WO2012003856A1

WO2012003856A1 - Method and device for data processing in an optical communication network

Info

Publication number: WO2012003856A1
Application number: PCT/EP2010/059550
Authority: WO
Inventors: Arne Striegler; Mohammad Saeed Alfiad
Original assignee: Nokia Siemens Networks Oy
Priority date: 2010-07-05
Filing date: 2010-07-05
Publication date: 2012-01-12
Also published as: EP2591581A1

Abstract

A method and a device for data processing in an optical communication network are provided, wherein a phase modulation is conducted comprising several phase states; and wherein a phase state change between different phase states is gradually conducted. Furthermore, a communication system is suggested comprising at least one such device.

Description

Method and device for data processing in an optical communication network

The invention relates to a method and to a device for data processing in an optical communication network. In

addition, a communication system is suggested comprising at least one such device.

In optical communication networks, high spectral efficiency (determined in (bits/s)/Hz) is a key parameter for a cost- efficient network operation. For this reason, modulation formats such as differential phase shift keying (DPSK) or quadrature phase shift keying (QPSK) can be used to provide a robust, spectral efficient transmission system. The spectral efficiency can be further increased via

polarization multiplexing (POLMUX) ; in particular, e.g., polarization multiplexed QPSK ( POLMUX-QPSK) .

POLMUX-QPSK with coherent detection is a modulation format that can be utilized in next-generation networks as it has advantages like high tolerance towards accumulated

chromatic dispersion (CD) and polarization mode dispersion (PMD) in combination with a high spectral efficiency.

However, modulation formats enhancing the spectral

efficiency get increasingly susceptible to signal

distortions induced by nonlinear effects on the optical fiber. Effects such as self- and cross-phase modulation and four-wave mixing result in distortions and may thus limit the reach of the signals. This leads to high costs for the customers, because the signal has to be regenerated by additional hardware (e.g., expensive regenerators). Such high costs contravene the previously mentioned goal of avoiding costs by increasing the overall spectral

efficiency . Signal distortions suffer from so-called bit pattern effects that become apparent by using on-off-keyed signals, because the data is modulated via the signal's amplitude. In phase modulated signals the bit pattern depends on return-to-zero (RZ) or no-return-to-zero (NRZ) pulse shaping. However, due to the different phase states of the pulses, amplitude fluctuations also contribute to bit pattern effects as second order effects.

The problem to be solved is to overcome the disadvantages mentioned above and in particular to provide a modulation format that provides an improved transmission performance with reduced bit pattern effects.

This problem is solved according to the features of the independent claims. Further embodiments result from the depending claims. In order to overcome this problem, a method for data processing in an optical communication network is provided,

- wherein a phase modulation is conducted comprising several phase states;

- wherein a phase state change between different

phase states is gradually conducted.

Hence, the change of the phase state is in particular conducted continuously, stepwise or systematically

controlled and not abruptly. Such gradually conducted phase state change comprises, e.g., a smooth adaptation between phase states and thereby reduces high frequency modulations thereby allowing the optical signal power to remain

substantially constant.

The approach presented herein provides a modulation format, which has a high spectral efficiency and is robust against distortions caused by non-linear effects. For example, an increase of about 300% transmission reach compared to yet existing 40G POLMUX-QPSK modulation can be achieved.

In an embodiment, the phase state change is conducted over a given period of time from one phase state to a resulting phase state.

In another embodiment, the given period of time is a portion of a duration of a bit period.

It is noted that the given period of time may be more than 50% of the duration of the bit period.

In a further embodiment, the phase states are based on a multi-level electrical signal, wherein level changes of this multi-level electrical signal are gradually conducted

Hence, the electrical signal can be fed to the phase modulation, in particular to a phase modulator conducting the phase modulation. The electrical signal can be such multi-level data signal, wherein the stages or levels of the multi-level data signal are mapped to phase states of the optical signal. The transition between different levels of the electrical signal can be gradually conducted thereby avoiding abrupt changes and thus high frequencies in the phase modulated signal.

Thus, the gradually changing phase states can be obtained by applying a gradually changing electrical signal to the phase modulator.

Hence, the phase states can be mapped to the multi-level electrical signal. Two or more phase states may be used. A state change of the phase state can be regarded as phase shift. In a next embodiment, a level change of the multi-level electrical signal is conducted over a given period of time from one level to a resulting level. It is also an embodiment that the phase state change is provided by a phase modulator, in particular by a

- frequency modulator;

- directly modulated light source;

- non-linear effect, in particular a cross phase

modulation;

- non-linear element, in particular a non-linear

fiber .

The light source may be a (continuous wave) laser source.

Pursuant to another embodiment, the phase modulation is based on a bipolar modulation or any m-array modulation.

It is noted that "m" may be an integer larger than 1.

According to an embodiment, the phase modulation is

combined with polarization multiplexing.

Utilizing polarization multiplexing doubles the spectral efficiency.

According to another embodiment, a first carrier of a first polarization and a second carrier of a second polarization are provided at different frequencies.

This enables polarization multiplexing with a carrier offset. It is noted that several polarizations can be supplied, wherein at least two of the several polarizations have carriers at different frequencies.

Advantageously, distortions by non-linear effects between the two polarization planes can be further reduced by introducing an offset of the carrier frequency of the two polarization planes.

The two polarization portions of a signal are thus shifted in time by chromatic dispersion during the transmission. Inter-channel non-linear effects can be reduced by

providing an increased channel spacing and dispersion.

Furthermore, cross-polarization effects can be

significantly reduced by using such different carrier frequencies.

In a further embodiment, the carriers of different

frequencies are provided each by a separate light source, e.g., utilized in a transmitter of the optical

communication network.

In a next embodiment, the carriers of different frequencies are provided by a single light source wherein the light signal of the single light source is split into two parts, - wherein to the first part of the light signal a

linearly increasing phase shift over time can be added in particular by a first Mach-Zehnder modulator; and

- wherein to the second part of the light signal a linearly decreasing phase shift over time can be added in particular by a second Mach-Zehnder modulator .

Hence, frequency shifts in opposite directions can be realized together with the carrier offset. Such an

additional modulator stage can be combined with an optional pulse carver (in case a RZ signal is required) . It is noted that the carrier offset may be achieved by different modulators as the Mach-Zehnder modulator indicated above.

It is also noted that a portion of the linearly increasing phase shift over time can be added to the first part of the light signal. For example, a serrated signal can be used to provide such portion of linear increasing phase shift over time (for a predefined period of time) . The problem stated above is also solved by a device for processing data in an optical network

- comprising a phase modulator,

- said phase modulator being arranged to conduct a phase modulation utilizing several phase states, wherein a phase state change between different phase states is gradually conducted.

In yet an embodiment, the phase modulator provides a phase- modulated signal based on a multi-level electrical signal, wherein a level change of the multi-level electrical signal is conducted over a given period of time from one level to a resulting level.

According to a next embodiment, the device comprises

- a light source that conveys a light signal to the phase modulator;

- a splitter, wherein the phase modulator is

connected to the splitter. Pursuant to yet an embodiment, the device comprises another phase modulator that is connected to the splitter.

It is noted that the other phase modulator can be supplied by the same light source or by a different light source providing two polarized optical signals, e.g., with an offset of a predetermined frequency.

According to an embodiment, the splitter is a polarization beam splitter or a polarization multiplexer.

The problem stated supra is also solved by a method for processing data, in particular demodulating data, wherein said data were in particular modulated as described above, wherein the method analyzes a slope of a phase change and/or an absolute phase state of a signal, in particular by considering at least one preceding phase state.

Thus, the problem can be solved by a demodulator for processing data, wherein said demodulator is arranged for analyzing a slope of a phase change and/or for analyzing an absolute phase state of a signal in particular by

considering a preceding phase state.

Furthermore, the problem stated above is solved by a communication system comprising at least one device as described herein.

The problem stated above is also solved by a device

comprising or being associated with a processing unit is arranged to conduct the steps of the method stated herein .

Embodiments of the invention are shown and illustrated in the following figures:

Fig.l shows a schematic block diagram of a POLMUX-RZ-PSK transmitter structure with two- and four- dimensional constellation diagrams;

Fig.2 shows a schematic block diagram of a coherent

receiver processing the POLMUX-RZ-DQPSK signals conveyed by the transmitter shown in Fig.l;

Fig.3 shows a schematic block diagram of the digital

signal processing block as indicated in Fig.2; Fig.4 shows a schematic diagram of a transmitter th

generates a CA-POLMUX-PSK modulation format; Fig.5 shows an exemplary diagram of an unfiltered

electrical signal y_ei as a function of time;

Fig.6 shows a diagram based on Fig.5 visualizing as how a demodulator can detect a signal by analyzing an absolute phase state as well as a slope of a phase change .

A next generation product based on a POLMUX-QPSK modulation format will exemplarily be described hereinafter. Fig.l shows a schematic block diagram of a POLMUX-RZ-DQPSK transmitter structure with two- and four-dimensional constellation diagrams 116, 117. A signal from a light source 101 (e.g., a CW-laser) is fed to a Mach-Zehnder-Modulator MZM 102 where it is modulated with an electrical signal 103, e.g. a substantially

sinusoidal signal. The output of the MZM 102 is split into a branch 104 and into a branch 105. The outputs of the branches 104, 105 are combined by a polarization beam splitter PBS 106, which provides a modulated output signal 107.

The branch 104 comprises two parallel MZMs 108, 109, wherein the MZM 108 is connected with a (π/2) phase shifter 110. At the MZM 108, a modulation with an electrical signal 111 (also referred to as precoded I-signal) is conducted and at the modulator MZM 109, a modulation with an

electrical signal 112 (also referred to as precoded Q- signal) is conducted.

The branch 105 comprises two parallel MZMs 113, 114, wherein the MZM 113 is connected with a (π/2) phase shifter 115. At the MZM 113, a modulation with the electrical signal 111 is conducted and at the modulator MZM 114, a modulation with the electrical signal 112 is conducted. As can be seen from the two-dimensional constellation diagrams 116, the transmitter of POLMUX-RZ-DQPSK provides a similar signal as does a common DQPSK modulator. The transmitter of Fig.l provides two structures, one for each polarization. To obtain return-to-zero (RZ) , a so-called pulse carver can be added after the CW-laser. This pulse- carver, according to the example of Fig.l, is realized by the MZM 102. The signal from the pulse carver is split up into the two branches 104, 105, by, e.g., using a 3dB splitter 118. Both branches 104, 105 are separately DQPSK- modulated using a common QPSK-modulator . After modulation, the two DQPSK-modulated signals are combined by the PBS 106, which multiplexes the signals from the branches 104, 105 onto orthogonal polarizations. In an eye diagram, the effect of the pulse carver can be determined as the output of the transmitter contains pulses. Every pulse (the middle) carries two phases of the two distinct signals. In total 16 combinations are possible. The rate of pulses equals the total bitrate divided by four. This means that one symbol contains information of 4 bits, thus resulting in 4 bits per symbol.

There are multiple ways to receive the POLMUX-RZ-DQPSK signal. Hereinafter, as an example, a polarization- diversity intra-dyne receiver detection is described. Fig.2 shows a schematic block diagram of a coherent receiver processing the POLMUX-RZ-DQPSK signals conveyed by the transmitter shown in Fig.l and described above. An incoming signal 201 is split by a PBS 202 into two orthogonal polarization components E_iriiX 203 and E_iriiY 204, which are a mixture of the two original signals as

originally transmitted. Both polarization components 203, 204 are fed to a 90° optical hybrid 205, 206, where they are mixed with an output signal of a LO-laser 207. For that purpose, the signal of the LO-laser 207 is fed to a PBS 208, where it is split into a component E_L0,_X 209 and a component E_L0,_y 210. The component 209 is conveyed to the 90° optical hybrid 205 and the component 210 is conveyed to the 90° optical hybrid 206. It is noted that the optical hybrid 205, 206 is in detail summarized by a block 229.

The LO-laser 207 may be a free-running laser and it may be aligned with the transmitter laser within a frequency range of several hundred megahertz. This alignment can be

controlled by a digital signal processing (DSP) that could be deployed in a digital signal processing block 211. The permissible frequency range of the LO-laser 207 depends on the DSP algorithms used for carrier phase estimation (CPE) .

Mixing the signal of the LO-laser 207 and the received signal 201 (i.e. the components 203, 204) in the 90° hybrids 205, 206 results in in-phase (I) and quadrature (Q) components, which are then fed to photodiodes 213 to 220, which can be single-ended or balanced photodiodes

(depending on, e.g., a complexity and/or a cost-efficiency of a particular scenario) .

Distortions from direct detected signal components can be minimized by using a high LO-to-signal power ratio. Hence, the signals from the photodiodes 213 to 220 are combined (via elements 221 to 224) and amplified (via amplifiers 225 to 228) . Then, the amplified signals are digitized by analog-to-digital converters (ADCs) of a unit 212. The output of this unit 212 can be processed by the previously mentioned DSP to recover the bit streams originally

transmitted.

The digital signal processing block 211 may control the gain of the drivers 225 to 228 and/or adjust the frequency of the LO-laser 207.

Fig.3 shows a schematic block diagram of the digital signal processing block 211. Such digital processing may be conducted in the electrical domain of the coherent receiver shown in Fig .2.

The signals fed to the digital signal processing block 211 are conveyed to a frequency domain equalization (FDE) stage 301, which is applied to estimate and compensate an

accumulated chromatic dispersion (CD) along the optical link. The FDE stage 301 is followed by a clock recovery 302 and a time domain equalization (TDE) stage 303 to

compensate the DGD/PMD, i.e. a residual CD after FDE and demultiplexing of the two polarizations.

In the FDE stage 301 the signal is transferred into the frequency domain using FFT . The frequency domain is better suited to compensate for the CD, because here the inverse linear part of the Schrodinger equation can be applied. After CD compensation in the FDE stage 301, the signal is transformed back to the time domain using IFFT. As CD compensation is applied per polarization (see Fig.3), the FDE stage 301 is not able to demultiplex the polarizations. Before the TDE stage 303, the clock recovery 302 is

conducted .

During the propagation along the optical fiber the

transmitted signal accumulates noise and the two

polarizations experience CD and PMD as well as intermixing effects between them. The polarizations E_iriiX and E_iriiY are a mixture of the two original signals as originally

transmitted. The PBS 202 splits the received signal 201 into two (arbitrary) orthogonal polarization components 203, 204.

If all signal impairments are assumed to be linear, a matrix H (transfer function) can be determined, which may be an approximation of the inverse matrix H to reverse the linear effects of the channel. The matrix H can be

summarized as H = [h_xx h_yx; h_xy h_yy] , which is represented by a butterfly structure of the TDE stage 303 shown in Fig.3. Multiplying the received signal with the transfer function H, an approximation of the transmitted signal can be determined. Hence, the TDE stage 303 can compensate for the residual CD, PMD and demultiplex the two polarizations.

In theory the CD may (substantially) totally be compensated in this TDE stage 303; however such compensation requires extensive calculations. It is also possible to determine the transfer function H using methods such as the constant modulus algorithm (CMA) or the least mean square (LMS) algorithm. Using these algorithms, the coefficients of the transfer function H can be adapted over time to be able to track fast changes regarding the polarization state of the signal or changes of the channel characteristics.

The TDE stage 303 may provide a limited tolerance towards nonlinear impairments. After the TDE stage 303, the signal is processed by a carrier recovery 304, which corrects an offset in frequency and phase between the transmitter and LO-laser 207 (e.g., by using the Viterbi-and-Viterbi algorithm) . A frequency offset can be estimated by

integrating the phase change over a large number of symbols or by estimating the shift in the frequency domain. After the frequency offset is reduced or (in particular

substantially) removed, carrier phase estimation (CPE) is applied to remove the phase offset. Next, a digital

decision is made on the symbols using a slicer 305. Then, a DQPSK decoder 306 determines the resulting bit stream.

Fig.3 also visualizes constellations that could be

associated with the various processing stages as indicated.

The approach provided herewith suggests a modulation format that could work with a common coherent receiver. The improvement is based on reducing bit pattern effects by phase modulation of a continuous wave signal, so that the signal after modulation has a (substantially) constant amplitude .

This modulation scheme can be applied to different

modulation formats such as bipolar-modulation, or m-array modulation. It can be combined with polarization

multiplexing to double the spectral efficiency.

Furthermore, it can be used in combination with

polarization multiplexed signals with a carrier offset between the polarization planes.

The abbreviation CA stands for "continuous amplitude" and is in particular used to indicate the modulation format suggested herein.

Fig . 4 shows a schematic diagram of a transmitter that generates a CA-POLMUX-PSK modulation format. A light signal is provided by a light source 401, e.g., a continuous wave laser, at a frequency fo- The light source 401 is coupled to a phase modulator 402. The phase modulator 402 is fed with an electrical (data) signal y_ei provided by a unit 403. The output of the phase modulator 402 is conveyed to a polarization beam splitter (PBS) 404 and the output of the PBS 404 is conveyed to an (optional) optical bandpass filter (OBF) 405.

As an option, the signal from the light source 401 is also fed to a phase modulator 406 to which an electrical (data) signal y_ei is conveyed by a unit 407. The output of the phase modulator 406 is conveyed to the PBS 404.

The phase modulator 402, 406 modulates the signal from the light source 401 according to, e.g., a 4-level electrical signal pursuant to the following mapping:

- (I == 1) AND (Q == 1) ^ y_el = 0

- (I == 0) AND (Q == 1) ^ y_el = 1 - (I == 1) AND (Q == 0) -> Y_ei = 2

- (I == 1) AND (Q == 1) -> Y_ei = 3

It is noted that this mapping is merely an example. Other mappings of signals of different levels may be applicable accordingly .

Fig.5 shows an exemplary diagram of an unfiltered

electrical signal y_ei as a function of time.

If two or more phase states are used, the mapping can be changed accordingly. A phase shift of ¾,,·^■ /2 is added to the signal by the phase modulator 402, 406. The phase is modulated such that the phase increases or decreases from one phase state to the next phase state over a time period

wherein T_symbol indicates a duration of one symbol. Such symbol may comprise one bit or several bits.

In contrast to commonly phase modulated signals that are generated by using a MZM, the phase does not abruptly jump to the discrete phase states; hence, high frequency modulations are avoided and the optical signal power can remain substantially constant.

The duration t_m0d of the phase state change and a bandwidth of the electrical filter have a significant impact on the frequency shift Af induced by the phase change Δφ pursuant to It is noted, however, that this equation is in particular valid for a linear increase of the phase as shown in Fig.5. In a more general sense, this equation reads: /« = .

The lower the modulation time t_moc the higher is the frequency shift Af . Furthermore, the higher the frequency shift Af, the higher the distortions induced by the

interplay of dispersion induced time shifts and non-linear effects .

A constellation diagram in a polarization plane reveals that the phase state changes between 0:~ and 3/2 - and the absolute value of the signal is (substantially)

constant. An eye diagram of the optical signal thus shows a signal power which is nearly constant with small

fluctuations that can be noticed as a result of optical band pass filtering.

It is an advantage of the modulation format suggested that the bit pattern effects are significantly reduced as the signal power is substantially constant. Therefore, no bit pattern dependent distortions are added based on non linear effects.

It is a further advantage of the solution provided that the signal peak power is reduced, because the mean signal power is the same as the peak power of the signal. In

conventional modulation formats the pulse peak power is higher than the mean power and as a result non-linear effects are higher in these modulation formats.

Advantageously, the receiver hardware may be maintained unchanged. A receiver as commonly used for POLMUX-QPSK or the like can be used. As an option, the light source 401 in Fig.l can be replaced by two light sources, wherein a first light source is connected to the phase modulator 402 and a second light source is connected to the phase modulator 406. The first light source may provide a continuous wave with an offset amounting to fo+Af and the second light source may provide a continuous wave with an offset amounting to fo~Af. The PBS 404 can be replaced by a polarization multiplexer.

Hence, the two polarized signals are obtained with an offset amounting to 2Af.

It is noted that the phase shift can be realized by a frequency modulator or by directly modulating the light source, e.g., a laser diode.

It is further noted that the phase shift can be provided by a non-linear effect, e.g., by a cross-phase-modulation, thereby using a non-linear element (for example a highly non-linear fiber) . Also, a gradual phase change could be utilized accordingly.

For DPSK modulation, a delay line interferometer and/or a balanced detection can be used, because in such scenario pulses are carved out by the phase information. Hence, a traditional DPSK receiver can be used and the transmission performance can be increased.

Fig.6 shows the diagram of Fig.5, wherein an interval between a point 601 and a point 602 can be used to detect the signal by analyzing the slope of the phase change by a demodulator. An interval between a point 603 and a point 604 can be used to detect the signal by analyzing the absolute phase state.

Hence, the demodulation can be achieved by analyzing the absolute phase value using a steady-state of the phase (with a duration amounting to T_mmw— t_moa) . Also, the demodulation can be achieved by analyzing the slope during the gradual phase change (which lasts for a duration i_m(ili) : Here, an information of a preceding phase state is required as well, because the slope depends on the phase state of the preceding bit (or symbol) .

Both techniques can be combined; in such case more than two samples are required for processing purposes. The

demodulation may be optimized by adapting the parameter t,_rii)d, i.e. in case of the slope analysis, t_mod may be set as long as possible (e.g., t_{n K}i— 3_s «*¾o/) and in case of the absolute phase state, £_7>!1,.; may have to remain short. Hence, a suitable compromise can be configured to provide

appropriate results.

Further Advantages:

The CA phase modulation format suggested is robust against non-linear effects. The CA modulation format in combination with carrier offset significantly increases the reach of the transmission. Hence, the number of components providing 3R functionalities (re^¬ shape, re-time, re-amplify/re-generate) can be

reduced . b) Legacy receivers can be used. c) The maximum reach can be increased in particular for fiber types with a low dispersion coefficient. d) The modulation format can be further improved by

providing a dispersion map that is optimized. e) If the L-Band is used for low dispersion fibers, the reach can be further increased, because the absolute value of the dispersion coefficient at this wavelength is higher.

List of Abbreviations:

ADC analog-to-digital converter

AOM acousto-optic modulator

CA continuous amplitude

CD chromatic dispersion

CMA constant modulus algorithm

CO-POLMUX carrier-offset POLMUX

CPE carrier phase estimation

CW continuous wave

DAC digital-to-analog converter

DDO direct detection optical

DGD differential group delay

DPSK differential phase shift keying

DQPSK differential QPSK

DSP digital signal processor

FDE frequency domain equalization

FFT fast Fourier transform

Gbps gigabit per second

IFFT inverse FFT

INT interleaver

LD laser diode

LMS least mean square

LO local oscillator

MIMO multiple-input multiple-output

MOD modulator

MZDLI Mach-Zehnder delay interferometer

MZM Mach-Zehnder modulator

NRZ non-return-to-zero

OBF optical bandpass filter

PBS polarization beam splitter

PD photodiode

PDM polarization division multiplexing

PMD polarization mode dispersion

POLMUX polarization multiplexing

QAM quadrature amplitude modulation

QPSK quadrature phase shift keying RF radio-frequency

RX receiver

RZ return-to-zero

SNR signal-to-noise ratio TDE time domain equalization

TX transmitter

Claims

A method for data processing in an optical

communication network,

- wherein a phase modulation is conducted comprising several phase states;

- wherein a phase state change between different

phase states is gradually conducted.

The method according to claim 1, wherein the phase state change is conducted over a given period of time from one phase state to a resulting phase state.

The method according to claim 2, wherein the given period of time is a portion of a duration of a bit period .

The method according to any of the preceding claims, wherein the phase states are based on a multi-level electrical signal, wherein level changes of this multi-level electrical signal are gradually conducted

The method according to claim 4, wherein a level change of the multi-level electrical signal is conducted over a given period of time from one level to a resulting level.

The method according to any of the preceding claims, wherein the phase state change is provided by a phase modulator, in particular by a

- frequency modulator;

- directly modulated light source;

- non-linear effect, in particular a cross phase

modulation;

- non-linear element, in particular a non-linear

fiber . The method according to any of the preceding claims, wherein the phase modulation is based on a bipolar modulation or any m-array modulation.

The method according to any of the preceding claims, wherein the phase modulation is combined with

polarization multiplexing.

The method according to any of the preceding claims, wherein a first carrier of a first polarization and a second carrier of a second polarization are provided at different frequencies.

A device for processing data in an optical network

- comprising a phase modulator,

The device according to claim 10, wherein the phase modulator provides a phase-modulated signal based on a multi-level electrical signal, wherein a level change of the multi-level electrical signal is conducted over a given period of time from one level to a resulting level .

The device according to any of claims 10 or 11,

- comprising a light source that conveys a light

signal to the phase modulator;

- comprising a splitter, wherein the phase modulator is connected to the splitter.

The device according to claim 12, comprising another phase modulator that is connected to the splitter.

The device according to any of claims 12 or 13, wherein the splitter is a polarization beam splitter or a polarization multiplexer. A demodulator for processing data, wherein said demodulator is arranged for analyzing a slope of a phase change and/or for analyzing an absolute phase state of a signal in particular by considering a preceding phase state.