Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L25/00—Baseband systems
  • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
  • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
  • H04L25/03006—Arrangements for removing intersymbol interference
  • H04L25/03012—Arrangements for removing intersymbol interference operating in the time domain
  • H04L25/03019—Arrangements for removing intersymbol interference operating in the time domain adaptive, i.e. capable of adjustment during data reception
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
  • H04B10/60—Receivers
  • H04B10/66—Non-coherent receivers, e.g. using direct detection
  • H04B10/69—Electrical arrangements in the receiver
  • H04B10/697—Arrangements for reducing noise and distortion
  • H04B10/6971—Arrangements for reducing noise and distortion using equalisation
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L25/00—Baseband systems
  • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
  • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
  • H04L25/03006—Arrangements for removing intersymbol interference
  • H04L2025/03592—Adaptation methods
  • H04L2025/03598—Algorithms
  • H04L2025/03611—Iterative algorithms
  • H04L2025/03636—Algorithms using least mean square [LMS]

Definitions

• the present invention relates to an equalizer and a corresponding equalization method for a four-level pulse amplitude modulation (PAM-4) signal.
• the equalizer of the present invention is a nonlinear equalizer based on the Volterra model.
• Next-generation ultra-high-speed short-reach optical fiber links will utilize small, cheap, and low-power consumption transceivers. These requirements for transceiver size, price and power- consumption are mainly imposed by the limited space for equipment in data centers.
• the transceivers should further support intra- and inter-data center connections ranging from a few hundred meters up to several tens of kilometers, respectively.
• DSP digital signal processing
• a conventional PAM-4 transmission system is shown in Fig. 11.
• Data encoded by a forward error correction (FEC) block can be partially equalized by DSP at the transmitter side, and can be converted into an analog signal by a digital-to-analog converter (DAC).
• DAC digital-to-analog converter
• the data can then be equalized in the analog domain, for instance, by a continuous- time linear equalizer (CTLE).
• CTL continuous- time linear equalizer
• this signal is amplified using a modulator driver (MD).
• MD modulator driver
• DFB distributed feedback laser
• EAM electro-absorption modulator
• TOSA transmit optical subassemblies
• DML direct-modulated laser
• VCSEL vertical-cavity surface- emitting laser
• a photo diode PIN-positive-intrinsic negative or APD-avalanche photo diode
• the output of the photodiode is proportional to the power of the optical signal.
• the photodiode output is usually amplified by a trans- impedance amplifier (TIA).
• TIA trans- impedance amplifier
• the photodiode and the TIA can be integrated in receiver optical subassemblies (ROSA) that may also include an automatic gain control circuit (AGC), in order to adjust the electrical signal to an analog-to-digital (ADC) input, when electronic equalization is used.
• ROSA receiver optical subassemblies
• ADC automatic gain control circuit
• An equalizer of the receiver is used to recover signals suffering from noise and inter-symbol interference (ISI).
• ISI inter-symbol interference
• the local oscillator must be locked to the input signal, i.e. to the transmitter oscillator responsible for data clocking.
• the two oscillators must be synchronized. Small deviations are allowed, since it is impossible to perfectly track the transmitter clock source.
• Clock extraction is supported by a timing recovery (TR) block that controls ADC sampling frequency and phase.
• TR timing recovery
• the performance of this block is strongly influenced by noise that is partly filtered out by specific filters. However, some imperfections such as bandwidth limitation and chromatic dispersion may result in a very weak timing function. Therefore, the signal used for timing recovery has to be partially compensated to enable correct ADC clocking.
• the equalized signal can be used for clock extraction, in order to decrease the clock jitter.
• This signal can be further processed by a maximum-likelihood sequence estimator (MLSE) to improve a bit error rate (BER) before the error correction block (FEC decoder) that delivers the final decisions.
• MLSE maximum-likelihood sequence estimator
• BER bit error rate
• FEC decoder error correction block
• the MLSE introduces an additional complexity that can be avoided in low- power consumption applications.
• Feed-forward (FFE) and decision feedback equalizers (DFE) can be found in many practical systems, while nonlinear equalizers (NLE) are less deployed, although they can bring a significant gain in some special applications.
• a conventional hybrid FFE-DFE architecture is shown in Fig. 12.
• the quantized data is low-pass filtered and then equalized by the FFE and DFE. Filter coefficients of both equalizers are controlled by the same error signal e.
• the FFE can use an oversampled signal, in order to improve the performance, and to be less sensitive to the sampling phase. Two or three samples per symbol period may improve the FFE performance, which also depends on the channel impairments. However, a performance and complexity trade-off must be done at high baud rates.
• the DFE is symbol-based and uses only one sample per symbol. Such one sample per symbol equalizers are often used, due to their complexity and not significant gain by introducing more samples.
• the filter coefficients can be updated in blind or training mode. Normally, long training sequences are not available at the receiver side, whereas some short training sequences can be periodically inserted (better to avoid) to help the adaptive filters to converge faster and to avoid ill convergence.
• the ill convergence includes suboptimum convergence (which leads to suboptimum BER), false convergence (stable coefficients, but BER almost 0.5), and evolving coefficients to very high values (can go to infinity).
• the equalizer may rely on decisions that are not error-free, but still good enough to enable the correct filter tap values setting (DD mode).
• the peak distortion criterion and the mean square error (MSE) criterion also known as least mean square (LMS) algorithm, are the two most considered criteria for adaptive systems.
• the peak distortion one is also known as the zero forcing algorithm (ZFA) that inverts the channel transfer function, whereas the MSE criterions adds the noise spectral density before inversion.
• ZFA zero forcing algorithm
• the MSE provides better performance, because the ZFA enhances noise at spectral nulls, but in adaptive systems and when noise is not significant they behave similarly.
• the equalizer of Fig. 12 can be a linear transversal filter with outputs
• a coefficient adaptation for DD-LMS algorithm is defined by where ⁇ is called the gradient factor and denotes a small constant that controls the magnitude of the weight adjustment, ⁇ i is a decision, and y is again the FFE output.
• ⁇ is called the gradient factor and denotes a small constant that controls the magnitude of the weight adjustment
• ⁇ i is a decision
• y is again the FFE output.
• the error signal is obtained by error averaging, which improves equalizer acquisition performance, and reduces the noise in the estimate of the gradient factor. Such systems become less prone to ill convergence.
• the equalizer tracking speed is directly proportional to the ⁇ value, whereas the 3-db equalizer bandwidth can be approximated by represents the symbol rate.
• Equalizers based on the Volterra model i.e. equalizers using a Volterra filter, can be efficiently used for modeling, for instance, distortion in semiconductor laser diodes, the transfer function of a single mode fiber, or the nonlinear propagation inside multimode interference couplers. Such equalizers are also proposed for compensating nonlinear effects in direct-detection systems, as well as in coherent systems.
• a P th order discrete Volterra filter with filter input x, filter output y, and memory length M can be described as wherein w r are r order Volterra kernels.
• Volterra kernels are symmetric, which is exploited in this equation by considering only coefficients with non-decreasing indices fa, i.e. fa > fa- ⁇ . In this case, the number of Volterra coefficients can be calculated by
• the input vector x is defined by:
• the Volterra filter can be updated by using DD-LMS.
• ACM autocorrelation matrix
• ACF autocorrelation function
• the kernels of each order can be updated at different speeds, and for the 3 rd order filter the following gradient vector ⁇ can be used:
• x is an input vector of the polynomial processing with unit variance, and is defined by
• the main problem here is to find polynomials that result in an optimum acquisition performance, and especially to find coefficients of the polynomials, so as to achieve a diagonal ACM.
• the orthogonalization of a Volterra equalizer for PAM-4 signals has not been discussed in the existing literature.
• the present invention aims to improve the conventional equalizers.
• the present invention has the object to provide an equalizer for a PAM-4 signal with improved acquisition performance, especially in a noisy environment. That is, faster channels acquisition with at the same time decreased probability of ill acquisitions is desired.
• the ACM of the equalizer when used for the PAM-4 signal, should be diagonal.
• the equalizer should be as close as possible to its optimum point. Sub- optimum equalizer states should accordingly be avoided.
• the equalizer should not be more complex compared than conventional equalizers.
• a first aspect of the present invention provides an equalizer for a PAM-4 signal, the equalizer comprising a filter, a processing unit configured to apply polynomial processing to an input signal x of the equalizer, in order to output a processed signal q to the filter, an estimation unit configured to estimate a noise standard deviation ⁇ of noise on an output signal y of the filter, and a calculation unit configured to calculate polynomial coefficients based on the estimated noise standard deviation ⁇ , wherein the polynomial processing in the processing unit bases on orthogonal polynomials and on the calculated polynomial coefficients.
• the equalizer of the first aspect is able to derive orthogonal polynomials, especially the coefficients for the orthogonal polynomials, especially for PAM-4 signals in a noisy environment. This is due to the fact that the coefficients are calculated based on the noise on the equalized signal. Specifically, the estimated noise standard deviation estimation enables the equalizer to provide the best tracking performance in time-variant channels. Further, the estimation prohibits incorrect equalizer acquisition in hard channels. With the equalizer of the first aspect, faster channel acquisition is possible, while the orthogonal polynomials decrease the probability of ill acquisitions. Accordingly, fast channel tracking is enabled (power variations, crosstalk etc.), and suboptimum states are mostly avoided.
• the filter is a Volterra filter.
• the equalizer thus bases on the Volterra model.
• the Volterra equalizer of this implementation form can be easily provided by transforming a conventional Volterra equalizer without adding complexity.
• the estimation unit is configured to estimate the noise standard deviation ⁇ according to the formula wherein is the noise standard deviation of an i PAM-4 level Li defined by the formula
• the estimation unit is configured to estimate the noise standard deviation PAM-4 level Li by finding a best Gaussian fitting of a histogram of an obtained data set Su
• the noise standard deviation can in this manner be estimated very accurately and efficiently.
• the estimation unit is configured to obtain the data set Si within borders Bi and Bi+i defined by the formula
• the estimation unit is configured to use mean square error for finding the best Gaussian fitting.
• the processing unit is configured to set the noise standard deviation ⁇ to a start value ⁇ at the beginning of the polynomial processing, wherein
• a highest coefficient of any orthogonal polynomial is equal to 1.
• a mean value of any polynomial is equal to 0, and all polynomials are orthogonal.
• the calculation unit is configured to calculate the polynomial coefficients according to the formulas
• orthogonal polynomials comprise the following polynomials
• a, b, c and d are polynomial coefficients calculated by the coefficient calculation unit.
• the calculating unit is configured to calculate the coefficients a, b, c and d according to
• the processing unit is configured to apply the polynomial processing to an input signal x of the equalizer defined according to the formula
• a and b are polynomial coefficients calculated by the coefficient calculation unit.
• a second aspect of the present invention provides a method for equalizing a PAM-4 signal, wherein the method comprises applying polynomial processing to an input signal x, in order to output a processed signal q to a filter, estimating a noise standard deviation ⁇ of noise on an output signal y of the filter, and calculating polynomial coefficients based on the estimated noise standard deviation ⁇ , wherein the polynomial processing bases on orthogonal polynomials and on the calculated polynomial coefficients.
• the method can particularly be carried out by the equalizer of the first aspect. That is, the processing step may be carried out by the processing unit of the equalizer, the estimating step by the estimation unit of the equalizer, and the calculating step by the calculating unit of the equalizer.
• Implementation forms of the method according to the second aspect may add further steps according to the above-described implementation forms of the equalizer according to the first aspect, respectively.
• the method of the second aspect thus achieves all the advantages of the equalizer, and its implementation forms, of the first aspect.
• a third aspect of the present invention provides a computer program product comprising a program code for performing, when running on a computer, the method according to the second aspect or possible implementation forms thereof. Accordingly, all advantages of the method of the second aspect and its possible implementation forms are achieved.
• Fig. 1 shows an equalizer according to an embodiment of the present invention.
• Fig. 2 shows a method according to an embodiment of the present invention.
• Fig. 3 shows an equalizer according to an embodiment of the present invention.
• Fig. 4 shows an ACM of an equalizer according to an embodiment of the present invention.
• Fig. 6 shows and estimation of ⁇ based on histograms.
• Fig. 7 shows a PAM-4 experiment with an equalizer according to an embodiment of the present invention.
• Fig. 8 shows (a) an averaged eye diagram and (b) a performance of an equalizer according to an embodiment of the present invention.
• Fig. 9 shows (a) a 3 rd order coefficients evolution for a conventional Volterra equalizer and (b) a 3 rd order coefficients evolution for an equalizer according to an embodiment of the present invention.
• Fig. 10 shows (a) a 1 st order coefficients evolution for a conventional Volterra filter and
• FIG. 11 shows a PAM-4 transmission system.
• Fig. 12 shows a conventional equalizer.
• Fig. 13 shows an ACM of a conventional equalizer based on the Volterra model.
• Fig. 1 shows an equalizer 100 according to an embodiment of the present invention.
• the equalizer 100 is configured to equalize PAM-4 signals, especially in a noisy environment.
• the equalizer 100 comprises a filter 101, a processing unit 102, an estimation unit 103, and a calculation unit 104.
• the filter 101 bases preferably on the Volterra model or Wiener model, i.e. is preferably a Volterra filter (or Wiener filter).
• the filter 101 is arranged to receive a signal q from the processing unit 102, and to output an equalized signal y.
• the processing unit 102 is configured to apply polynomial processing to an input signal x of the equalizer 100. After applying the polynomial processing, the processing unit 102 outputs the processed signal q to the filter 101.
• the polynomial processing in the processing unit 102 bases particularly on orthogonal polynomials, and on calculated polynomial coefficients. These coefficients are calculated, and provided to the processing unit 102, by the calculation unit 104.
• the estimation unit 103 is configured to estimate a noise standard deviation ⁇ of noise on the output signal y of the filter 101, and to provide this estimation to the calculation unit 104.
• the calculation unit 104 is configured to calculate the polynomial coefficients based on the provided estimated noise standard deviation ⁇ . Fig.
• the method comprises a step 201, in which polynomial processing is applied to an input signal x, in order to output a processed signal q to a filter 101.
• This step 201 may be carried out by the processing unit 102 of equalizer 100.
• the method comprises a further step 202, in which a noise standard deviation ⁇ of noise on an output signal y of the filter is estimated.
• This step 202 may be carried out by the estimating unit 103.
• the method comprises a further step 203, in which polynomial coefficients are calculated based on the estimated noise standard deviation ⁇ .
• This step 203 may be carried out by the calculation unit 104.
• the polynomial processing carried out in step 201 bases on orthogonal polynomials, and on the polynomial coefficients calculated in step 203 (the feedback of these coefficients is indicated in Fig. 2 by the arrow from 203 to 201).
• Fig. 3 shows another embodiment of an equalizer 100 according to the present invention, which builds on the embodiment of Fig. 1.
• the equalizer 100 includes further a decision unit 301, a LMS unit 302, and a subtractor unit 303.
• the decision unit 301 is configured to receive the filter output signal y, and to output a decision d.
• the subtractor unit 303 is configured to combine this decision d with the negative of the output signal y of the filter 101, in order to generate an error signal e.
• the LMS unit 302 is configured to receive the error signal e, and further to receive a gradient factor ⁇ , which denotes a small constant that controls a magnitude of a filter weight adjustment, an ACM diagonal s, and the signal q that is input into the filter 101.
• the LMS unit 302 is further configured to output a filter coefficient w to the filter 101.
• orthogonal polynomials up to n th order may be defined with coefficients according to: Odd-order polynomials have only odd coefficients, and even-order polynomials have only even coefficients.
• Coefficients for polynomials up to the 4 th order can be represented by the following matrix:
• the coefficients are selected by the calculation unit 104 of equalizer 100 preferably such that the following equations hold (self-orthogonal):
• the orthogonal polynomials can be found according to: i.e., the orthogonal polynomials used by the processing unit 102 comprise the following polynomials.
• a, b, c and d are the polynomial coefficients, which are calculated by the coefficient calculation unit 104 of the equalizer 100.
• the mean value of any polynomial, odd or even is always 0.
• all, i.e. odd and even, polynomials are always orthogonal.
• the orthogonality conditions generate more equations, which can be used to calculate the coefficients.
• the orthogonality is preferably checked only between odd or between even polynomials.
• the highest coefficient is always 1.
• the second polynomial mean value must be 0.
• the kernels defined in (1) are transformed by the polynomial processing unit 102, which operates based on the above-found polynomials and coefficients.
• the diagonal autocorrelation matrix is then defined by R qq . Finding the inverse matrix is trivial from the diagonal vector of R qq that is
• equation (2) can be simplified and the updating algorithm is
• each kernel is preferably controlled by its own gradient factor ⁇ , and the final speed is mainly influenced by the gradient factor ⁇ .
• the ⁇ working range can be adjusted to specific cases.
• the parameter ⁇ can be freely set to zero, whereas setting ⁇ to larger values improves stability and accelerate acquisition at higher BERs (ISI and noise scenario).
• the noise variance affects the updating algorithm, and ⁇ can be estimated and set correctly.
• the acquisition at the beginning may be a bit slower than in the optimum case, when the noise standard deviation ⁇ is better known, but after the acquisition phase the channel may vary (PMD, power variations etc.), and the filter should track such variations.
• the tracking performance depends on the gradient factor ⁇ and the standard deviation ⁇ .
• the gradient factor ⁇ is normally unchanged after the acquisition period. Nevertheless, the tracking capability can be improved, when the polynomial coefficients are calculated using the true value of ⁇ . Therefore, the noise standard deviation ⁇ is - as already shown in and described with respect to the Figs. 1 and 2 - estimated by the estimation unit 103 on the equalized signal y after the filter 101.
• the estimated value is provided to the calculation unit 104, which calculates the polynomial coefficients using the above formulas (3), (4), and (5). Later, formula (6) is used to finally orthogonalize the equalizer 100.
• the noise standard deviation ⁇ is particularly estimated by using
• K updates (103 ⁇ K ⁇ 104) update all coefficients with 10 -4 ⁇ ⁇ ⁇ 5xl0 -4 . 6. If channel is static, set ⁇ ⁇ 10 -4 .
• the above procedure enables the correct acquisition with a high probability.
• a bit pattern generator (BPG) generates binary symbols that are combined to get PAM-4 symbols.
• BPG bit pattern generator
• TOSA After signal amplification by a modulator driver (MD), TOSA outputs an optical PAM-4 signal, which is optically amplified before a ROSA detects the optical signal.
• the electrical PAM-4 signal is electrically amplified and captured by the real-time scope.
• the clock recovery based on Mueller and Miiller phase detector was used in a second-order phase- locked loop (PLL) with a 4-MHz bandwidth to compensate for the frequency offset and timing jitter.
• PLL phase-locked loop
• Fig. 8 shows in (a) the averaged eye diagram over three symbol intervals at the input power of 0 dBm, after a linear equalizer with 55 taps and one sample per symbol.
• the tap evolution is very specific and unstable for a conventional Volterra equalizer that is visible in Fig. 9 (a) representing the 3 rd order kernels. Even after two million updates (symbols), the 3 rd order kernels are not settled well, and likely cause 1 st order kernels instabilities.
• the equalizer 100 is very stable after 5x10 5 symbols, as is indicated in Fig. 9 (b) showing the 3 rd order kernels evolution.
• the conventional Volterra equalizer requires approximately a four times longer time to stabilize taps. It is interesting that both equalizers after 10 6 symbols have similar BER performance. At lower BERs, the parameter ⁇ can be freely set to zero, whereas setting ⁇ to larger values improves stability and accelerate acquisition at higher BERs (ISI and noise scenario).
• the 2 nd order coefficients are not influenced. However, the 1 st order coefficients evolution is similar to the 3 rd order kernels. Much more acquisition time is required for the conventional Volterra equalizer shown in Fig. 10 in (a) as for the equalizer 100 shown in Fig. 10 in (b).

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• 2017
  • 2017-04-19 WO PCT/EP2017/059262 patent/WO2018192647A1/en active Application Filing
  • 2017-04-19 DE DE112017007031.7T patent/DE112017007031T5/de active Pending

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