Equalizing device for compensating rapid state of polarization changes of an optical signal

Abstract

The invention presents an equalizing device, a corresponding method and an optical signal with a frame structure for enabling the method. The equalizing device includes a first 2×2 MIMO equalizer configured to perform a first equalization on the digital signal, supported by a 2×2 MIMO channel estimation of the channel based on the digital signal. Further, the device includes a second 2×2 MIMO equalizer, arranged after the first equalizer and configured to perform a second equalization on the digital signal, supported by a State of Polarization (SOP) estimation of the optical signal based on the digital signal.

Claims

1. An equalizing device configured to process a digital signal derived from an optical signal transmitted over a channel, the equalizing device comprising: a first 2×2 multiple input multiple output (MIMO) equalizer configured to perform a first equalization on the digital signal, supported by a 2×2 MIMO channel estimation of the channel based on the digital signal, and a second 2×2 MIMO equalizer, arranged after the first equalizer, configured to perform a second equalization on the digital signal, supported by a state of polarization (SOP) estimation of the optical signal based on the digital signal.

2. The equalizing device according to claim 1, wherein: the first equalizer is configured to, by performing the first equalization, compensate residual chromatic dispersion (CD), polarization-mode dispersion (PMD), and changes of the SOP of the optical signal slower than a first threshold, and the second equalizer is configured to, by performing the second equalization, compensate changes of the SOP of the optical signal faster than the first threshold.

3. The equalizing device according to claim 1, wherein: at least one of the first equalizer and the second equalizer is a training-aided equalizer.

4. The equalizing device according to claim 1, wherein: the first equalizer is configured to perform the 2×2 MIMO channel estimation based on a first training sequence contained in the digital signal, and the second equalizer is configured to perform the SOP estimation based on a second training sequence contained in the digital signal.

5. The equalizing device according to claim 1, wherein: the first equalizer is configured to perform the 2×2 MIMO channel estimation based on a first training sequence included in a frame of the optical signal, and the second equalizer is configured to perform the SOP estimation individually for each of multiple additional training sequences included in the frame, wherein a length of each training sequence of the multiple additional training sequences is shorter than a length of the first training sequence.

6. The equalizing device according to claim 5, wherein: the second equalizer is configured to, by performing the SOP estimation for a particular training sequence of the multiple additional training sequences, perform the second equalization for a first data sequence arranged directly before the particular training sequence and for a second data sequence arranged directly after the particular training sequence in the frame.

7. The equalizing device according to claim 4, wherein: the first and second training sequences are based on Perfect-Square Minimum-Phase Constant-Amplitude Zero-Autocorrelation (PS-MP CAZAC) code.

8. The equalizing device according to claim 1, wherein: the first equalizer is implemented in the frequency domain (FD) or in the time domain (TD), and/or the second equalizer is implemented in the FD or in the TD.

9. The equalizing device according to claim 1, further comprising: a chromatic dispersion (CD) equalizer arranged before the first equalizer and configured to perform equalization on the digital signal, supported by a CD estimation of the optical signal based on the digital signal.

10. The equalizing device according to claim 9, comprising: a dual-stage equalizer which includes the CD equalizer and the first equalizer, and the second equalizer.

11. The equalizing device according to claim 9, further comprising: a single-stage equalizer that includes the CD equalizer, the first equalizer, and the second equalizer.

12. The equalizing device according to claim 1, further comprising: one or more Digital Signal Processors (DSPs) configured to perform digital signal processing on the digital signal that includes processing for symbol detection and/or processing of fractional oversampled data.

13. A method for processing a digital signal derived from an optical signal transmitted over a channel, the method comprising: performing a first 2×2 multiple input multiple output (MIMO) equalization on the digital signal, supported by a 2×2 MIMO channel estimation of the channel based on the digital signal, and performing a second 2×2 MIMO equalization on the digital signal, supported by a state of polarization (SOP) estimation of the optical signal based on the digital signal.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) The above described aspects and implementation forms of the present invention will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which

(2) FIG. 1 shows an equalizing device according to an embodiment of the invention.

(3) FIG. 2 shows an optical receiver according to an embodiment of the invention.

(4) FIG. 3 shows an equalizing device according to an embodiment of the invention.

(5) FIG. 4 shows an equalizing device according to an embodiment of the invention.

(6) FIG. 5 shows a structure of a frame for an optical signal according to an embodiment of the invention.

(7) FIG. 6 shows training sequences in the frame of the optical signal for compensating slower and faster SOP changes.

(8) FIG. 7 shows a method according to an embodiment of the invention,

(9) FIG. 8 shows a performance evaluation of an equalizing device according to an embodiment of the invention for 200G DP-QPSK.

(10) FIG. 9 shows a performance evaluation of an equalizing device according to an embodiment of the invention for 400G DP-16QAM.

DETAILED DESCRIPTION OF EMBODIMENTS

(11) FIG. 1 shows an equalizing device 100 according to an embodiment of the invention. The equalizing device 100 is particularly configured to process a digital signal 101. The digital signal 101 is derived, e.g., may be generated from, e.g., by an optical receiver 200, from an optical signal 201 transmitted over a transmission channel 202 (see FIG. 2).

(12) The device 100 comprises a first 2×2 MIMO equalizer 102 and a second 2×2 MIMO equalizer 105, which is arranged after the first equalizer 102. The first equalizer 102 and the second equalizer 105 may thereby be decoupled from another.

(13) The first 2×2 MIMO equalizer 102 is configured to perform a first equalization 103 on the digital signal 101. The first equalization 103 is supported by a 2×2 MIMO channel estimation 104 of the channel 202 based on the digital signal 101. In particular, the first equalization 103 takes a channel estimation result (i.e. An estimate of the channel state) as an input. The second 2×2 MIMO equalizer 105 is configured to perform a second equalization 106 on the digital signal 101. The second equalization 106 is supported by a SOP estimation 107 of the optical signal 201 based on the digital signal 101. In particular, the second equalization takes a SOP estimation result (i.e. An SOP estimate) as an input.

(14) The equalizing device 100 is configured to, by means of the first equalizer 102, compensate residual CD, PMD, and slower changes of the SOP of the optical signal 201, and is configured to, by means of the second equalizer 105, compensate faster changes of the SOP of the optical signal 201.

(15) FIG. 2 shows an optical receiver 200 according to an embodiment of the invention. The optical receiver 200 includes at least one device 100 as shown in FIG. 1. The optical receiver 200 may particularly be a coherent optical receiver, i.e. May be a receiver configured to receive and process a coherent optical signal.

(16) The optical receiver 200 is configured to receive the optical signal 201 over the transmission channel 202, and to derive, e.g., generate, the digital signal 101 from the received optical signal 201. For instance, the optical receiver 200 may to this end comprise a coherent detector configured to derive an RF signal from the optical signal 201, and may further comprise an ADC configured to sample the RF signal. The digital signal 101 may in this case be a sampled version of the RF signal derived from the optical signal 201.

(17) The optical receiver 200 is configured to, by means of the equalizing device 100, compensate CD, PMD, as well as slower and faster changes of the SOP of the optical signal 201.

(18) FIG. 3 and FIG. 4 each show an equalizing device 100 according to an embodiment of the invention. Each equalizing device 100 builds on the equalizing device 100 shown in FIG. 1. Accordingly, same elements in FIG. 1 and in FIG. 3 or FIG. 4 are labeled with the same reference signs and function likewise.

(19) In particular, two possible structures for the equalizing device 100 of FIG. 1 are shown in FIG. 3 and FIG. 4, respectively. In both examples, the equalizing device 100 comprises a CD equalizer 300 and the two 2×2 MIMO equalizers 102 and 105 shown in FIG. 1. The CD equalizer 300 is used for performing CD equalization 301 on the input digital signal 101, wherein the CD equalization 301 is supported by a CD estimation 302 of the optical signal 201 based on the digital signal 101. That is, the CD equalization 301 takes a CD estimation result as an input. The first equalizer 102 is used for compensating residual CD, PMD, and slower changes of the SOP of the optical signal 201. The second equalizer 105 is used for compensating faster changes of the SOP of the optical signal 201. The first and second equalizers 102 and 105 can, respectively, be implemented either in FD or in TD.

(20) FIG. 3 shows specifically an equalizing device 100 comprising a dual-stage frequency-domain equalizer (FDE) followed by a SOP time-domain equalizer (TDE). FIG. 4 shows specifically an equalizing device 100 comprising a single-stage FDE followed by a SOP TDE. The 2×2 MIMO equalizers 102 and 105 (in FIG. 3 and also in FIG. 4) are training-aided equalizers, i.e. They are arranged to do the 2×2 MIMO channel estimation 104 and the SOP estimation 107, respectively, based on one or more training sequences. For instance, the 2×2 MIMO channel estimation 104 may be based on a first training sequence and the SOP estimation 107 may be based on a second training sequence. Each or both of the first and second training sequences may be contained in the digital signal 101. The first and second training sequences may be either or both based on PS-MP CAZAC code.

(21) Both equalizing devices 100 as illustrated in FIG. 3 and FIG. 4, respectively, include also DSP units or modules, which are, for instance, used for symbols detection and/or allowing processing fractional oversampled data. In particular, DSP units of the equalizing devices 100 shown in FIG. 3 and FIG. 4, respectively, include units for carrying out at least one of serial/parallel conversion, an Overlap-Discard (OLD) method, Fast Fourier Transform (FFT) or inverse FFT (IFFT), Frame Alignment, Folding Decimation, signal buffering, carrier frequency offsetting, carrier phase compensation, symbol alignment or the like.

(22) Equalization performed in the FD may particularly be based on the OLD method, which includes transferring 50% overlapping blocks of the serial data (of the data signal 101) into FD by a discrete FFT, applying a compensating function to each block, transferring the signal back into TD by discrete inverse FFT (IFFT), and cutting off the overlap to restore the serial data signal 101. For an efficient hardware implementation, the oversampling factor m.sub.sps Should be chosen such that
mod{Nm.sub.sps,2}=0,

(23) With {0<m.sub.sps≤2} And with N is the length of the PS-MP CAZAC sequence (first or second training sequence).

(24) FIG. 5 shows the structure of a frame 500 of an optical signal 201 according to an embodiment of the invention. The optical signal 201 typically includes a sequence of such frames 500. The frame 500 includes a plurality of data sequences 501, a longer training sequence 502 and a plurality of shorter training sequences 503. The shorter training sequences 503 are arranged such in the frame 500 that a shorter training sequence 503 is arranged between each two subsequent (along the time axis) data sequences 501. The longer training sequence 502 may be arrange before the data sequences 501 and shorter training sequences 503, respectively.

(25) The longer training sequence 502 can be used for 2×2 MIMO channel estimation 104 of the channel 202, over which the optical signal 201 is transmitted. That means, the longer training sequence 502 can be provided as an input to the first equalizer 102 of the device 100 shown in FIG. 1, 3 or 4, in particular for performing the 2×2 MIMO channel estimation 104. In other words, the longer training sequence 502 is a suitable sequence for performing 2×2 MIMO channel estimation 104.

(26) The shorter training sequences 503 can each be used for SOP estimation 107 of the optical signal 201. That means, each shorter training sequence 503 can be provided as an input to the second equalizer 105 of the device 100 shown in FIG. 1, 3 or 4, in particular for performing the SOP estimation 107. In other words, the shorter training sequences 503 are suitable sequences for performing SOP estimation 107.

(27) The training sequences 502, 503, i.e. Both the shorter training sequences 503 and the longer training sequence 502, may be built by using a PS-MP CAZAC sequence (i.e. Based on a PS-MP CAZAC code) or more generally using a Frank-Zadoff sequence. The sequence may be defined as:

(28) $c\left[n\right]=\mathrm{Exp}\left(\pm j\frac{2\pi }{\sqrt{N}}\left(\mathrm{mod}\left\{n,\sqrt{N}\right\}+1\right)\left(.Math.\frac{n}{\sqrt{N}}.Math.+1\right)\right),$

(29) Where N is the sequence length in symbols. The minimum number of distinct phases of the above polyphase code given by √{square root over (N)} Is obtained for sequences length N=2.sup.p Symbols with p∈{1, 2, 3, . . . }. However, for lengths N=2.sup.2p′ Symbols with p′∈{1, 2, 3, . . . } The constellation plot of a PS-MP CAZAC sequence refers to a log(N)PSK modulated signal (i.e. p′=1 refers to BPSK, p′=2 to QPSK, p′=3 to 8 PSK and so on).

(30) The training sequences 502 and 503 for both the 2×2 MIMO channel estimation 104 and the SOP estimation 107, respectively, are defined as:

(31) ${\mathrm{ts}}_{\varkappa }=\left[{\mathrm{gi}}_{\mathrm{xf}},\underset{\underset{\mathrm{inclue}x\mathrm{times}{c}_x}{︸}}{c_x,c_x,,.Math.,c_x},{\mathrm{gi}}_{\mathrm{xb}}\right]{\mathrm{ts}}_y=\left[{\mathrm{gi}}_{\mathrm{yf}},\underset{\underset{\mathrm{inclue}x\mathrm{times}{c}_y}{︸}}{c_y,c_y,,.Math.,c_y},{\mathrm{gi}}_{\mathrm{yb}}\right],$

(32) With χ≥1. The PS-MP CAZAC blocks and the guard intervals (gis) are particularly defined as:
c.sub.x=[c[0],c[1], . . . ,c[N−1]],
c.sub.y=[c[N/2],c[N/2+1], . . . ,c[N−1],c[0],c[1], . . . ,c[N/2−1]],
gi.sub.xf=[c[N−N.sub.GI],c[N−N.sub.GI+1], . . . ,c[N−1]]
gi.sub.xb=[c[0],c[1], . . . ,c[N.sub.GI−1]]
gi.sub.yf=[c[N/2−N.sub.GI],c[N/2−N.sub.GI+1], . . . ,c[N/2−1]]
gi.sub.yb=[c[N/2],c[N/2+1], . . . ,c[N/2+N.sub.GI−1]]

(33) In general, N.sub.TS1<<N.sub.TS, e.g., for a 64 gbd system at N.sub.TS=96 symbols (with a PS-MP CAZAC block of N.sub.GI=64 symbols and including gis of length N.sub.GI=16 symbols) and N.sub.TS1=4 symbols (GI usually not required for SOP estimation).

(34) In the following, training-aided 2×2 MIMO channel estimation) 104 and SOP estimation 107 are outlined for the FD (2×2 SOP Matrix FD estimation). The noiseless transmission system can be modeled as:

(35) $\left[\begin{array}{c}{R}_x\left[k\right]\\ R_y\left[k\right]\end{array}\right]=\left[\begin{array}{cc}{H}_{\mathrm{xx}}\left[k\right]& H_{\mathrm{xy}}\left[k\right]\\ H_{\mathrm{yx}}\left[k\right]& H_{\mathrm{yy}\left[k\right]}\end{array}\right]\left[\begin{array}{c}{C}_x\left[k\right]\\ C_y\left[k\right]\end{array}\right]$

(36) Where R.sub.x, R.sub.y And C.sub.x, C.sub.y Refer to the x- and y-polarization received and sent PS-MP CAZAC sequences in FD, respectively.

(37) To perform the 2×2 MIMO channel estimation 104, the left and the right matrix of the above equation need to be multiplied from the left hand-side by:

(38) $\left[\begin{array}{cc}{C}_x^{*}\left[k\right]& 0\\ 0& C_y^{*}\left[k\right]\end{array}\right]$

(39) Such to obtain the following H.sub.A[k] and H.sub.B [k]:

(40) $H_A\left[k\right]=R_x\left[k\right]C_{\mathrm{x1}}^{*}\left[k\right]=H_x\left[k\right]C_{\varkappa }\left[k\right]C_{\varkappa }^{*}\left[k\right]+H_{\mathrm{xy}}\left[k\right]C_x\left[k\right]C_y^{*}\left[k\right]=H_{\mathrm{xx}}\left[k\right]C_x\left[k\right]C_x^{*}\left[k\right]+H_{\mathrm{xy}}\left[k\right]C_x\left[k\right]C_x^{*}\left[k\right]e^{\frac{jN}{2}}{H}_B\left[k\right]=R_y\left[k\right]C_y^{*}\left[k\right]=H_{\mathrm{yy}}\left[k\right]C_y\left[k\right]C_y^{*}\left[k\right]+H_{\mathrm{yx}}\left[k\right]C_y\left[k\right]C_x^{*}\left[k\right]=H_{\mathrm{yy}}\left[k\right]C_y\left[k\right]C_y^{*}\left[k\right]+H_{\mathrm{yx}}\left[k\right]C_y\left[k\right]C_y^{*}\left[k\right]e^{\frac{jN}{2}}$

(41) Transferring these H.sub.A[k] and H.sub.B[k] into the TD yields:
h.sub.A[n]=r.sub.x[n]*c*.sub.x[n−N]=h.sub.xx[n]*δ.sub.0[n]+h.sub.xy[n]*δ.sub.N/2[n]
h.sub.B[n]=r.sub.y[n]*c*.sub.y[n−N]=h.sub.yy[n]*δ.sub.0[n]+h.sub.yx[n]*δ.sub.N/2[n]

(42) Where:

(43) ${\delta }_L\left[n\right]=\{\begin{array}{c}1n=L\\ 0\mathrm{Otherwise}\end{array}$

(44) The TD windowing is required to extract the four channel components from H.sub.A[k] and H.sub.B [k] such that:
h.sub.xx[n]=h.sub.A[n]rect[n]
h.sub.xy[n]=h.sub.A[n−N]rect[n]
h.sub.yx[n]=h.sub.B[n−N]rect[n]
h.sub.yy[n]=h.sub.B[n]rect[n]

(45) Where:

(46) $\mathrm{rect}\left[n\right]=\{\begin{array}{c}0N_{\mathrm{TDW}}\ge n\le N-N_{\mathrm{TDW}}\\ 1\mathrm{Elsewhere}\end{array}{N}_{\mathrm{CIR}}\le N_{\mathrm{TDW}}\le N/4$

(47) Since the 2×2 SOP estimation 107 is performed by the second 2×2 MIMO equalizer after the first 2×2 MIMO equalizer 102, the residual channel impulse response (CIR) is given only by the delta SOP rotation matrix, so that N.sub.CIR=1 symbol.

(48) In addition, knowing that the 2×2 SOP matrix is given by:

(49) $h_{SOP}\left[n\right]=\left[\begin{array}{cc}{h}_v\left[n\right]& h_u\left[n\right]\\ -h_u^{*}\left[n\right]& h_v^{*}\left[n\right]\end{array}\right]$

(50) The following averaging can be performed:
h.sub.v[n]=(h.sub.xx[n]+h*.sub.yy[n])/2
h.sub.u[n]=(h.sub.xy[n]−h*.sub.yx[n])/2

(51) Based on the h.sub.v[n] And h.sub.u[n], the taps of the second 2×2 MIMO equalizer 105 can be calculated.

(52) Since the second 2×2 MIMO equalizer 105 handles with data sampled at 1Sa/S the following matrix inversion is performed:
w.sub.SOP[n]=h.sub.SOP.sup.−1[n]

(53) If the second 2×2 MIMO equalizer 105 is implemented in FD, then four additional ffts are required to convert the four channel elements into the FD. In case the length of the second equalization 106 is different than that of the SOP estimation 107, zero-padding or truncation may be performed (usually at the TD windowing stage).

(54) In the following, training-aided 2×2 MIMO channel estimation) 104 and SOP estimation 107 are outlined in detail for the TD (2×2 SOP Matrix TD estimation). In case the SOP estimation 107 is performed in TD (lower complexity for shorter training sequences) h.sub.A [n] and h.sub.B [n] can be obtained as:

(55) $h_A\left[i\right]=\underset{n=0}{\overset{N-1}{.Math.}}{r}_{\varkappa }\left[\mathrm{mod}\left\{n+i,N\right\}\right]c_x^{*}\left[n\right]h_B\left[i\right]=\underset{n=0}{\overset{N-1}{.Math.}}{r}_y\left[\mathrm{mod}\left\{n+i,N\right\}\right]c_y^{*}\left[n\right]$

(56) For i∈{0, 1, 2, . . . , N−1}.

(57) The remaining operations are then carried out as described above for the FD case.

(58) FIG. 6 shows training sequences 502 and 503 in the frame 500 of the optical signal 201 that can be used for compensating slower and faster SOP changes. FIG. 6 specifically illustrates the equalization approach performed by the equalizing device 100 of FIG. 1, 3 or 4, based on the structure of the frame 500 of the optical signal 201 (as also shown in FIG. 5).

(59) PMD, residual CD, and slower SOP changes can be compensated with support of 2×2 MIMO channel estimation 104 based on the first (longer) training sequence 502, particularly for data sequence 501 arranged prior and posterior this first training sequence 502. In a similar way, faster SOP changes can be compensated with support of SOP estimation 107 based on a given second (shorter) training sequence 503, particularly for data sequences 501 arranged prior and posterior the given second training sequence 503. That means, the second equalization 106 may be performed for a data sequence 501 arranged directly before a given training sequence 503 and for a data sequence 501 arranged directly after the given training sequence 503 in the frame 500. For instance, in FIG. 6 the second and third data sequences 501 (from the left side, i.e. The ones labeled d.sub.y1, d.sub.x1 and d.sub.y2, d.sub.x2) are compensated with support of SOP estimation 107 performed with the shorter training sequence 503 arranged in between these data sequences 501. The second and third data sequences 501 (i.e. The ones labeled d.sub.y2, d.sub.x2 and d.sub.y3, d.sub.x3) are compensated with support of SOP estimation 107 performed with the training sequence 503 arranged in between these data sequences 501. This approach is preferably carried out with a buffer, particularly one that enables equalization with half-frame delay.

(60) FIG. 7 shows a method 700 according to an embodiment of the invention. The method 700 is for processing a digital signal 101 derived from an optical signal 201 transmitted over a channel 202. The method 700 may be carried out by the device 100 shown in FIG. 1 (or FIG. 3 or 4) or by the optical receiver 200 shown in FIG. 2,

(61) The method 700 comprises a step 701 of performing a first 2×2 MIMO equalization 103 on the digital signal 101, supported by a 2×2 MIMO channel estimation 104 of the channel 202 based on the digital signal 201. This step 701 may be carried out by a first 2×2 MIMO equalizer 102. The method 700 also comprises a step 702 of performing a second 2×2 MIMO equalization 106 on the digital signal 101, supported by a SOP estimation 107 of the optical signal 201 based on the digital signal 101. This step 702 may be carried out by a second 2×2 MIMO equalizer 105.

(62) FIG. 8 and FIG. 9 show simulation results as proof of concept for the device 100 and method 700, respectively. In particular, performance evaluation for 200G DP-QPSK (FIG. 8) and for 400G DP-16QAM (FIG. 9) is illustrated, respectively. It can be seen that in both cases, the device 100 performs significantly better (lower Required Optical Signal-to-Noise Ration (ROSNR) at a Bit Error Rate (BER) of 10.sup.−2 Penalty) for all SOP rotations, particularly faster SOP rotations up to 100 Mrad/s.