 252 which corresponds to the optical signal 250 transmitted over the optical channel 209 and influenced by the optical channel 209.

The optical sender 201 comprises a laser diode 203 for providing an optical carrier signal with a center frequency f _T and a given laser line-width 204. The optical sender 201 further comprises a QPSK modulator 205 for modulating the optical carrier signal with a user data signal to provide a modulated optical data signal. The optical sender 201 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 250 to be transmitted.

The optical channel 209 comprises a plurality of amplifier stages and optical fibers for transmitting the optical signal 250. An output of the optical channel 209 is coupled to an input of the coherent receiver 200, such that the coherent receiver 200 receives the received optical signal 252 which corresponds to the optical signal 250 transmitted over the optical channel 209 at its input.

The coherent receiver 200 comprises a de-multiplexer 223, a polarization beam splitter (PBS) 225, two 6-port 90-degree optical hybrids 227, 229, two sets of balanced detectors 233, two sets of trans-impedance amplifiers (TIA) 235, four analog-digital converters (ADC) 237 and a digital signal processing device (DSP) 239, 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 223 is coupled to the input port of the coherent receiver 200 and receives the received optical signal 252 at its input. The de-multiplexer 223 demultiplexes the received optical signal 252 into a plurality of demultiplexed optical signals following a plurality of receiving paths in the coherent receiver 200. Fig. 2 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 225 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 227 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 229. A second input, which is a LO input, of the first 6-port 90- degree optical hybrid 227 receives a Local Oscillator signal from a laser diode 231 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 229.

The 90° Optical Hybrids 227, 229 comprise two inputs for signal and LO and four outputs mixing signal and LO. The 90° Optical Hybrids 227, 229 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 227, 229 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 233. 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 227, 229 mixes the incoming signal with the four quadrature states associated with the reference signal in the complex-field space. Each of the optical hybrids 227, 229 then delivers the four light signals to two pairs of balanced detectors 233 which detect a respective optical signal and provide a corresponding electrical signal to the succeeding set of trans-impedance amplifiers 235, one trans-impedance amplifier for each pair of balanced detectors 233. The electrical signals amplified by the trans-impedance amplifiers 235 are analog-digitally converted by the set of AID converters 237 and then provided as digital signals 254 to a digital signal processing 239. 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 237 and digital signal processing 239 may be preferably integrated on a single-chip.

The optical system 202 is based on a coherent detection scheme which detects not only the optical signal's amplitude but phase and polarization as well. With the optical coherent detection system's 202 increased phase compensation capability and spectral efficiency, more data can be transmitted within the same optical bandwidth. Moreover, because coherent detection allows an optical signal's phase and polarization to be detected and compensated, transmission impairments which previously presented challenges to accurate data reception, can be mitigated electronically when the received optical signal 252 is converted into the electronic domain.

The optical system 202 provides a method to stabilize frequency difference between the sender 201 and the receiver 200 within close tolerances. A Local Oscillator Frequency Offset is determined as f _R -f _T , wherein f _R is the frequency of the received optical signal 252 and f _T is the frequency of the optical signal 250 to be transmitted over the optical channel 209. The optical system 202 further provides the capability to minimize or mitigate frequency chirp or other signal inhibiting noise and the availability of an "optical mixer" to properly combine the signal and the local amplifying light source or local oscillator (LO). For an improved operation of the optical system 202, the DSP part 239 compensates the phase response of the optical channel 209 by using the received optical signal 252 according to the method as described with respect to Fig. 1 . This results in a higher precision of the optical receiver 200 compared to an optical receiver that does not apply such a phase compensation method. A coherent optical receiver 200 implementing the method as described with respect to Fig. 1 offers the following advantages: • An increase of receiver sensitivity compared to receivers not implementing phase compensation by filter banks according to the method described with respect to Fig. 1 and therefore, permitting longer transmission distances.

• Increasing the modulation schemes, i.e. the degree of the modulation scheme, of complex modulation formats such as BPSK, QPSK or 16QAM.

• Higher precision in concurrent detection of a light signal's amplitude, phase and polarization allowing more detailed information to be conveyed and extracted, thereby increasing tolerance to network impairments, such as chromatic dispersion and polarization mode dispersion, and improving system performance.

• Better rejection of interference from adjacent channels in Dense Wavelength Division Multiplex (DWDM) systems, allowing more channels to be packed within the transmission band.

• Higher degree of security for secured communications.

Fig. 3 shows a block diagram of a coherent optical receiver 300 for receiving a time- domain digital signal 252 representing an optical signal 250 transmitted over an optical channel 209 according to an implementation form. The coherent optical receiver 300 comprises a processor 301 for compensating a phase response of the optical channel 209 according to the method 100 as described with respect to Fig. 1 . The optical channel 209, the time-domain signal 252 and the optical signal 250 may correspond to the optical channel, the time-domain signal and the optical signal as described with respect to Fig. 2. In an implementation form, the processor 301 is a digital signal processor or a side- processor of a digital signal processor. In an implementation form, the processor 301 is a micro-controller or a microprocessor. In an implementation form, the processor 301 is an application specific integrated circuit (ASIC). In an implementation form, the processor 301 comprises an ASIC part and a digital signal processor part.

Fig. 4 shows a schematic diagram of a method 400 for digitally compensating a phase response of an optical channel in frequency domain by using a filter bank 405, 413 according to an implementation form. The polyphase network 405 may correspond to a polyphase network as described with respect to Fig. 1 .

The method 400 comprises: partitioning 401 a time-domain digital signal 402 representing an optical signal transmitted over the optical channel into overlapping sub-sequences 402a, 402b, 402c. The time-domain digital signal 402 is partitioned into an exemplary number of five blocks designated by the numbers 1 to 5. A first sub-sequence 402a is obtained by selecting the first and the second blocks with numbers 1 and 2. A second subsequence 402b is obtained by selecting the second and the third blocks with numbers 2 and 3. A third sub-sequence 402c is obtained by selecting the third and the fourth blocks with numbers 3 and 4.

The method 400 further comprises: decomposing 403 the overlapping sub-sequences 402a, 402b, 402c in decomposed signal components 404a, 404b, 404c, 404d, 404e. An exemplary number of five decomposed signal components is obtained from the

overlapping of sub-sequences by sub-sampling the overlapping sub-sequences as follows: a last element of the third sub-sequence 402c constitutes the first element of the first decomposed signal component 404a, a last element of the second sub-sequence 402b constitutes the second element of the first decomposed signal component 404a and a last element of the first sub-sequence 402a constitutes the third element of the first

decomposed signal component 404a. A second-last element of the third sub-sequence 402c constitutes the first element of the second decomposed signal component 404b, a second-last element of the second sub-sequence 402b constitutes the second element of the second decomposed signal component 404b and a second-last element of the first sub-sequence 402a constitutes the third element of the second decomposed signal component 404b. A third-last element of the third sub-sequence 402c constitutes the first element of the third decomposed signal component 404c, a third-last element of the second sub-sequence 402b constitutes the second element of the third decomposed signal component 404c and a third-last element of the first sub-sequence 402a constitutes the third element of the third decomposed signal component 404c. A second element of the third sub-sequence 402c constitutes the first element of the fourth decomposed signal component 404d, a second element of the second sub-sequence 402b constitutes the second element of the fourth decomposed signal component 404d and a second element of the first sub-sequence 402a constitutes the third element of the fourth decomposed signal component 404d. Afirst element of the third sub-sequence 402c constitutes the first element of the fifth decomposed signal component 404e, a first element of the second sub-sequence 402b constitutes the second element of the fifth decomposed signal component 404e and a first element of the first sub-sequence 402a constitutes the third element of the fifth decomposed signal component 404e.

The method 400 further comprises: filtering 405 the decomposed signal components 404a, 404b, 404c, 404d, 404e in the polyphase network 405 obtaining polyphase filtered sub- signals 406. The first decomposed signal component 404a is filtered with a first polyphase component AF1 of the polyphase network. The second decomposed signal component 404b is filtered with a second polyphase component AF2 of the polyphase network. The third decomposed signal component 404c is filtered with a third polyphase component AF3 of the polyphase network. The fourth decomposed signal component 404d is filtered with a fourth polyphase component AF4 of the polyphase network. The fifth decomposed signal component 404e is filtered with a fifth polyphase component AF5 of the polyphase network.

In an implementation form, the polyphase components AF1 , AF2, AF3, AF4, AF5 are realized as an FIR filter as described above with respect to Fig. 1 . In an implementation form, the polyphase components AF1 , AF2, AF3, AF4, AF5 are implemented in lattice structure according to the illustration of Fig. 6.

The method 400 further comprises: transforming 407 the polyphase filtered sub-signals 406 into frequency domain by using a Fast Fourier Transform 407 obtaining frequency sub-band signals 408 and equalizing 409 the frequency sub-band signals 408 by using a sub-band equalizer 409 obtaining equalized frequency sub-band signals 410. In an implementation form, the sub-band equalizer 409 comprises an FIR filter. In an implementation form, the sub-band equalizer 409 comprises an MR filter.

The method 400 further comprises: transforming 411 the equalized frequency sub-band signals 410 back into time domain by using an inverse Fast Fourier Transform 411 obtaining equalized sub-sequences 412 and filtering 413 the equalized sub-sequences 412 in the polyphase network 413 obtaining equalized polyphase filtered sub-sequences 416. A first one of the equalized sub-sequences 416 is filtered with a first polyphase component SF1 of the polyphase network. A second one of the equalized sub-sequences 416 is filtered with a second polyphase component SF2 of the polyphase network. A third one of the equalized sub-sequences 416 is filtered with a third polyphase component SF3 of the polyphase network. A fourth one of the equalized sub-sequences 416 is filtered with a fourth polyphase component SF4 of the polyphase network. A fifth one of the equalized sub-sequences 416 is filtered with a fifth polyphase component AF5 of the polyphase network.

In an implementation form, the polyphase components SF1 , SF2, SF3, SF4, SF5 are realized as FIR filters as described above with respect to Fig. 1 . In an implementation form, the polyphase componentsSFI , SF2, SF3, SF4, SF5 are implemented by lattice structures according to the illustration of Fig. 6.

In an implementation form, the prototype filter comprised by the polyphase components AF1 , AF2, AF3, AF4, AF5 or the polyphase components SF1 , SF2, SF3, SF4, SF5 has a linear phase characteristic.

The method 400 further comprises: reconstructing 415 the output sub-sequences 420b, 420c, 420d compensated by the negative of the phase response of the optical channel by applying a block overlap procedure 415 to the equalized polyphase filtered sub-sequences 416. The first element of the first block 420b of the overlapping sub-sequences is reconstructed by adding the first element of the third equalized sub-sequence 416c with the second element of the fifth equalized sub-sequence 416e. The second element of the first block 420b of the overlapping sub-sequences is reconstructed by adding the first element of the second equalized sub-sequence 416b with the second element of the fourth equalized sub-sequence 416d. The third element of the first block 420b of the overlapping sub-sequences is reconstructed by adding the first element of the first equalized subsequence 416a with the second element of the third equalized sub-sequence 416c.

The first element of the second block 420c of the overlapping sub-sequences is

reconstructed by adding the second element of the third equalized sub-sequence 416c with the third element of the fifth equalized sub-sequence 416e. The second element of the second block 420c of the overlapping sub-sequences is reconstructed by adding the second element of the second equalized sub-sequence 416b with the third element of the fourth equalized sub-sequence 416d. The third element of the second block 420c of the overlapping sub-sequences is reconstructed by adding the second element of the first equalized sub-sequence 416a with the third element of the third equalized sub-sequence 416c. The further blocks 420d and the following blocks not depicted in Fig. 4 are reconstructed analogously. The number of 5 sub-sequences is only an exemplary number. Typical numbers of sub-sequences are powers of two, for example 8, 16, 32, 64, 128, 512, 1024, 2048 etc.

In an implementation form, the block overlap procedure 415 comprises an overlap-discard procedure as described above with respect to Fig. 1 .

Fig. 5 shows a block diagram of a device for compensating a phase response of an optical channel according to an implementation form.

An input signal 504 passes through a polyphase network 505 and an FFT transform 507. The polyphase network 505 corresponds to the polyphase network as described with respect to Figures 1 and 4. The input signal 504 is a digitalized optical signal transmitted over an optical network as described above with respect to Fig. 2. The input signal 504 is partitioned into overlapping subsequences before passing the polyphase network 505 and the FFT 507. The input signal 504 is transformed into frequency sub-band signals 508a, 508b, 508c, where a first element of the first frequency sub-band signal 508a corresponds to the first time instant n as depicted in Fig. 5, a second element of the first frequency sub- band signal 508a corresponds to the second time instant n+1 as depicted in Fig. 5 and a third element of the first frequency sub-band signal 508a corresponds to the third time instant n+2 as depicted in Fig. 5. Analogously, a first element of the second frequency sub- band signal 508b corresponds to the first time instant n, a second element of the second frequency sub-band signal 508b corresponds to the second time instant n+1 and a third element of the second frequency sub-band signal 508b corresponds to the third time instant n+2; a first element of the third frequency sub-band signal 508c corresponds to the first time instant n, a second element of the third frequency sub-band signal 508c corresponds to the second time instant n+1 and a third element of the third frequency sub- band signal 508c corresponds to the third time instant n+2 and analogously for the further frequency sub-band signals not depicted in Fig. 5. The sub-band signals are denoted by m, m+1 , m+2 etc.

Each of the frequency sub-band signals 508a, 508b, 508c is filtered by an associated equalizer 509a, 509b, 509c, for each sub-band m, m+1 , m+2 obtaining equalized frequency sub-band signals 510 for m, m+1 , m+2 etc. The equalizers 509a, 509b, 509c are implemented as FIR filters.

The equalized frequency sub-band signals 510 are passing an I FFT transform 511 and a polyphase network 513 obtaining an output signal 516. The polyphase network 513 corresponds to the polyphase components of the polyphase network as described with respect to Figures 1 and 4.

Fig. 6 illustrates a lattice filter in FIR structure. The values ko, ki , ... k _n represent filter coefficients by which the respective branches are multiplied and the blocks designated by „T" are delay elements delaying the signal by the time interval T corresponding to the sampling period. The coefficients k ₀ , ki , ... k _n can be implemented in a very short word- length by using, for example, a canonical signed digit (CSD) representation.

In an implementation form of the special case of CD compensation with the linear group delay within the whole signal bandwidth, both groups of polyphase components at the AFB and SFB are realized by a simple1 -tap filter with unitary value. If all the polyphase components of the AFB have one coefficient with unitary value and half of the polyphase components of the SFB have one coefficient with unitary value and the other half have all coefficients equal to zero this corresponds to the arrangement as the overlap discard processing method. It means that the prototype filter at the SFB has half the length of the prototype of the AFB and they are both trivial all ones filters. The "discard components" refer to zero-taps of this trivial polyphase components. In another implementation form half the polyphase components of the AFB have all-zero coefficients and half have one unitary coefficient. On the SFB side all the polyphase components have one unitary coefficient. This corresponds to the overlap-add implementation. Furthermore, the multi-tap FD filter only realizes linear group delay such that there is only one non-zero FIR tap per sub-band. Practically, this relates to a shift register realizing a delay with a single tap filtering function.

In an implementation form, 256 symbol ISI corresponding to 512 samples at 2 samples per symbol ADC is realized. Compared to conventional FD CD compensation using 1024-FFT with 50% overlap for compensating a maximum of +/- 30.000 ps/nm of residual CD, the CD compensation according to this implementation form requires only a 256-FFT with a 5- tap delay equalizer and achieves the same performance, i.e. compensates a maximum of +/- 30.000 ps/nm of residual CD. The 5-tap equalizer only requires one complex

multiplication. Thus, the computational efficiency is significantly increased and thus the gate counts are similarly decreased.

The optical signal-to-noise ratio (OSNR) penalty of a 112G PDM-QPSK at 28 GBaud has been investigated based on linear simulations 2 samples per symbol. Using an FFT-size of 1024 samples, the 2 dB OSNR penalty at a bit error rate (BER) of 10 ^"3 is shifted from 43.000 ps/nm when using overlap-discard method FD EQ to 51 .000 ps/nm when using the filter bank with 1 -tap sub-band equalizer (not shown in the fig. 9) and the same FFT size according to the implementation form described here. Similarly, for a 512 FFT, the CD tolerance is extended from 22.000 ps/nm with overlap-discard method FD EQ to 30.000 ps/nm when using the filter bank structure with 1 -tap subband EQ and the same FFT size according to the implementation form described here.

Thus, filter bank based FD EQ according to aspects of the invention extends the CD tolerance at a given FFT-size or requires a smaller FFT size at a given CD tolerance.

In an implementation form, a trivial prototype filter is used which implements a 50% block overlap for each FFT block. After the I FFT, the first and the last 25 percent of each consecutive output block is discarded. The CD compensation function is realized by a multi-tap structure with only one non-zero component. Therefore, there is only one complex multiplication per frequency component. Zero taps act just like a shift register implementing a group delay for this frequency component. Zero taps require only memory of a shift register with very low complexity. Tremendous improvements compared to the existing solution, i.e. overlap-discard FD EQ, are achieved.

The following performances have been reached: When using existing 1024 FFT and extending CD tolerance to 100.000 ps/nm and beyond, ultra-long haul uncompensated transmission of 7000 km of SSMF is allowed. When reducing the FFT size to 256 to achieve 30.000 ps/nm, standard long-haul transmission is allowed and the complexity is reduced.

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 recognise 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 recognise 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 practised otherwise than as specifically described herein.