SIGNAL EQUALIZER IN A COHERENT OPTICAL RECEIVER

Abstract

A signal equalizer for compensating impairments of an optical signal received through a link of a high speed optical communications network. At least one set of compensation vectors are computed for compensating at least two distinct types of impairments. A frequency domain processor is coupled to receive respective raw multi-bit in-phase (I) and quadrature (Q) sample streams of each received polarization of the optical signal. The frequency domain processor operates to digitally process the multi-bit sample streams, using the compensation vectors, to generate multi-bit estimates of symbols modulated onto each transmitted polarization of the optical signal. The frequency domain processor exhibits respective different responses to each one of the at least two distinct types of impairments.

Claims

1. A signal equalizer for compensating impairments of an optical signal received through a link of a high speed optical communications network, the signal equalizer comprising: means for computing at least one set of compensation vectors for compensating at least two distinct types of impairments; a frequency domain processor coupled to receive respective raw multi-bit in-phase (I) and quadrature (Q) sample streams of each received polarization of the optical signal, the frequency domain processor comprising: for each received polarization: a respective Fast Fourier Transform (FFT) block connected to receive the raw multi-bit sample streams of the received polarization, the FFT block being operative to compute a respective complex-value array representative of a frequency-domain spectrum of the received polarization, a width of the array being selected based on an expected maximum chromatic dispersion of the received optical signal; and a respective transpose-and-add block for adding the complex-value array to a transposed version of itself to generate a corresponding intermediate array; a cross-compensation block for digitally processing the respective intermediate arrays of each of the received polarizations to generate a set of modified arrays, each modified array being representative of a frequency-domain spectrum of a respective one of the transmitted polarizations; and a respective Inverse Fast Fourier transform (IFFT) block for processing each modified array to generate the multi-bit estimates of symbols modulated onto the corresponding transmitted polarization of the optical signal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Further features and advantages of the present invention will become apparent from the following detailed description, taken in combination with the appended drawings, in which:

[0026] FIG. 1 is a block diagram schematically illustrating principal elements and operations of a coherent optical receiver known from Applicant's U.S. Pat. Nos. 7,555,227; 7,627,252; 7,532,822; 7,606,498; and 7,636,525;

[0027] FIGS. 2a and 2b are a block diagram schematically illustrating principal elements and operations of the dispersion compensation block of FIG. 1, known from Applicant's U.S. Pat. No. 7,894,728;

[0028] FIG. 3 is a block diagram schematically illustrating principal elements and operations of a coherent optical receiver in accordance with an embodiment of the present invention;

[0029] FIG. 4 is a block diagram schematically illustrating principal elements and operations of the equalizer of FIG. 3;

[0030] FIGS. 5a and 5b illustrate representative LMS loops for computing polarization compensation vectors in accordance with a first embodiment of the present invention;

[0031] FIG. 6 illustrates a representative LMS loop for computing polarization compensation vectors in accordance with a second embodiment of the present invention; and

[0032] FIGS. 7a and 7b illustrate representative frequency domain filters usable in the LMS loop of FIG. 6.

[0033] It will be noted that throughout the appended drawings, like features are identified by like reference numerals.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0034] The present invention provides an agile signal equalizer for compensating dispersion and polarization impairments in a coherent optical receiver of a high speed optical network. Embodiments of the present invention are described below, by way of example only, with reference to FIGS. 3-7.

[0035] FIG. 3 illustrates principle elements of a coherent optical receiver which incorporates an agile signal equalizer 52 in accordance with the present invention. As may be seen in FIG. 3, the agile signal equalizer 52 combines the functionality of the dispersion compensation and polarization compensation blocks 14 and 18 of the system of FIG. 1. Thus, the agile signal equalizer 52 is capable of correcting timing errors between I and Q sample streams of each received polarization, compensating moderate to severe chromatic dispersion, and compensating polarization effects to thereby de-convolve symbols modulated onto each of the transmitted polarizations from the received signals.

[0036] As described in Applicant's U.S. Pat. No. 7,555,227 issued Jun. 30, 2009, separating the dispersion and polarization compensation blocks, in the manner described above in respect of FIGS. 1 and 2, has the advantage of enabling different compensation response times for each compensation block. Thus, the dispersion compensation block 14 is very wide to enable compensation of moderate to severe dispersion, and the associated slow response (for recalculating the compensation coefficients C.sub.X and C.sub.Y) is acceptable because dispersion is typically a slowly changing phenomenon. Conversely, the polarization compensation block 18 is, by comparison, very narrow, to facilitate a rapid response to polarization rotation transients. Combining both dispersion and polarization compensation into a common equalizer would be beneficial because it reduces the total number of gates required by the compensation circuitry, thereby reducing power consumption and associated heat dissipation problems. However, these potential advantages come at a cost of reductions in either or both of dispersion compensation performance and responsiveness to polarization transients.

[0037] The present invention overcomes this difficulty by providing an agile signal equalizer 52 which has sufficient width to enable compensation of moderate-to-severe dispersion. A high-speed Least Mean Squares (LMS) update block 54 provides recalculation of compensation coefficients at a sufficiently high speed to enable tracking of polarization transients. A representative coherent optical receiver incorporating the signal equalizer is described below with reference to FIG. 3. A representative embodiment of the signal equalizer 52 is illustrated in FIG. 4. Representative embodiments of the LMS update block 54 are described below with reference to FIGS. 5-7.

[0038] As may be seen in FIG. 3, a coherent optical receiver incorporating the signal equalizer 52 of the present invention generally comprises a Polarization Beam Splitter 4; 90 optical hybrid 8; photodetectors 10; and A/D converters 12, all of which may operate as described above with reference to FIG. 1. The raw digital sample streams I.sub.X, Q.sub.X, and I.sub.Y, Q.sub.Y generated by the A/D converters 12 are then supplied to the signal equalizer 52. If desired, timing control methods described in Applicant's co-pending U.S. patent application Ser. No. 11/550,042 filed Oct. 17, 2006, including the use of elastic stores (not shown in FIG. 3) between the A/D converters 12 and the equalizer 52 may be used to ensure at least coarse phase alignment between samples at the equalizer input.

[0039] In general, the equalizer 52 operates to compensate chromatic dispersion and polarization rotation impairments. Consequently, the compensated signals 20 output from the equalizer 52 represent multi-bit estimates X(n) and Y(n) of the symbols encoded on each transmitted polarization of the received optical signal. The symbol estimates 20 X(n), Y(n), are supplied to a carrier recovery block 22 for LO frequency control, symbol detection and data recovery, such as described in Applicant's U.S. Pat. No. 7,606,498 issued Oct. 20, 2009.

[0040] In the embodiment of FIG. 4, the equalizer 52 generally follows the construction of the dispersion compensators 14 described above with reference to FIGS. 1 and 2. Thus, the raw digital sample streams I.sub.X, Q.sub.X, and I.sub.Y, Q.sub.Ygenerated by the A/D converters 12 are deserialized (at 24) and the resulting m-word input vectors {r.sup.I.sub.X+jr.sup.Q.sub.X} and {r.sup.I.sub.Y+jr.sup.Q.sub.Y} latched into the respective X- and Y-polarization FFT blocks 26. The arrays {R.sup.A.sub.X} and {R.sup.A.sub.Y} output by the FFT blocks 26 are then supplied to a Frequency Domain Processor (FDP) 56, as will be described below.

[0041] The modified arrays {V.sup.A.sub.X} and {V.sup.A.sub.Y} output by the FDP 56 are supplied to respective IFFT blocks 30, and the resulting time domain data 34 processed using respective overlap-and-add as described above with reference to FIG. 2a, to yield the equalizer output 20 in the form of complex valued vectors {v.sup.I.sub.X+jv.sup.Q.sub.X} and {v.sup.I.sub.Y+jv.sup.Q.sub.Y}, each of which encompasses m complex valued estimates X(n) and Y(n) of the transmitted symbols.

[0042] In the embodiment of FIG. 4, the FDP 56 comprises a respective transpose-and-add functional block 58 for each polarization, and a cross-compensation block. The transpose-and-add block 58 operates in generally the same manner as described above with reference to FIG. 2b. Thus, the X-polarization transpose-and-add block 58X operates to add the FFT output array {R.sup.A.sub.X} to a transposed version of itself {R.sub.X.sup.A}, with respective different compensation vectors {C.sup.O.sub.X} and {C.sup.T.sub.X}, to yield intermediate array {T.sup.A.sub.X}. As described above, compensation vectors {C.sup.O.sub.X} and {C.sup.T.sub.X} can be computed to at least partially compensate chromatic dispersion of the optical link and/or to compensate residual sample phase errors in the raw digital signals generated by the A/D converters 12. Of course, the Y-polarization transpose-and-add block 58X will operate in an exactly analogous manner.

[0043] The cross-compensation block 60 applies X-polarization vectors H.sub.XX, H.sub.XY to the X-polarization intermediate array {T.sup.A.sub.X}, and Y-polarization vectors H.sub.YY, H.sub.YX to the Y-polarization intermediate array {T.sup.A.sub.Y}. The multiplication results are then added together to generate modified vectors {V.sup.A.sub.X} and {V.sup.A.sub.Y}, as may be seen in FIG. 4. The X- and Y-polarization vectors H.sub.XX, H.sub.XY, H.sub.YY and H.sub.YX are preferably computed using a transform of the total distortion at the output of the equalizer 52, as will be described in greater detail below. At a minimum, the X- and Y-polarization vectors H.sub.XX, H.sub.XY, H.sub.YY and H.sub.YX impose a phase rotation which compensates polarization impairments of the optical signal, and so de-convolve the transmitted symbols from the raw digital sample streams I.sub.X, Q.sub.X, and I.sub.Y, Q.sub.Y generated by the A/D converters 12. Those of ordinary skill in the art will recognise that the illustrated cross-compensation block 60 implements an inverse-Jones matrix transfer function, which compensates the polarization effects. In this formulation, the vectors H.sub.XX, H.sub.XY, H.sub.YY and H.sub.YX are provided as the coefficients of the inverse-Jones matrix. The width of the inverse-Jones matrix is equal to that of the intermediate arrays {T.sup.A.sub.X} and {T.sup.A.sub.Y}, and so is based on the expected maximum dispersion of the received optical signal to be compensated by the equalizer 52.

[0044] Preferably, the X- and Y-polarization vectors H.sub.XX, H.sub.XY, H.sub.YY and H.sub.YX are computed at sufficient speed to enable tracking, and thus compensation, of high-speed polarization rotation transients. This may be accomplished using the Least Mean Squares (LMS) update loop illustrated in FIG. 4, and described in greater detail below with reference to FIGS. 5 and 6.

[0045] FIG. 5a shows an LMS update loop, according to one embodiment of the invention, for calculating polarization vectors H.sub.XX and H.sub.YX. A directly analogous LMS loop for calculating the polarization vectors H.sub.XY and H.sub.YY is shown in FIG. 5b. In the embodiment of FIGS. 5a and 5b, the carrier recovery block 22 operates as described in Applicant's U.S. Pat. No. 7,606,498 issued Oct. 20, 2009. Thus, the carrier recovery block 22 is divided into two parallel processing paths 60 (only the X-polarization path 60X is shown in FIG. 5a, and the Y-polarization path 60y is shown in FIG. 5b), each of which includes a decision circuit 62 and a carrier recovery loop comprising a carrier phase detector 64 and a phase rotator 66. In general, the phase rotators 66 use a carrier phase estimate generated by the respective carrier phase detector 64 to compute and apply a phase rotation k(n) to the symbol estimates X(n) and Y(n) received from the signal equalizer 52. The decision circuits 62 use the phase-rotated symbol estimates X(n)e.sup.jk(n) and Y(n)e.sup.jk(n) to generate recovered symbol values X(n) and Y(n), and the phase detectors 64 operate to detect respective phase errors between the rotated symbol estimates X(n)e.sup.jk(n) and Y(n)e.sup.jk(n) and the corresponding recovered symbol values X(n) and Y(n).

[0046] Referring to FIG. 5a, the H.sub.XX LMS update loop receives the phase error .sub.X(n) of each successive symbol estimate X(n), which is calculated by the phase detector 64 as described in Applicant's U.S. Pat. No. 7,606,498 issued Oct. 20, 2009. In addition, the rotated symbol estimate X(n)e.sup.jk(n) and its corresponding decision value X(n) are also received from the carrier recovery block 22, and compared (at 68) to obtain a complex symbol error value e.sub.X, which is indicative of residual distortion of the symbol estimate X(n). In some embodiments it is desirable to format the optical signal into data bursts comprising a plurality of data symbols separated by a SYNC burst having a known symbol sequence. In such cases, a selector can be used to supply a selected one of the decision values X(n) and the known SYNC symbols to the comparator 68. With this arrangement, the selector can be controlled to supply the known SYNC symbol sequence to the comparator during each SYNC burst, so that the error value e.sub.X is computed using the known SYNC symbols rather than the (possibly erroneous) decision values X(n).

[0047] In order minimize calculation complexity through the LMS update loop, the resolution of the complex symbol error e.sub.X is preferably lower than that of the symbol estimate X(n). For example, in an embodiment in which the symbol estimate X(n) has a resolution of 7 bits for each of the real and imaginary parts (denoted herein as 7+7 bits), the complex symbol error e.sub.X may have a resolution of, for example, 3+3 bits. It will be noted, however, that the present invention is not limited to these resolution values.

[0048] The phase error .sub.X(n) is processed, for example using a Look-up-Table (LUT) 70, to generate a corresponding complex value .sub.X having a unit amplitude and the same phase as .sub.X(n), with a desired resolution (e.g. 3+3 bits) matching that of the symbol error e.sub.X. This allows the phase error and symbol error .sub.X to be multiplied together (at 72) to obtain a complex vector d.sub.X indicative of the total residual distortion of the symbol estimate X(n).

[0049] Applicant's U.S. Pat. No. 7,635,525 issued Dec. 22, 2009 describes methods and systems for signal acquisition in a coherent optical receiver. As described in U.S. Pat. No. 7,635,525, during a start-up operation of the receiver (or during recovery from a loss-of frame condition), LO frequency control, clock recovery, dispersion compensation and polarization compensation loops implement various methods to acquire signal, and stabilize to steady-state operation. During this acquisitions period, the rotated symbol estimates X(n)e.sup.jk(n) and their corresponding decision values X(n) are probably erroneous. Accordingly, in the embodiment illustrated in FIGS. 5a and 5b, a window select line may be used to zero out those values of the distortion vector d.sub.X which are computed from non-sync symbols. Values of the distortion vector d.sub.X. which are computed from the known SYNC symbols are likely to be valid, even during signal acquisition, and thus are left unchanged.

[0050] In the illustrated embodiments, values of the distortion vector d.sub.X are generated at the symbol timing. In the case of Nyquist sampling, this is half the sample rate of the raw digital sample streams I.sub.X, Q.sub.X, and I.sub.Y, Q.sub.Y generated by the A/D converters 12, and it is therefore necessary to adjust the timing of the error values d.sub.X to match the sample timing. In the case of T/2 sampling (that is, the sample period is one/half the symbol period T, which satisfies the Nyquist criterion), retiming of the error values d.sub.X can be accomplished by inserting one zero between each successive error value. If desired, Interpolation or other filtering can be performed upon the retimed stream of error values to enhance the loop stability and performance.

[0051] The resulting T/2 sampled symbol distortion vector is then input to a Fast Fourier Transform (FFT) block 74, which calculates the frequency domain spectrum of the symbol distortion vector d.sub.X.

[0052] Preferably, the width of the FFT block 74 corresponds with that of the intermediate array {T.sup.A.sub.X}. With this arrangement, each value of the intermediate array {T.sup.A.sub.X} can be truncated at 76 to match the resolution of the FFT block output (e.g. 3+3 bits), and then a conjugate of the truncated array multiplied with the FFT output array (at 78), to compute a low-resolution correlation between {T.sup.A.sub.X} and the FFT output. This correlation vector is then scaled (at 80) to obtain an update vector {U.sub.XX}, which is accumulated (at 82) to obtain a vector representation of the total distortion of the intermediate array {T.sup.A.sub.X}. Truncating the total distortion vector, for example by taking the 7+7 most significant bits, yields the cross-compensation vector H.sub.XX.

[0053] As noted above, directly analogous methods can be used to compute each of the other cross-compensation vectors H.sub.XY, H.sub.YY and H.sub.YX, which are therefore not described herein in detail.

[0054] In embodiments in which the compensation vectors {C.sup.O.sub.X}, {C.sup.T.sub.X}, {C.sup.O.sub.Y} and {C.sup.T.sub.Y} are computed to compensate only residual sample phase errors in the raw digital sample streams I.sub.X, Q.sub.X, and I.sub.Y, Q.sub.Y, the symbol error e.sub.X will contain substantially all of the dispersion of the received optical signal 2. In this case, the dispersion will propagate through the LMS update loop(s) and the resulting cross compensation vectors H.sub.XX, H.sub.XY, H.sub.YY and H.sub.YX will provide at least partial compensation of the dispersion, in addition to applying a phase rotation to de-convolve the symbols modulated onto each polarization of the transmitted optical signal, from the raw digital sample streams I.sub.X, Q.sub.X, and I.sub.Y, Q.sub.Y.

[0055] In embodiments in which the compensation vectors {C.sup.O.sub.X}, {C.sup.T.sub.X}, {C.sup.O.sub.Y} and {C.sup.T.sub.Y} are computed to compensate both residual sample phase errors and chromatic dispersion, the symbol error e.sub.X will contain only a residual portion of the dispersion. In these embodiments, the cross-compensation vectors H.sub.XX, H.sub.XY, H.sub.YY and H.sub.YX will provide little or no additional dispersion compensation, but will still apply the needed phase rotation to de-convolve the symbols modulated onto the transmitted polarizations.

[0056] A limitation of the embodiment of FIG. 5 is that noise tends to increase as the speed of the tracking of polarization rotation transients increases, e.g. to 50 kHz. It would be preferable to provide low noise, accurate, compensation, while at the same time enabling close tracking of polarization rotation transients of 50 kHz or more. FIG. 6 illustrates a modification of the LMS update loop of FIG. 5, in which this issue is addressed.

[0057] In the embodiment of FIG. 6, the H.sub.XX LMS update loop of FIG. 5a is modified by the addition of a supercharger block 84, which is inserted into the LMS loop between the scaling function 80 and the accumulator 82. In this embodiment, it is assumed that the compensation vectors {C.sup.O.sub.X}, {C.sup.T.sub.X}, {C.sup.O.sub.Y} and {C.sup.T.sub.Y} are computed to compensate at least the majority of the chromatic dispersion, as described above. In this case, the inventors have observed that as the polarization rotation rate tend towards zero, the intermediate arrays {T.sup.A.sub.X} and {T.sup.A.sub.Y} become highly de-correlated with the output of the respective LMS loop FFTs 74, and the resulting update vectors have very low magnitudes. Conversely, as the polarization rotation rate increases, the intermediate arrays {T.sup.A.sub.X} and {T.sup.A.sub.Y} become significantly correlated with their respective FFT outputs, and this is reflected in an increasing magnitude of the update vectors.

[0058] The inventors have further observed that under these conditions the time duration of the majority of a time domain version of the update vector {U.sub.XX} is relatively short. This limited time duration occurs because of the limited memory inherent in optical polarization effects. The long memory effects of chromatic dispersion have already been substantially compensated, as noted above. Any residual dispersion or other long memory effects generally only need slow tracking.

[0059] The supercharger block 84 exploits these observations by implementing an arrangement in which: 1) portions of the update vector {U.sub.XX} that lie outside the time duration of a polarization effect are suppressed; 2) fully detailed updates are allowed to slowly accumulate, enabling the slow tracking of long memory effects such as chromatic dispersion and line filtering; and 3) the magnitude of the enhanced update vector {U.sub.XX} supplied to the accumulator 82 is scaled in proportion to the polarization rotation rate.

[0060] The suppression of portions of the update vector {U.sub.XX} lying outside the time duration of a polarization effect reduces the noise contribution from those portions, and so allows a higher LMS tracking speed without excessive added noise. However, since this suppression is incomplete, fully detailed updates are allowed to slowly accumulate, thereby enabling accurate tracking of slowly-changing impairments such as chromatic dispersion and line filtering. Indeed, rather than suppressing, the illustrated embodiment actually enhances the magnitude of the relevant time domain portions of the update vector. Finally, scaling the magnitude of the update vector {U.sub.XX} in proportion to the polarization rotation rate effectively increases the update step size of the important aspects of the update vectors during high speed transients, substantially without affecting the ability of the LMS update loop to provide accurate compensation (via a small update step size) during periods of low-speed polarization rotation.

[0061] As may be appreciated, there are various ways in which the Supercharger function may be implemented. In the embodiment of FIG. 6, the supercharger 84 is implemented as a frequency-domain digital filter 86 which receives the update vector {U.sub.XX} and a summation block 88 for adding the filter output vector {S.sub.XX} to the update vector {U.sub.XX} to yield the enhanced update vector {U.sub.XX}.

[0062] If desired, a threshold block 90 can be inserted at the output of the digital filter 86, as shown in dashed line in FIG. 6. The threshold block 90 can implement any of a variety of suitable linear and/or nonlinear functions to improve loop performance. A low gate-count embodiment is to implement a zeroing function, in which the raw filter output {S.sub.XX} from the digital filter 86 is multiplied by zero whenever the magnitude of {S.sub.XX} is less than a predetermined threshold. This can be done individually for each term of {S.sub.XX}, or by making one decision for the whole vector based upon a vector magnitude metric, such as peak absolute value or sum of the squared magnitude of each of the vector terms.

[0063] As may be appreciated, the frequency domain filter 86 may be implemented in various ways. FIG. 7a illustrates a low-gate-count embodiment in which the frequency domain filter 86 is implemented as a cascade of summation blocks. Thus, for example, consider an embodiment in which the update vector {U.sub.XX} has a width of N=128 taps. These 128 taps can be separated into K=16 groups of 8 taps each. Within each group, the complex values on each tap are summed {at 92}, to yield a corresponding group sum B(k). A respective weighted summation value S(k) is then computed (at 94) for each group, using the group sum values B(k) of the group, and those of the three nearest neighbouring groups. In the embodiment of FIG. 6, for each group k, the weighted summation value S(k) is computed using the equation

[00001]$S\left(k\right)=\underset{i=k-3}{\overset{k+3}{.Math.}}.Math..Math.w\left(i\right).Math.B\left(i\right),$

where the weighting factor w(i)=2.sup.|ki|, and modular arithmetic on the i provides the desirable circular wrap around characteristic.

[0064] For example, consider group k=8. The group sum B(k=8) will be the sum of the complex values on taps i=64 . . . 71 of the update vector. The weighted summation value S(k) will be computed as a weighted sum of the respective group sums B(i), i=5 . . . 11. The respective weighting factor w(i) applied to each group sum B(i) will be w(i)=2.sup.0=1 for i=k, and then descending by powers of two for each of the three neighbouring groups. Thus, w(i)=2.sup.1 for i=k1; w(i)=2.sup.2 for i=k2; and w(i)=2.sup.3 for i=k3.

[0065] The filter output vector {S.sub.XX}, comprising the weighted summation value S(k) for each group, is optionally processed by the threshold block 90, and then added (at 88) to each of the group tap values of the update vector {U.sub.XX} to yield the enhanced update vector {U.sub.XX}. Thus, continuing the above example, the weighted summation value S(k=8) will be added back to each of the complex values on taps i=64 . . . 71 of the update vector {U.sub.XX}.

[0066] With this arrangement, the value of S(k) will depend on the degree of correlation between the X-Polarization intermediate array {T.sup.A.sub.X} and the FFT output vector. When the X-Polarization intermediate array {T.sup.A.sub.X} and the FFT output vector are highly correlated, S(k) will have relatively large magnitude (in embodiments in which the threshold block 90 is used, S(k) will often be larger than the threshold), and so will have a strong effect on the enhanced update vector {U.sub.XX}, thereby improving the ability of the LMS update loop to track a rapidly changing polarization angle.

[0067] Conversely, when the X-Polarization intermediate array {T.sup.A.sub.X} and the FFT output vector are highly uncorrelated (that is, when the polarization angle of the received optical signal is not significantly changing), S(k) will have a very low magnitude (in embodiments in which the threshold block 90 is used, S(k) will usually be lower than the threshold, and thus forced to zero), and so will have little or no effect upon the enhanced update vector {U.sub.XX}, thereby keeping the added noise to a small level.

[0068] FIG. 7b illustrates an alternative embodiment in which the frequency domain filter 86 is implemented as an IFFT 96, Time-domain filter (TDF) 98 and FFT 100 blocks in sequence. In this case, the IFFT block 96 converts the update vector {U.sub.XX} to the time-domain, so that the TDF 98 can implement a windowing function that suppresses portions of the update vector {U.sub.XX} lying outside an expected duration of the polarization effect. The thus windowed time-domain update vector is then converted back into the frequency domain by the FFT block 100, to yield the output vector {S.sub.XX}. Various other time-domain filter functions may also be implemented by the TDF 98 (either in addition to or instead of the windowing function) as desired.

[0069] The above description uses frequency domain LMS. Other adaptive methods can be used. Zero-forcing is a well known alternative algorithm, which suffers from less than optimal noise filtering. Time domain versions of LMS or other algorithms could be used. This frequency domain version of LMS has the advantage of a small gate-count and relatively fast convergence.

[0070] The configuration of FIG. 4 can be simplified by omitting the multiplication of the arrays {R.sup.A.sub.X} and {R.sup.A.sub.Y} by the compensation vectors {C.sup.O.sub.X} and {C.sup.O.sub.Y}. Mathematical equivalence, to yield identical modified vectors {V.sup.A.sub.X} and {V.sup.A.sub.Y}, can be obtained by dividing the transpose compensation vectors {C.sup.T.sub.X} and {C.sup.T.sub.Y} by {C.sup.O.sub.X} and {C.sup.O.sub.Y}, respectively, and multiplying cross compensation vectors H.sub.XX and H.sub.XY by {C.sup.O.sub.X}, and multiplying H.sub.YY and H.sub.YX by {C.sup.O.sub.Y}. In a simple implementation, the {C.sup.O.sub.X} and {C.sup.O.sub.Y} multiplication blocks in the embodiment of FIG. 4 are omitted. The compensation vectors {C.sup.T.sub.X} and {C.sup.T.sub.Y} and cross compensation vectors H.sub.XX, H.sub.XY, H.sub.YY and H.sub.YX are then computed using the techniques described above, which will yield the appropriate values.

[0071] Other ways may be used for separating the response to slow long memory effects from the response to more rapid short memory effects. Pattern matching, transient speed measurement, time moments, error rates, nonlinear equalization, Jones Matrix calculations, and parameter estimations, are examples of methods that may be used, with varying gate-count requirements. Some of the slower parts of functions could be implemented in firmware.

[0072] Power based scaling or other scaling methods can be used to enhance the speed of the LMS tracking of the slower frequency components.

[0073] The embodiments of the invention described above are intended to be illustrative only. The scope of the invention is therefore intended to be limited solely by the scope of the appended claims.