Abstract:
A signal processing method and a signal processing arrangement for coherent receivers are provided. The method includes the steps of receiving a coherent complex signal, extracting orthogonal in-phase and quadrature signal components from the coherent complex signal, quantizing the orthogonal signal components independently, combining the quantized orthogonal signal components as real and imaginary part of a complex number resulting in a first signal, and soft differential decoding the first signal resulting in a second signal.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention refers to a method and to an arrangement for signal processing in a communication system (e.g. an optical communication system). 
       BACKGROUND OF THE INVENTION 
       [0002]    In order to meet the growing demand for internet bandwidth with traffic growth rates around 40-50% per year, telecommunication component providers face the task of increasing the spectral efficiency of fiber utilization. After 10 Gbit/s systems became successful in the 1990&#39;s, solutions for 40 Gbit/s became available in the last years. Standardization and research are now focused on the development of 100 Gbit/s systems with coherent Polarization Multiplexed (PolMux) Quadrature Phase Shift Keying (QPSK). Since polarization multiplexing utilizes both light polarizations, it is possible to send the signal at a rate of ˜25-28 Gsymbols per second, thus fitting nicely into the standard 50 GHz grid for DWDM optical systems. Coherent reception makes it possible to compensate for most linear transmission impairments, like Chromatic Dispersion (CD) and Polarization-Mode Dispersion (PMD) after sampling in the digital domain. 
         [0003]      FIG. 1  shows a conventional coherent receiver for polarization multiplex signals. A received polarization division multiplex signal (PolMUX signal)  14  comprising two orthogonal optical signals is split by a Polarisation Beam Splitter (PBS)  1  into two orthogonal component signals x and y. Each of these component signals is split by optical 90°-hybrids  2  and  3  into an in-phase component (xi; yi) and a quadrature-phase component (xq; yq). Therefore frequency and phase of a local carrier generated by a local oscillator (LO)  4  must be adjusted by a carrier recovery unit  12  to agree with that of the received PolMUX signal. After analogue-to-digital conversion by AD-converters (ADC)  5 - 8  a sampled and quantized representation of the received optical signal is available in digital form referred to as component values XI, XQ; YI, YQ. Such values contain statistic noisy distortions, deterministic channel degradations such as chromatic dispersion, and random time-varying distortions mainly due to polarization effects. A dispersion compensation unit  9  is usually added for first coarse chromatic dispersion compensation. In addition, a clock recovery subsystem  10  is necessary for extracting a correct sampling clock frequency and a correct sampling clock phase from the received signal. Adaptive equalization estimates the channel and removes deterministic channel distortions. Then, the carrier recovery  12  corrects the phase offset caused by the local oscillator (LO)  4 . Finally, forward error correction (FEC)  13  is used to correct for statistical errors. 
         [0004]      FIG. 2  shows the rotation of a Quadrature Phase Shift Keying (QPSK) constellation diagram relative to either polarization component x or y in presence of a phase offset Δφ(t) introduced by the transmitter and receiver laser to the signal. Writing the analog signal E in (t) in the complex base-band, a phase offset Δφ(t) can be modeled by E out (t)=E in (t)e jΛφ . In more detail  FIG. 2  shows the Quadrature Phase Shift Keying (QPSK) constellation diagram  21  without the phase rotation and the Quadrature Phase Shift Keying (QPSK) constellation  22  in presence of the phase offset Δφ(t)  23 . 
         [0005]      FIG. 3  shows an example of a cycle slip for a Quadrature Phase Shift Keying (QPSK) system in presence of a constant phase offset Δφ(t). In more detail  FIG. 3  shows the phase  31  (rad) as a function of the number of received symbols  32  and an example of a cycle slip  33 . A cycle slip occurs if the signal constellation is rotated by ±90°, 180°. Depending on the signal-to-noise ratio (SNR) and the laser phase noise, there is a finite probability that cycle slips occur. All the subsequent phase estimates are offset by the degree of the cycle slip and decoded incorrectly in a coherent system. This can lead to burst errors thus making a stable communication impossible. The probability of cycle slips can be reduced by using lasers with a narrower linewidth or by increasing the SNR, which may lead to more expensive communication systems. 
         [0006]    A much simpler way to combat cycle slips can be obtained by introducing differential encoding to the signal. In conventional differential formats, the bit information is modulated onto the phase difference between two or more subsequent symbols. For example, in differentially encoded Binary Phase-Shift Keying (BPSK) systems a binary “1” may be transmitted by adding 180° to the current phase and a binary “0” by adding 0° to the current phase. In differentially encoded QPSK, the phase-shifts are 0°, 90°, 180°, −90° corresponding to data “00”, “01”, “11”, “10”. If a cycle slip occurs, it leads to a single symbol error only, since it&#39;s the differential phase which carries the information. 
         [0007]    However, binary differential decoding may lead to a performance loss, as every bit error in the coherent domain is translated to two bit errors after differential decoding at relevant signal-to-noise ratio (SNR) values. The binary decoding algorithm can be given by: 
         [0000]        z   I ( t )=Re {sgn( r ( t ))sgn( r *( t−T ))};  z   Q ( t )=Im {sgn( r ( t ))sgn( r *( t−T ))}  (1)
 
         [0008]    where r(t) is the coherent complex signal and z(t) is the complex differentially decoded signal with z I (t) being the real part or the in-phase, z Q (t) being the imaginary part or the quadrature, and T is the symbol duration. 
         [0009]      FIG. 4  illustrates the bit error rate (BER) of a Quadrature Phase Shift Keying (QPSK)  43  compared with a binary differentially decoded QPSK  44  and with a standard soft decoding (incoherent demodulation) of QPSK  45  (DQPSK). In more detail  FIG. 4  shows that the loss by binary differentially decoded QPSK  44  with respect to Phase Shift Keying (QPSK) is about ˜0.7 dB at a BER of 5e-3. The loss itself is not as relevant in the first place as the implication of differential decoding itself. As shown in  FIG. 1 , in the coherent receiver, the carrier recovery stage  12  is followed by the Forward error Correction (FEC) stage  13 . Generally, coding benefits from soft information, whenever a quantized version of the output signal is used for decoding instead of hard-decision bits. In this way, the decoding algorithm can utilize information of the symbol uncertainty in order to improve decoding performance. At coding overheads of ˜7% that are common in optical communication, the soft decoding channel capacity is ˜1 dB higher than the hard decision channel capacity. However, there is the problem of transferring soft-information of differentially encoded QPSK from the coherent to the differentially decoded domain.  FIG. 4  shows that the standard soft decoding of QPSK (DQPSK)  45  leads to a significant penalty compared with binary differentially decoded QPSK  44  of ˜1.7 dB at a BER of 5e-3. 
         [0010]    The output signal of the DQPSK decoder is given by: 
         [0000]        z   I ( t )=Re { r ( t ) r *( t−T )};  z   Q ( t )=Im { r ( t ) r *( t−T )}  (2)
 
         [0011]    Binary differential decoding of QPSK has a limited decoding penalty, less than soft differential decoding, but suffers a performance loss in combination with hard-decision FEC that is inferior to soft-decision counterparts. Another possibility would be to avoid differential encoding altogether. However this approach would require stable lasers and generally leads to increased system costs. 
         [0012]    In the wireless systems literature it has been shown that the differential encoding penalty of general PSK modulation formats can be completely compensated using iterative decoding. Cited for example are D. Marsland, P. T. Mathiopoulos, “ On the Performance of Iterative Noncoherent Detection of Coded M - PSK Signals”, IEEE Transactions on Communications,  vol. 48, no. 4, pp. 588-596, April 2000; Peter Hoeher, Senior Member, IEEE, and John Lodge, ““ Turbo DPSK”: Iterative Differential PSK Demodulation and Channel Decoding”, IEEE Transactions on Communications,  vol. 47, no. 6, pp. 837-843, June 1999; and H. Arslan, G. E. Bottomley, R. Ramesh, G. Brismark, “ Coherent MAP Detection of DQPSK Signals in non - ISI Channels”, Wireless Communications and Networking Conference,  1999.  WCNC.  1999  IEEE.  In the cited documents the differential decoder is regarded as the inner code of a serially concatenated code structure. The outer code is a convolutional code with error correction capabilities. Using the turbo principle, soft information is iterated between the differential decoder and the outer code employing an interleaver in between. The soft decision is computed according to the maximum a posteriori (MAP) principle. In principle, it is possible to replace the convolutional code by a soft output low density parity check (LDPC) or turbo code with a low overhead, as they are typically used in fiber optics, in order to compensate for the differential penalty. However, this has neither been demonstrated in fiber optic literature, nor has an assessment of the complexity increase taken place. Further examples for the mitigation of the differential encoding are given in L. Lampe et al., “ Coded Modulation for DPSK on Fading Channels”, Globecom  99, where multi-level coding is used in combination with convolutional codes, and in H. Leib et al., “ Data - Aided Noncoherent Demodulation of DPSK”, IEEE Trans. Comm.  Vol. 43 (1995), pp. 722 and S. Calabrò et al., “ Improved Detection of differential Phase Shift Keying through Multi - Symbol Phase Estimation”, ECOC  2005, where recursive structures are employed that however cannot be implemented in parallelized receivers. 
         [0013]    The problem to be solved is to avoid the disadvantage mentioned above and in particular to reduce the performance loss of the soft differential decoding of QPSK in the combination with Forward error Correction (FEC). A cost efficient technique is needed that approaches the optimal performance of soft differential decoding of QPSK in the combination with Forward error Correction (FEC) without the complexity of MAP computation and iterative decoding, and which can be easily implemented in parallelized receivers. 
       SUMMARY OF THE INVENTION 
       [0014]    In order to overcome the above-described need in the art, the present invention discloses a signal processing method for coherent receivers, comprising the steps of receiving a coherent complex signal, extracting orthogonal in-phase and quadrature signal components from the coherent complex signal, quantizing the orthogonal signal components independently, combining the quantized orthogonal signal components obtaining a first signal (in particular, a complex signal), and soft differential decoding the first signal obtaining a second signal. 
         [0015]    It is also an embodiment, that the first signal ( 61 ) includes a real part ( 693 ) and an imaginary part. 
         [0016]    In a further embodiment, the signal processing method further comprises the step of feeding the second signal to a forward error correction unit. 
         [0017]    In other embodiments of the present invention, the coherent complex signal is fed by a carrier recovery unit. 
         [0018]    In a further embodiment, the step of soft differential decoding the first signal obtaining a second signal includes the steps of time-delaying the first signal obtaining a third signal, complex conjugating the third signal obtaining a fourth signal, multiplying the fourth signal with the first signal obtaining a fifth signal, and phase shifting the fifth signal obtaining the second signal. 
         [0019]    In a next embodiment, the coherent complex signal includes a Quadrature Phase Shift Keying (QPSK) signal. 
         [0020]    It is also an embodiment, that the signal processing method further comprises the step of clipping the orthogonal signal components independently. 
         [0021]    In a further embodiment, the step of quantizing the orthogonal signal components independently includes linear quantization of the orthogonal signal components. 
         [0022]    In an alternative embodiment, the step of quantizing the orthogonal signal components independently includes non linear quantization of the signal components. 
         [0023]    In other embodiments of the present invention, the non linear quantization of the orthogonal signal components includes compression of the orthogonal signal components. 
         [0024]    In a next embodiment of the invention, the non linear quantization of the orthogonal signal components includes expansion of the orthogonal signal components. 
         [0025]    The problem stated above is also solved by a signal processing arrangement for coherent receivers, comprising means for receiving a coherent complex signal, means for extracting orthogonal in-phase and quadrature signal components from the coherent complex signal, means for quantizing the orthogonal signal components independently, means for combining the quantized orthogonal signal components obtaining a first signal, wherein the first signal includes a real part and an imaginary part, and means for soft differential decoding the first signal obtaining a second signal. 
         [0026]    In a next embodiment, the means for quantizing the orthogonal signal components independently include a quantization and clipping unit. 
         [0027]    In other embodiments of the present invention, the means for quantizing the orthogonal signal components independently include a compressor unit configured to perform compression of the orthogonal signal components. 
         [0028]    In a next embodiment, the means for quantizing the orthogonal signal components independently include an expander unit configured to perform expansion of the orthogonal signal components. 
         [0029]    The problem stated above is also solved by a receiver of a communication system including the signal processing arrangement described above. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0030]    The invention is explained by way of example in more detail below with the aid of the attached drawings. 
           [0031]      FIG. 1  a high level block diagram which shows a conventional coherent receiver for polarization multiplex signals. 
           [0032]      FIG. 2  is an illustration which shows the rotation of a Quadrature Phase Shift Keying (QPSK) constellation diagram in presence of a phase offset. 
           [0033]      FIG. 3  is an illustration which shows a cycle slip for a Quadrature Phase Shift Keying (QPSK) system. 
           [0034]      FIG. 4  illustrates the bit error rate (BER) of a Quadrature Phase Shift Keying (QPSK) compared with a binary differentially decoded QPSK and with a standard soft decoding of QPSK (DQPSK). 
           [0035]      FIG. 5  is a high level block diagram which illustrates the signal processing arrangement and the method of processing a coherent complex signal according to an embodiment of the invention. 
           [0036]      FIG. 6  is high level block diagram which illustrates the soft decision code I.5 from the fiber optic communication standard ITU-T G.975.1. 
           [0037]      FIG. 7  illustrates the performance of the soft differential decoding method in combination with a soft decision forward error correction (FEC) according to an embodiment of the invention. 
       
    
    
     DESCRIPTION OF THE INVENTION 
       [0038]    As regards the description of  FIGS. 1 to 4 , reference is made to the background of the invention. 
         [0039]    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 particular 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 recognize additional modifications, applications, and embodiments within the scope thereof and additional fields in which the present invention would be of significant utility. 
         [0040]      FIG. 5  is high level block diagram ( 50 ) which illustrates the signal processing arrangement and the method of processing a coherently demodulated complex signal r(t) according to an embodiment of the invention. The coherently demodulated complex signal r(t) is fed from a carrier recovery unit (for example the carrier recovery unit  12  shown in  FIG. 1 ) to a noise limiting unit  52 . The in-phase component  56  of the coherent complex signal r(t) is extracted by the in-phase component extractor unit  54  and quantized by the quantization unit  58 . Independently from the in-phase component, the quadrature component  57  of the coherent complex signal r(t) is extracted by the quadrature component extractor  55  and quantized by the quantization unit  59 . The in-phase component  56  and the quadrature component  57  of the coherently demodulated complex signal r(t) are combined ( 60 ) as real ( 693 ) and imaginary ( 694 ) part of a complex number, respectively, by the combiner  60 . The resulting signal  61  is then fed to a differential soft decoding unit  62  where differential soft decoding of the signal  61  is performed. In particular the signal  61  is fed to a time delay unit  63  which introduces a time delay T. The output  695  of the time delay unit  63  is then fed to a complex conjugate unit  64 . The output  696  of the complex conjugate unit  64  is then multiplied with the signal  61  by the multiplier  691 . The resulting signal  692  is fed to a π/4 phase shifter  69 . The output of the phase shifter z(t)  65  can then be processed by an error decoding module, (for example the forward error correction (FEC) unit  13  shown in  FIG. 1 ). 
         [0041]    In another embodiment of the invention, also shown in  FIG. 5 , the quantization units  58  and  59  further include a clipping unit, so that each of the quantization unit  58  and  59  can also be named quantization and clipping unit  66 . The clipping in combination with quantization leads to a significant noise reduction compared to standard soft differential decoding. 
         [0042]    According to an embodiment of the invention the quantization units  58  and  59  perform a linear quantization. 
         [0043]    In another embodiment of the invention, also shown in  FIG. 5 , the quantization performed by quantization units  58  and  59  can be non linear. In particular nonlinear mapping functions units can be included before and after the linear quantization and clipping units  66 , in particular a compressor unit  67  is included before the quantization and clipping units  66  and an expander unit  68  is included after the quantization and clipping units  66 . Further benefits can be gained by using the nonlinear mapping functions units  67  and  68 . The optimum clipping amplitude and nonlinear mapping functions depend on the type of forward error correction (FEC). 
         [0044]      FIG. 6  is high level block diagram which illustrates the soft decision code I.5 from the fiber optic communication standard ITU-T G.975.1. In particular  FIG. 6  shows a Reed-Solomon encoder unit  611 , a Product encoder unit  612 , a transmission line  615 , a Product decoder unit  613  and a Reed-Solomon decoder unit  614 . The performance of the soft differential decoding of DQPSK according to an embodiment of the invention is demonstrated on the soft decision code I.5 from the fiber optic communication standard ITU-T G.975.1 shown in  FIG. 6 . The encoder uses two concatenated codes, with an outer Reed-Solomon hard-decision code and a soft-decision block-turbo product code using Hamming codes as sub-codes. The soft-decision code utilizes 2-3 soft bits. The decoding involves several iterations that are typical for turbo codes. The outer Reed-Solomon code then corrects the residual errors. The soft-decoding of the inner code is performed using the Chase algorithm as described in R. M. Pyndiah, “ Near - Optimum Decoding of Product Codes: Block Turbo Codes”, IEEE Transactions on Communications,  vol. 46, no. 8, pp. 1003-1010, August 1997. 
         [0045]      FIG. 7  illustrates the performance of the soft differential decoding method in combination with a soft decision forward error correction (FEC) according to an embodiment of the invention. In more detail,  FIG. 7  shows the bit error rate (BER) of a coherent Quadrature Phase Shift Keying (QPSK)  78  before being processed by a forward error correction (FEC) unit; the BER of a binary differentially decoded QPSK  79  before being processed by a forward error correction (FEC) unit; the BER of a standard soft decoding of QPSK (DQPSK)  80  before being processed by a forward error correction (FEC) unit; the BER of a coherent Phase Shift Keying (QPSK)  73  after being processed by a forward error correction (FEC) unit; the BER of a soft differential decoded QPSK (DQPSK)  74 , according to an embodiment of the invention, at 3 bits of non linear quantization (including compression and expansion) and a clipping level of 0.6, after being processed by a forward error correction (FEC) unit (soft-decision FEC); the BER of a soft differential decoded QPSK (DQPSK)  75 , according to an embodiment of the invention, at 3 bits of linear quantization and a clipping level of 0.6, after being processed by a forward error correction (FEC) unit (soft-decision FEC); the BER of a soft differential decoded QPSK (DQPSK)  76 , according to an embodiment of the invention, at 3 bits of quantization and a clipping level of 1, after being processed by a forward error correction (FEC) unit (soft-decision FEC); the BER of a soft differential decoded QPSK (DQPSK)  77 , according to an embodiment of the invention, at 10 bits of quantization and a clipping level of 3, after being processed by a forward error correction (FEC) unit (soft-decision FEC) 
         [0046]    Only the performance of the inner soft-code is evaluated, since it is sufficient to describe the overall code performance. The penalty  81  after forward error correction (FEC) decoding is ˜0.7 dB at 3 bits of quantization and is thus identical to the penalty caused by binary differential decoding. This is the minimum possible penalty that can be achieved without using iterative concatenated convolution codes as discussed before. Decoding with 2 bits quantization gives a penalty of ˜0.7 dB as well, although it is not shown in  FIG. 7 . Just for comparison, also the FEC performance for different clipping levels is shown. For example, if the clipping level is 0.6, then the signal is quantized between the amplitude of [−0.6; 0.6]. The original signal amplitudes without noise are assumed as [−1; 1]. The optimum choice of the clipping function ensures best performance. 
         [0047]      FIG. 7  shows as well the performance for 10 bits of quantization and a high clipping level of 3, which corresponds to a standard soft DQPSK decoding or differential demodulation of QPSK. It is apparent that the output BER of the FEC (after forward error correction) is a function of the input BER (before forward error correction), so that the resulting performance deterioration directly depends on the worse BER before the FEC. 
         [0048]    The described method, according to an embodiment of the invention, makes it possible to compute soft information after differential decoding, while having the minimum differential loss of binary decoding. 
         [0049]    The described method, according to an embodiment of the invention, can be implemented on an integrated circuit in the digital domain, for example on an application-specific integrated circuit (ASIC), field-programmable gate array (FPGA) or similar technologies. The parameters of quantization in the soft differential decoding algorithm have to be optimized with respect to the given FEC algorithm. The quantization levels in the differential decoder have to be adjusted to the quantization levels of the FEC. No iterations between the differential decoding and FEC are required and they can function in a strictly feed-forward setting. 
         [0050]    The present invention is not limited to the details of the above described principles. The scope of the invention is defined by the appended claims and all changes and modifications as fall within the equivalents of the scope of the claims are therefore to be embraced by the invention. Mathematical 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.