FIELD OF THE INVENTION The invention relates to an optical communication system and to a method of processing data for optical network. In particular, the invention relates to a method of increasing robustness of optical transmission towards linear and nonlinear polarization-dependent impairments .

BACKGROUND OF THE INVENTION

Fiber-optic communications are experiencing a phase of rapid progress characterized by the introduction of advanced Digi ^¬ tal Signal Processing (DSP) capabilities. The recent techno ^¬ logical development in the field of silicon technology, Ana ^¬ log-Digital-Converters (ADC) and Digital-Analog-Converters (DAC) enables the efficient implementation of Polarization Division Multiplexing (PDM) systems with coherent receivers.

At the same time the exponential growth of data traffic pro ^¬ vides a strong motivation to enhance spectral efficiency and pushes the data-rate per channel to 100 Gb/s and beyond.

Both the increased data-rate and the use of phase and polari- zation modulation make the novel systems more susceptible to transmission impairments and demand for better mitigation algorithms . Several transmission impairments that afflict fiber-optic communications exhibit a pronounced dependence on the State Of Polarization (SOP) of the transmit signals.

The most prominent example is Polarization Mode Dispersion (PMD) . Although it is an important concern for legacy systems, this effect may have a minor relevance for coherently detected channels with advanced PMD compensation capabilities

Polarization Dependent Loss (PDL) is another linear effect depending on the SOP of the transmit signals and which con- sists in polarization-selective loss (or gain) of the fiber, the amplifiers and, in general, of any device traversed by the optical signal. A coherent, as well as a non-coherent, receiver may undergo a performance penalty in the presence of PDL. The performance degradation depends on the orientation between the polarization of the launched signal and the PDL element .

Besides linear effects, also some nonlinear fiber effects ex ^¬ hibit polarization dependence. Recently, many authors (see e.g. A.Bononi, et al . , "Cross-Phase Modulation Induced by OOK Channels on Higher-Rate DQPSK and Coherent QPSK Channels", IEEE/OSA Journal of Lightwave Technology, vol.27, no.18, Sept. 2009 and M. Winter, et al . , "Polarization-Multiplexed Transmission System Outage due to Nonlinearity-Induced Depo ^¬ larization", European Conference on Optical Communication (ECOC) 2010, Torino, Italy, Sept. 2010) pointed out that channels using advanced modulation formats suffer from the presence of co-propagating On-Off-Keying (OOK) channels due to cross-channel effects as Cross-Phase Modulation (XPM) and Cross-Polarization Modulation (XPolM) . As shown in D. Sperti, et al . , "Nonlinear Polarization Effects in a Hybrid 100Gb/s PDM-QPSK - 10Gb/s OOK System", Proc. Fotonica 2010, paper Ά2.4, Pisa, Italy, May 2010, the impact of XPM and XPolM de ^¬ pends on the relative SOP of the co-propagating channels.

In conclusion, due to a variety of transmission impairments, the performance of an optical transmission system and, par- ticularly, of coherently detected channels, depends on the SOP along the link.

Since polarization phenomena are intrinsically stochastic, the sensitivity to polarization-dependent effects introduces an element of unpredictability into the system performance. The availability requested from a transport system can be guaranteed by introducing suitable system margins. However, for most realizations of the polarization phenomena (i.e. for most of the time) this may lead to unnecessary waste of ca ^¬ pacity. A conventional approach to cope with the statistic nature of PMD is the use of polarization scramblers and Forward Error Correction (FEC) . By changing continuously the SOP of the transmitted signal the persistence of worst case situations can be avoided. If polarization scrambling is fast enough with respect to the length of the code words, a properly de ^¬ signed FEC may restore correctly the transmitted payload.

The use of a polarization scrambler at the transmitter only has been described in B. Wedding and C.N.Haslach, "Enhanced PMD Mitigation by Polarization Scrambling and Forward Error Correction", Optical Fiber Communication Conference and Exhibit (OFC) , Anaheim, California, March 2001.

Employing polarization scrambling to combat all types of polarization-dependent impairments could be an extension of these PMD mitigation methods. However, polarization scram- bling suffers from several drawbacks. First, it requires additional active optical components with increased equipment costs and installation and operation ex ^¬ penditures .

Further, even the fastest polarization scramblers cannot avoid significant error burstiness. For example, the "fast polarization scramblers" discussed in "Experimental Demon ^¬ stration of Broadband PMD Mitigation through Distributed Fast Polarization Scrambling and FEC" (X. Liu et al . , European Conference on Optical Communication 2004, Stockholm, Sweden, Sept. 2004) achieve a maximal scrambling rate of 20 MHz. At a transmission rate of 100 Gb/s this corresponds to a scram ^¬ bling period of approximately 5000 symbols. Correspondingly, the error bursts that occur while traversing the worst case SOP's extend over several hundreds of bits. Although their length lies below the burst error correcting capability of most FEC solutions, they may have a clear impact on the FEC performance .

Since the Net Coding Gain (NCG) of an FEC code holds under the assumption of uniformly distributed errors (see for exam- pie the ITU-T Recommendation G.975.1, "Forward Error Correc ^¬ tion for High Bit-Rate DWDM Submarine Systems", 02/2004), random error correction capability drops significantly in the presence of correlated errors.

Moreover, in the presence of polarization scrambling the re- ceiver may experience an artificial time-variant channel. In the case of a direct detection receiver the time variance may disturb mainly the clock recovery circuit. Previous work (H. Bulow, "Receiver for PMD Mitigation by Polarization Scrambling", US 7,486,898 B2, Feb.3, 2009) describes a complex jitter compensation mechanism for the clock recovery of a direct detection receiver in the presence of fast polarization scrambling . However, in a coherent receiver with advanced DSP the time variance disturbs not only the clock recovery but all channel estimation and equalization functions. In addition, in a PDM system it impairs the ability of the receiver to discriminate the polarization multiplexed tributaries. Therefore, for the ^¬ se systems an additional limit may determine the maximum fea ^¬ sible scrambling rate and prevents effective impairment miti ^¬ gation through FEC.

The problem to be solved is to overcome the disadvantages stated above and in particular to provide a solution that in ^¬ crease the robustness of optical transmission towards linear and nonlinear polarization-dependent impairments without un ^¬ necessary waste of capacity.

SUMMARY OF THE INVENTION

In order to overcome the above-described need in the art, the present invention discloses a method of processing data, com ^¬ prising the steps of: mapping a sequence of data bits to a first sequence of symbols, the symbols belonging to a four- dimensional constellation space, multiplying the first se- quence of symbols by a periodic sequence of orthogonal four- dimensional matrices to obtain a second sequence of symbols.

It is also an embodiment that multiplying the first sequence of symbols by a periodic sequence of orthogonal four- dimensional matrices to obtain a second sequence of symbols includes a sequence of periodic orthogonal transformations.

In a further embodiment, each orthogonal transformation includes a rotation in the four-dimensional constellation space .

In a next embodiment of the invention, each orthogonal trans- formation includes a reflection in the four-dimensional con ^¬ stellation space.

In a next embodiment of the invention, the method further comprises the steps of organizing the first sequence of sym ^¬ bols in frames and extending each of the frames with prede- fined training symbols.

In other embodiments of the present invention, In other embodiments of the present invention, the method further comprises differentially encoding the first sequence of symbols.

In a next embodiment, the method further comprises converting the second sequence of symbols to analog electrical signals by means of digital-analog converters.

In other embodiments of the present invention, the method further comprises modulating the analog electrical signals by means of optical modulators to obtain optical signals. In a further embodiment, the method further comprises trans ^¬ mitting the optical signals.

In a next embodiment, the method further comprises receiving the optical signals, wherein receiving the optical signals includes coherent demodulation of the optical signals. In a next embodiment, the modulation is implemented in a sin ^¬ gle carrier system.

In a further embodiment, multiplying the first sequence of symbols by a periodic sequence of orthogonal four-dimensional matrices to obtain a second sequence of symbols is implement- ed in the time domain at each signaling interval.

According to an alternative embodiment of the invention, the modulation is implemented in a multi-carrier signaling system, preferably in an Orthogonal Frequency Division Multi ^¬ plexing (OFDM) system. It is also an embodiment that multiplying the first sequence of symbols by a periodic sequence of orthogonal four- dimensional matrices to obtain a second sequence of symbols is implemented in the frequency domain. The problem stated above is also solved by transmitter for optical signals, comprising a symbol mapper configured to map a sequence of data bits to a first sequence of symbols, the symbols belonging to a four-dimensional constellation space, and a transformation unit configured to perform a sequence of periodic orthogonal transformations by multiplying the first sequence of symbols by a periodic sequence of orthogonal four-dimensional matrices to obtain a second sequence of sym ^¬ bols.

The method and the transmitter provided, in particular, bears the following advantages: a) They increase the robustness of optical transmission towards linear and nonlinear polarization-dependent im ^¬ pairments without unnecessary waste of capacity. b) They have relatively broad applications and they can be easy implemented. c) Remarkable performance improvement can be achieved. d) They do not require additional active optical compo ^¬ nents with increased equipment costs and installation and operation expenditures.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is explained by way of example in more detail below with the aid of the attached drawings.

Fig.l is a schematic representation of a single-carrier transmitter 100 using a time-variant 4D constellation according to an embodiment of the invention. Fig.2 is a schematic representation of a single-carrier receiver 200 using a time-variant 4D constellation according to an embodiment of the invention.

Fig.3 is a schematic representation of an Orthogonal Frequen ^¬ cy Division Multiplexing (OFDM) transmitter 300 using a time- variant 4D constellation according to an embodiment of the invention .

Fig.4 is a schematic representation of an Orthogonal Frequency Division Multiplexing (OFDM) receiver 400 using a time- variant 4D constellation according to an embodiment of the invention.

Figure 5 is a schematic representation of the resulting di ^¬ rect 4D transformation block.

Figure 6 is a schematic representation of the resulting inverse 4D transformation block. DESCRIPTION OF THE INVENTION

Illustrative embodiments will now be described with reference to the accompanying drawings to disclose the teachings of the present invention. While the present invention is described herein with reference to illustrative embodiments for partic ^¬ ular applications, it should be understood that the invention is not limited thereto. Those having ordinary skill in the art and access to the teachings provided herein will recog ^¬ nize additional modifications, applications, and embodiments within the scope thereof and additional fields in which the present invention would be of significant utility.

A simple and effective method is provided which increases the robustness of optical transmission towards linear and nonlin ^¬ ear polarization-dependent impairments.

According to one embodiment of the invention, the method is applicable to single-carrier signaling. According to an alternative embodiment of the invention the method is applica- ble to multi-carrier signaling (Orthogonal Frequency Division Multiplexing - OFDM) . For both embodiments coherent demodula ^¬ tion is assumed.

According to one embodiment of the invention, the method uses a periodic sequence of orthogonal transformations (in time domain for single-carrier system and in frequency domain for OFDM systems) to change the polarization coupling angle of the transmitted signal. The receiver is able to achieve per ^¬ fect synchronization of the periodic sequence by exploiting suitably embedded training symbols. The orthogonal transfor- mations leave demodulation and channel equalization unaffect ^¬ ed and are reversed before de-mapping and decoding.

Fig.l is a schematic representation of a single-carrier transmitter 100 using a time-variant 4D (4-Dimensional) con- stellation according to an embodiment of the invention. The time-variant signal constellation employed avoids the persis ^¬ tence of unfavorable polarization states by using different regions of the vectorial signal space over time.

The channel encoder 102 maps the payload 101 to code words providing FEC capability, thereby adding the required redun ^¬ dancy and providing the requested error resilience.

The symbol mapper 103 maps the resulting encoded bit stream to a sequence of 4D constellation points. At each signaling interval, the mapper 103 uses a set of typically adjacent en- coded bits to select a signal vector from the signal constel ^¬ lation according to a predefined binary labeling (or addressing scheme) . In the case of PDM transmission the signal vec ^¬ tor belongs to the 4-Dimensional (4D) space spanned by the in-phase and quadrature components of two fixed orthogonal polarization axes. Single polarization transmission can be regarded as a special case in which the projection of the signal points on either polarization axis is constantly zero.

Optionally, the sequence of symbols can be differentially en ^¬ coded to convey information in the signal transitions and make the systems more resilient to phase cycle slips.

The sequence of symbols may be organized in frames and frame synchronization 112 may be provided. A training insertion unit 104 extends each frame with predefined training symbols, which will be used at the receiver to achieve frame synchro- nization. The training symbols can be prepended as preamble, appended as a postamble or else distributed along the frame. After framing, an additional transmit processing unit 105 can apply any necessary additional transmit processing.

Next, the 4D transformation block 106 uses a periodic se ^¬ quence <H> of 4D orthogonal matrices to convert the input sequence <v> of 4D points into the new sequence <w> defined by wk = ^H k ^v k (1) with xn[k]

XQ2[k]

w.

YI2[k] (2) YQ2[k]_ and

Each transformation represents a rotation and/or reflection in the 4D signal space and the sequence of 4D orthogonal ma ^¬ trices corresponds to rotations or reflections in the signal space. At each signaling interval the next orthogonal matrix is applied to the original 4D signal vector selected by the symbol mapper 103. Thus a transformed 4D signal point is ob ^¬ tained that is passed to two IQ modulators 110 and further processed. Since the polarization rotation is applied to the time-discrete constellation points rather than to the modu ^¬ lated signal, the transmit pulses remain undistorted and the spectrum unaffected. This allows to take arbitrary sequences of orthogonal transformations, even with abrupt steps between two successive transformations, without generating disconti- nuities in the analog signal. Consequently, the described method could be seen as selecting the transmit point from a different 4D constellation at every signaling interval.

Since a different, completely arbitrary, orthogonal transfor- mation matrix can be applied at every signaling interval, the impact of polarization-dependent impairments can be averaged in the time domain at symbol rate. This results in a per ^¬ fectly uniform symbol error distribution, which improves the error correction capability of the FEC decoder. In order to maximize the averaging effect the separation between consecu ^¬ tive 4D transformations should be maximized.

The periods of the sequence <H> coincide with the frames of the transmit signal.

Subsequently, the resulting sequence <v> of 4D points might undergo Digital Up-Conversion (DUC) 107 and additional pro ^¬ cessing at higher sampling rate (e.g. digital filtering) by means of a Nyquist rate transmit processing unit 108.

The resulting signal is passed to a Digital-Analog Conversion (DAC) stage 109 that yields 4 time-continuous electrical sig- nals used to drive the optical modulators 110.

The two IQ modulators 110 generate the projections of the op ^¬ tical signal on two orthogonal polarization axes, which are eventually merged via a polarization combiner 111. The two IQ modulators 110 (e.g. consisting of a combination of digital and analog components) use the time-discrete sequence of 4D points to generate a continuous optical signal. Modulation, accordingly, could be seen as the generation of a train of optical pulses in response to a sequence of input constella ^¬ tion points. Fig.2 is a schematic representation of a single-carrier receiver 200 using a time-variant 4D (4-Dimensional) constella ^¬ tion according to an embodiment of the invention.

The impinging optical signal 201 is decomposed along two or- thogonal polarization axes by the polarization splitter 211. Two IQ demodulators 210 recover the in-phase and quadrature components of both polarizations. Before entering the Digital Signal Processing (DSP) block the four resulting signals are sampled by the ADC stage 209 at sufficient rate to fulfill Nyquist' s criterion.

The use of a frame structure with training symbols makes da ^¬ ta-aided processing a particularly convenient choice. The re ^¬ ceive processing block 208 at Nyquist rate might include frame, timing and carrier frequency synchronization, and channel equalization.

The processed signal is subject to Digital Down-Conversion (DDC) 207, which reduces the sampling rate to a sample per symbol .

The resulting 4D sequence <z> is transformed by the inverse 4D transformation block 206 according to <H > into the new sequence <s> defined by with xn[k]

XQ3[k]

m[k] (5)

YQ3[k] and XI4[k]

XQ4[k]

(6) YI4[k]

YQ4[k] and ( ) ^T denotes transposition. The matrix-vector multiplica ^¬ tion in (4) is obviously an orthogonal transformation and leaves the noise statistics unchanged. Next, the resulting signal may undergo additional receive processing 205 at sym ^¬ bol rate. This may include carrier phase correction and esti ^¬ mation of residual error for equalizer adjustment.

After removal of the training symbols by means of a training removal unit 204, the symbol de-mapper 203 provides the bits (in case of hard decision FEC) or the bit metrics (in case of soft-decision FEC) to the subsequent channel decoder 202. If the transmitter uses differential encoding, the symbol de- mapper 203 should implement the corresponding differential decoding rule. Frame synchronization 212 may be also provid- ed .

Since a single 4D symbol is associated with several bits, small residual error burstiness can still be present before the channel decoder. This phenomenon is common to most FEC solutions for high-order constellations and can be solved by inserting a short bit-interleaver between channel encoder and mapper and the corresponding bit-de-interleaver between de- mapper and channel decoder.

Fig.3 is a schematic representation of an Orthogonal Frequen ^¬ cy Division Multiplexing (OFDM) transmitter 300 using a time- variant 4D (4-Dimensional) constellation according to an embodiment of the invention.

Differently from a single-carrier system, in an OFDM system the mapping of the encoded bits to the constellation points occurs in the frequency domain rather than in the time do ^¬ main .

The channel encoder 302 maps the payload 301 to code words providing FEC capability. The symbol mapper 303 selects a 4D constellation point per-subcarrier and OFDM symbol. For each OFDM symbol and each subcarrier the symbol mapper 303 uses a set of typically adjacent encoded bits to select a signal vector from the 4D signal constellation according to the predefined binary labeling A training insertion unit 304 can insert training symbols either on selected dedicated subcarriers or on all active sub- carriers at selected OFDM symbols. For convenience of imple ^¬ mentation, the frame length can be chosen to be a multiple of the number of used subcarriers. If necessary, further fre- quency domain processing 305 can be applied after framing.

The 4D transformation block 306 operates in analogy with the single-carrier case but on a per-subcarrier rather than on a per-symbol basis. Therefore, each subcarrier within an OFDM symbol experiences in general a different transformation. Frame synchronization 312 may be also provided. Subsequently, the resulting transformed subcarriers undergo zero-padding (e.g. insertion of virtual subcarriers) and Inverse Discrete Fourier Transform (IDFT) 307 to yield the time domain signal. Additional time domain processing 308 usually includes the insertion of a Cyclic Prefix (CP) .

The resulting signal is passed to a Digital-Analog Conversion (DAC) stage 309 that yields 4 time-continuous electrical sig ^¬ nals used to drive the optical modulators 310.

The two IQ modulators 310 generate the projections of the op- tical signal on two orthogonal polarization axes, which are eventually merged via a polarization combiner 311. The modu- lator uses the sequence of 4D points associated with the sub- carriers to generate a continuous optical signal. Modulation may involve a Fourier transform from the frequency into the time domain. Instead of operating on the modulated signal in the time do ^¬ main, the present embodiment of the invention operates on the individual subcarriers in the frequency domain. For each OFDM symbol and each subcarrier the orthogonal transformation is applied to the original 4D vectorial symbol selected by the mapper. Thus, the transformed subcarriers are obtained that are passed to the modulator and further processed.

Fig.4 is a schematic representation of an Orthogonal Frequency Division Multiplexing (OFDM) receiver 400 using a time- variant 4D (4-Dimensional) constellation according to an em- bodiment of the invention.

The impinging optical signal 401 is decomposed along two or ^¬ thogonal polarization axes by the polarization splitter 411. Two IQ demodulators 410 recover the in-phase and quadrature components of both polarizations. Before entering the Digital Signal Processing (DSP) block the four resulting signals are sampled by the ADC stage 409 at sufficient rate to fulfill Nyquist's criterion.

Time domain receive processing 408 might include frame syn ^¬ chronization, Cyclic Prefix (CP) removal, clock frequency and carrier frequency recovery. After Discrete Fourier Transform (DFT) and removal of the virtual subcarriers 406, the fre ^¬ quency domain signal is obtained. The 4D subcarriers are sub ^¬ ject to the inverse orthogonal transformation according to <H > . Additional frequency domain processing 405 may comprise channel equalization and timing phase recovery. After removal of the training symbols by means of a training removal unit 404, the symbol de-mapper 403 provides the bits (in case of hard decision FEC) or the bit metrics (in case of soft-decision FEC) to the subsequent channel decoder 402. If the transmitter uses differential encoding, the symbol de- mapper 403 should implement the corresponding differential decoding rule. Frame synchronization 412 may be also provid ^¬ ed .

Although the sequence <H> of orthogonal transformations be arbitrary and include also reflections, in most cases rotation matrices of the type

achieve sufficient averaging of the polarization-dependent impairments . As described herein, receive processing is designed to recov ^¬ er the transformed rather than the original 4D signal points. As a consequence, channel equalization, and polarization dis ^¬ crimination have to cope only with the physical channel and not with the artificial time-variance introduced at the transmitter. This allows to change rapidly the polarization state of the transmit signal without disturbing the receiver.

As described above, in order to recover the original 4D sig ^¬ nal points, the receiver is provided with perfect knowledge of the sequence of orthogonal transformations. This can be achieved by repeating periodically the sequence of orthogonal matrices on a frame basis and embedding suitable training symbols for synchronization purposes. After complete equali ^¬ zation and demodulation, the inverse orthogonal transfor- mation is applied to recover the original 4D points.

Moreover, a de-mapper provides the resulting estimated bits (in case of hard decision) or bit metrics (in case of soft- decision) to the FEC decoder, which in turn estimates the transmit payload. Since a different, completely arbitrary, orthogonal transfor ^¬ mation matrix can be applied to every subcarrier, the impact of polarization-dependent impairments can be averaged in the frequency domain at subcarrier granularity. This results in a perfectly uniform symbol error distribution, which improves the error correction capability of the FEC decoder. In order to maximize the averaging effect the separation between consecutive 4D transformations should be maximized.

Figure 5 is a schematic representation of the resulting di ^¬ rect 4D transformation block. Figure 6 is a schematic representation of the resulting in ^¬ verse 4D transformation block.

The present invention is not limited to the details of the above described principles. The scope of the invention is de ^¬ fined by the appended claims and all changes and modifica- tions as fall within the equivalents of the scope of the claims are therefore to be embraced by the invention. Mathe ^¬ matical conversions or equivalent calculations of the signal values based on the inventive method or the use of analogue signals instead of digital values are also incorporated. List of Abbreviations:

4D 4-Dimensional

ADC Analog-Digital Converter

CP Cyclic Prefix

DAC Digital-Analog Converter

DDC Digital Down-Conversion

DFT Discrete Fourier Transform

DSP Digital Signal Processing

DUC Digital Up-Conversion

FEC Forward Error Correction

IDFT Inverse Discrete Fourier Transform

NCG Net Coding Gain

OFDM Orthogonal Frequency Division Multiplexing

PDL Polarization Dependent Loss

PDM Polarization Division Multiplexing

PMD Polarization Mode Dispersion

SOP State Of Polarization

XPM Cross-Phase Modulation

XPolM Cross-Polarization Modulation

4D 4-Dimensional ^ ,

ADC Analog-Digital Converter

CP Cyclic Prefix

DAC Digital-Analog Converter

DDC Digital Down-Conversion

DSP Digital Signal Processing

DUC Digital Up-Conversion

FEC Forward Error Correction

FFT Fast Fourier Transform

IFFT Inverse Fast Fourier Transform

NCG Net Coding Gain

OFDM Orthogonal Frequency Division Multiplexing

PDL Polarization Dependent Loss

PDM Polarization Division Multiplexing

PMD Polarization Mode Dispersion

SOP State Of Polarization

XPM Cross-Phase Modulation

XPolM Cross-Polarization Modulation