Compensation for equalizer attenuation

Abstract

A receiver (20) includes an adaptive equalizer (24), a processor (36) and a decoder (32). The adaptive equalizer is configured to equalize a signal. The processor is configured to estimate a gain correction, which compensates for attenuation of the equalized signal by the equalizer due to noise present in the signal. The decoder is configured to decode the equalized signal. At least one of (i) equalization of the signal by the adaptive equalizer and (ii) decoding of the equalized signal by the decoder, is based on the gain correction.

Description

[0001] COMPENSATION FOR EQUALIZER ATTENUATION

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of U.S. Provisional Patent Application 63 / 719,670, filed November 13, 2024, whose disclosure is incorporated herein by reference.

[0003] FIELD OF THE INVENTION

[0004] The present invention relates generally to communication receivers, and particularly to methods and systems for compensating for equalizer attenuation.

[0005] BACKGROUND OF THE INVENTION

[0006] In many communication systems, the receiver employs an adaptive equalizer to compensate for channel distortion and improve signal quality. Adaptive equalizers adjust their coefficients ("taps") dynamically to minimize the effects of inter-symbol interference and other channel impairments. One common type of equalization is Minimum Mean Square Error (MMSE. In an MMSE equalizer, the adaptation aims to minimize the mean square error between the equalizer output and the desired signal. In a typical receiver, the equalized signal is processed by a decoder that may employ hard-decision or soft-decision decoding techniques to extract the transmitted information.

[0007] SUMMARY OF THE INVENTION

[0008] An embodiment of the present invention that is described herein provides a receiver including an adaptive equalizer, a processor and a decoder. The adaptive equalizer is configured to equalize a signal. The processor is configured to estimate a gain correction, which compensates for attenuation of the equalized signal by the equalizer due to noise present in the signal. The decoder is configured to decode the equalized signal. At least one of (i) equalization of the signal by the adaptive equalizer and (ii) decoding of the equalized signal by the decoder, is based on the gain correction.

[0009] In some embodiments, the processor is configured to estimate the gain correction by estimating a reciprocal of a Signal-to-Noise Ratio (SNR) of the signal. In a disclosed embodiment, the receiver further includes a multiplier, which is configured to scale the equalized signal responsively to the gain correction prior to providing the equalized signal to the decoder.

[0010] In another embodiment, the decoder is configured to amplify the equalized signal responsively to the gain correction prior to decoding the equalized signal. In yet another embodiment, the decoder is configured to scale-down one or more nominal constellation points, used for decoding the equalized signal, responsively to the gain correction. In still another embodiment, the decoder is configured to scale-down one or more decision thresholds, used for decoding the equalized signal, responsively to the gain correction.

[0011] In some embodiments, the decoder is configured to calculate soft metrics, for decoding the equalized signal, based on the equalized signal and on the gain correction. In an alternative embodiment, the decoder, the equalizer or the processor is configured to adjust a feedback signal, which is fed back from the decoder to the equalizer for adapting the equalizer, responsively to the gain correction.

[0012] In an embodiment, the processor is configured to estimate the gain correction by estimating an offset between at least one nominal constellation point and a corresponding histogram of the signal.

[0013] There is additionally provided, in accordance with an embodiment of the present invention, a method for communication including receiving a signal and equalizing the signal by an adaptive equalizer. A gain correction, which compensates for attenuation of the equalized signal by the equalizer due to noise present in the signal, is estimated. The equalized signal is decoded. At least one of (i) equalizing the signal and (ii) decoding the equalized signal, is based on the gain correction.

[0014] The present invention will be more fully understood from the following detailed description of the embodiments thereof, taken together with the drawings in which:

[0015] BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figs. 1-5 are block diagrams that schematically illustrate receivers that compensate for equalizer attenuation, in accordance with various embodiments of the present invention;

[0017] Fig. 6 is a flow chart that schematically illustrates a method for compensating for equalizer attenuation, in accordance with an embodiment of the present invention; and Fig. 7 is a flow chart that schematically illustrates a method for estimating a gain correction factor, in accordance with an embodiment of the present invention.

[0018] DETAILED DESCRIPTION OF EMBODIMENTS

[0019] OVERVIEW

[0020] In communication systems that employ adaptive equalizers, the signal amplitude at the output of the equalizer should match a nominal amplitude expected by the decoder. Any deviation from the expected amplitude may degrade the decoding performance, e.g., increase the Bit Error Rate (BER). When using MMSE equalizers, however, the actual equalizer gain reached by the adaptation process may be slightly lower than the desired gain. This attenuation occurs because noise present in the signal affects the adaptation process.

[0021] Embodiments of the present invention that are described herein address this challenge by estimating a gain correction that compensates for the equalizer-induced attenuation. This gain correction may be determined in various ways, including estimating the reciprocal of the Signal-to-Noise Ratio (SNR) of the signal, or analyzing offsets between nominal constellation points and corresponding signal histograms.

[0022] In various embodiments, the compensation may be applied at different stages of the receiver processing chain. In some implementations, the equalized signal is scaled using a multiplier prior to decoding, effectively setting the signal to its expected amplitude. Alternatively, the decoder itself may amplify the equalized signal before processing, or may scale down the nominal constellation points or the decision thresholds used in the decoding process. In a soft-decision decoder, the gain correction may be used to amplify soft-decoding metrics. In yet another embodiment, the gain correction may be applied in a feedback signal that is fed back from the decoder to the equalizer for use in adapting the equalizer.

[0023] The disclosed techniques ensure that the equalizer and the decoder are matched with regard to signal amplitude, notwithstanding noise-induced attenuation of the equalized signal. When using the disclosed techniques, the decoder operates at or close to its optical operating point, resulting in improved decoding performance.

[0024] SYSTEM DESCRIPTION

[0025] Fig. 1 is a block diagram that schematically illustrates a receiver that compensates for equalizer attenuation, in accordance with an embodiment of the present invention. Fig. 1 aims to illustrates the general compensation concept. More specific receiver configurations and compensation schemes are described in Figs. 2-5 further below.

[0026] Receiver 20 receives a signal modulated with data from a transmitter (not shown in the figure), and processes the received signal so as to extract the data. Receiver 20 may be part of any suitable communication system, e.g., an optical communication modem. The received signal typically comprises a sequence of modulated symbols. Any suitable modulation scheme can be used. Example schemes are four-level Pulse- Amplitude Modulation (PAM4) and 16-symbol Quadrature-Amplitude Modulation (QAM16).

[0027] The processing chain of receiver 20 comprises, among other blocks, an adaptive MMSE equalizer 24 and a decoder 28. Equalizer 24 is typically implemented as a digital filter comprising multiple programmable coefficients ("taps"). The equalizer further comprises suitable logic and / or software that adapts the coefficients to minimize the Mean Square Error (MSE) between the signal at the equalizer output and the optimal desired signal.

[0028] Decoder 28 receives the equalized signal from equalizer 24, and decodes the signal so as to extract the data modulated thereon. The data is typically provided as output of receiver 20. In some embodiments, decoder 28 applies hard decoding, in which the symbol amplitudes are compared to one or more decision thresholds. Such a decoder is also referred to as a "slicer". In other embodiments, decoder 28 applies soft decoding. In soft decoding, the decoder calculates soft metrics (e.g., Log-Likelihood Ratios - LLRs) for the data bits conveyed by the modulated symbols. The decoder then decides on the likely values of the bits depending on the soft metrics.

[0029] To adapt equalizer 24, receiver 20 comprises a feedback path 32 that informs the equalizer of the bit decisions made by decoder 28. The response of MMSE equalizer 24 can be written as:

[0030] Equation 1:

[0031]

[0032] wherein j / j denotes the equalizer output (the equalized signal) at time i, xtdenotes the equalizer input (the received signal) at time i, and tkdenote the equalizer taps.

[0033] The error of J / j relative to the hard value, or hard decision, is given by:

[0034] Equation 2:

[0035] ei = yi - yi

[0036] In a typical MMSE implementation, equalizer 24 adapts the equalizer taps periodically by:

[0037] Equation 3:

[0038]

[0039] MMSE adaptation aims to minimize the mean square value of of Equation 2 above. In practice, however, the actual values of the constellation points (symbol amplitudes) at the output of equalizer 24 tend to be lower than the target values that expected by decoder 28 (the values used in the adaptation of the equalizer). This effect is referred to herein as "equalizer attenuation".

[0040] The reason for equalizer attenuation is that the MMSE adaptation attempts to balance channel amplification and noise enhancement, and the solution is typically to add a small bias to the output and reduce the MSE. The bias is typically expressed as an additive term in the denominator which is proportional to 1 / SNR, wherein SNR denotes the signal-to-noise ratio of the received signal at the equalizer input.

[0041] The equalizer attenuation effect is demonstrated by a histogram depicted at the bottom of Fig. 1. The horizontal axis of the histogram denotes the amplitudes of the soft symbols at the output of equalizer 24 (input of decoder 28). The vertical axis denotes the number of soft symbols having each amplitude.

[0042] In the present example, the modulation scheme is PAM4 in which the constellation points (the nominal symbol amplitudes expected by decoder 28) are {-3, -1,1, 3}. The histogram bins that correspond to the nominal constellation points are marked as bold in the figure. The histogram exhibits four distributions corresponding to the four constellation points.

[0043] Close examination of the amplitude distributions, however, shows that the peaks of the distributions do not coincide exactly with the nominal constellation points. Rather, the peak of each histogram is slightly lower (in absolute value) than the corresponding constellation point. The offset is more prominent in the external constellation symbols (-3 and 3).

[0044] As can be appreciated, the equalizer attenuation effect is not optimal for minimizing the Bit Error Rate (BER) of decoder 28. In various embodiments, receiver 20 employs techniques that estimate and compensate for equalizer attenuation. The disclosed techniques thus match the actual signal amplitudes (e.g., average soft symbol amplitudes) at the equalizer output to the nominal amplitudes with which decoder 28 achieves optimal BER.

[0045] In some embodiments, processor 36 of receiver 20 comprises a gain correction estimation module 40. Module 40 estimates a gain correction factor denoted a, which compensates for the equalizer attenuation. In some embodiments, module 40 estimates a as 1+1 / SNR. The receiver may apply the gain correction factor in various ways and in various locations in the receiver's processing chain. Several non-limiting example implementations are described below. EXAMPLE COMPENSATION TECHNIQUES AND RECEIVER CONFIGURATIONS Fig. 2 is a block diagram that schematically illustrates a receiver that compensates for equalizer attenuation, in accordance with an embodiment of the present invention. In this example, receiver 20 further comprises a digital multiplier 44. Multiplier 44 scales the digital signal at the output of equalizer 24 by the gain correction factor a. The scaled signal is provided to decoder 28.

[0046] Fig. 3 is a block diagram that schematically illustrates a receiver that compensates for equalizer attenuation, in accordance with another embodiment of the present invention. In the example of Fig. 3, decoder 28 applies hard decoding to the equalized signal (soft symbols) provided by equalizer 24, by comparing the soft symbols to a set of nominal constellation points or to a set of decision thresholds.

[0047] Consider the PAM4 signal depicted at the bottom of Fig. 1 above, in which the nominal constellation points (the nominal symbol amplitudes) are {-3, -1,1, 3}. Without compensation for equalizer attenuation, decoder 28 would decode the equalized signal by comparing each soft symbol (denoted soft) to these constellation points, or to a set of three decision thresholds positioned mid-way between adjacent constellation points (i.e., thresholds set to -2, 0 and 2).

[0048] To compensate for equalizer attenuation, decoder 28 of Fig. 3 receives the gain correction factor a from module 40 is processor 36, and applies a in the comparison of the soft symbols to the constellation points or decision thresholds.

[0049] In one embodiment, decoder 28 scales (amplifies) each soft symbol by the factor a, and compares the scaled soft symbols soft ■ a) to the nominal constellation points {-3,-1,1,3}. In another embodiment, decoder 28 scales (amplifies) each soft symbol by the factor a, and compares the scaled soft symbols (soft ■ a) to the decision thresholds {-2,0,2}.

[0050] In yet another embodiment, decoder 28 scales-down the nominal constellation points by the factor a, and compares the values soft to the scaled-down constellation points {— 3 / a,— l / a,l / a, 3 / a}. In still another embodiment, decoder 28 scales-down the decision thresholds by the factor a, and compares the values soft to the scaled-down decision thresholds {— 2 / a,0, 2 / a}. For the sake of optimal decoding, scaling-down the constellation or decision thresholds is equivalent to scaling-up the signal.

[0051] In an alternative embodiment, to simplify the computation, the multiplicative correction factor a can be approximated by an additive offset given by f> = 1 — 1 / a. This approximation is valid since in practice a is usually close to unity. In the present context, the term "gain correction" includes multiplicative corrections (e.g., using a), additive corrections (e.g., using / ?), and any other suitable type of gain correction.

[0052] Thus, for example, instead of scaling the soft symbols by a, decoder 28 may shift the soft symbols by f. Similarly, instead of scaling-down the nominal constellation by a, decoder 28 may use a shifted constellation given by {— 3 + 3 / ?, — 1 + / ?, 1 — / ?, 3 — 3 / ?}. As another example, instead of scaling-down the decision thresholds by a, decoder 28 may use a shifted set of decision thresholds given by {— 2 + 2f>, 0 ,2 — 2f>}.

[0053] Fig. 4 is a block diagram that schematically illustrates a receiver that compensates for equalizer attenuation, in accordance with yet another embodiment of the present invention. In the example of Fig. 4, decoder 28 is a soft decoder that calculates soft metrics for the respective bits carried by the soft symbols, and decides on the values of the received bits based on the soft metrics.

[0054] In a typical embodiment the soft metrics are Log-Likelihood Ratios (LLRs) of the bits, but any other suitable soft metrics can be used. Generally, a soft metric of a received bit comprises a numerical value that indicates the likelihood that the transmitted value of the bit was "1" or "0".

[0055] In the embodiment of Fig. 4, decoder 28 receives the gain correction factor a from module 40 of processor 36, and calculates the soft metrics based on the soft symbols and on a. For example, decoder 28 may calculate the soft metrics based on soft / a instead of soft.

[0056] Consider, for example, a PAM4 signal in which each soft symbol soft carries two bits denoted x and y. In this example, without compensation for equalizer attenuation, the LLR of bit x is calculated by llrx = soft, and the LLR of bit y is calculated by Ury = 2 — abs(soft). These expressions for llrx and Ury hold for Gray mapping and reasonable assumptions on the noise.

[0057] In some embodiments, to compensate for equalizer attenuation, decoder 28 of Fig. 4 may instead calculate llrx = soft / a and Ury = 2 — abs(soft / af As noted above, the multiplicative correction factor a can be approximated by the additive offset p = 1 — 1 / a. Thus, in some embodiments decoder 28 may calculate llrx = soft ■ (1 — / ?) and Ury = 2 — 2f — abs(soft / af

[0058] The example above refers to PAM4. A similar solution can be used for QAM16, in which each symbol can be viewed as two PAM4 symbols in quadrature.

[0059] In an embodiment, decoder 28 may use a similar offset to compensate for DC offset in the equalized signal, if needed. Fig. 5 is a block diagram that schematically illustrates a receiver that compensates for equalizer attenuation, in accordance with another embodiment of the present invention. In this example, the gain correction factor a is accounted for in feedback path 32 from decoder 28 to equalizer 24. As seen, a multiplier 48 that multiplies the fed-back decisions is introduced in the feedback path.

[0060] Consider, for example, the nominal constellation {-3,-1, 1,3} used in the examples above. In the implementation of Fig. 5, decoder 28 still makes bit decisions using this nominal constellation. In the feedback to equalizer 24, on the other hand, decoder 28 feeds back scaled decisions of the form {—3a, —a, a, 3a}. The scaled-down feedback will cause equalizer 24 to scale-up its gain so that the equalized signal will match the decision points expected by the decoder.

[0061] One challenge in implementing the solution of Fig. 5 is the increase in the resolution (and therefore the bus width) of feedback path 32. Without compensation for equalizer attenuation, the decisions sent over feedback over path 32 are integer numbers ({-3, -1,1, 3}). After multiplication by a, however, the values {—3a, —a, a, 3a} fed-back to the equalizer are no longer integer and theoretically require finer resolution (and thus need to be represented by a larger number of bits).

[0062] To reduce the number of bits that represent {—3a, —a, a, 3a}, we may exploit the fact that a is close to 1. Therefore, the values {—3a, —a, a, 3a} may be restricted to contain two integer binary digits and several small factional digits, but they do not need to cover the entire range. For example, the representation of {—3a, —a, a, 3a} may be restricted to ±(b021+ b^0+ bi2-3).

[0063] Another option to increase the resolution on feedback path 32 without compromising bandwidth is to use lower precision values, but change the reference values between neighboring points. For example, to obtain a = (1 + 2-3), it is possible to alternate between 1 and 1 + 2-2.

[0064] The receiver configurations shown in Figs. 1-5 are example configurations that are chosen purely for the sake of conceptual clarity. Any other suitable configurations can be used in alternative embodiments. Receiver elements that are not mandatory for understanding of the disclosed techniques have been omitted from the figures for the sake of clarity.

[0065] In various embodiments, the various receiver elements, e.g., equalizer 24, decoder 28 and processor 36, may be implemented using suitable software, using suitable hardware such as one or more Application-Specific Integrated Circuits (ASICs) or Field-Programmable Gate Arrays (FPGAs), or using a combination of hardware and software elements. In some embodiments, certain functions of receiver 20, e.g., some or all of the functions of processor 36, may be implemented using one more general-purpose processors, which are programmed in software to carry out the techniques described herein. The software may be downloaded to the processors in electronic form, over a network, for example, or it may, alternatively or additionally, be provided and / or stored on non-transitory tangible media, such as magnetic, optical, or electronic memory.

[0066] Fig. 6 is a flow chart that schematically illustrates a method for compensating for equalizer attenuation, in accordance with an embodiment of the present invention. The method begins at a signal reception stage 60, with receiver 20 receiving a modulated signal for decoding. At an equalization stage 64, MMSE equalizer 24 equalizes the received signal. At a correction calculation stage 68, gain correction module 40 in processor 36 calculates the gain correction factor a (or, equivalently, the approximated offset ?). At a compensation stage 72, receiver 20 compensates for the equalizer attenuation using the gain correction factor. Any of the compensation scheme described above, or any other suitable scheme, can be used.

[0067] DIRECT MEASUREMENT OF THE GAIN CORRECTION FACTOR

[0068] In the embodiments described above, the gain correction factor was estimated by module 40 based on the SNR, e.g., as 1+1 / SNR. In alternative embodiments, module 40 can estimate a (or rather I- a) directly from the histogram of soft symbol values (e.g., the histogram at the bottom of Fig. 1).

[0069] Fig. 7 is a flow chart that schematically illustrates a method for estimating a gain correction factor, in accordance with an embodiment of the present invention. The method begins at a histogram construction stage 80, in which module 40 constructs a histogram of soft symbol values over a large number of symbols.

[0070] At an offset calculation stage 84, module 40 calculates the offsets (along the horizontal axis of the histogram) between the peaks of the histogram and the corresponding nominal constellation points. Module 40 may calculate the offsets of all four symbol distributions, or of any subset thereof (e.g., only for the distributions corresponding to the constellation points -3 and 3, in which the offset is more noticeable).

[0071] In various embodiments, module 40 may use any suitable technique for calculating the offset between a given peak of the histogram and the corresponding constellation point. In one example, module 40 fits the symbol distribution in the vicinity of the peak to a certain function (e.g., Quadratic function or other polynomial), calculates the location of the maximum of the polynomial, and then calculates the offset between this maximum and the constellation point. In other embodiments, module 40 finds the minima of the histogram, and derives the offsets from the minima (e.g., assuming that without offset the minima should fall in the mid-points between constellation points). In some embodiments, module 40 interpolates neighboring values of the distribution before calculating the locations of peaks or minima. Further alternatively, any other suitable estimation method can be used.

[0072] At a gain correction derivation stage 88, module 40 derives 1- a from the measured offset or offsets.

[0073] In some embodiments, when the resolution / accuracy of estimating 1- a is sufficient, processor 36 may use the offset for estimating the SNR of the signal.

[0074] ***

[0075] The techniques described in the present disclosure are not limited to any particular system or application. The methods and systems described herein can be used in any communication system that uses MMSE equalization, including wired systems, wireless systems, optical systems and the like.

[0076] It will thus be appreciated that the embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and sub-combinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art. Documents incorporated by reference in the present patent application are to be considered an integral part of the application except that to the extent any terms are defined in these incorporated documents in a manner that conflicts with the definitions made explicitly or implicitly in the present specification, only the definitions in the present specification should be considered.

Claims

CLAIMS1. A receiver, comprising:an adaptive equalizer, configured to equalize a signal;a processor, configured to estimate a gain correction, which compensates for attenuation of the equalized signal by the equalizer due to noise present in the signal; and a decoder, configured to decode the equalized signal,wherein at least one of (i) equalization of the signal by the adaptive equalizer and (ii) decoding of the equalized signal by the decoder, is based on the gain correction.

2. The receiver according to claim 1, wherein the processor is configured to estimate the gain correction by estimating a reciprocal of a Signal-to-Noise Ratio (SNR) of the signal.

3. The receiver according to claim 1 or 2, further comprising a multiplier, which is configured to scale the equalized signal responsively to the gain correction prior to providing the equalized signal to the decoder.

4. The receiver according to claim 1 or 2, wherein the decoder is configured to amplify the equalized signal responsively to the gain correction prior to decoding the equalized signal.

5. The receiver according to claim 1 or 2, wherein the decoder is configured to scaledown one or more nominal constellation points, used for decoding the equalized signal, responsively to the gain correction.

6. The receiver according to claim 1 or 2, wherein the decoder is configured to scaledown one or more decision thresholds, used for decoding the equalized signal, responsively to the gain correction.

7. The receiver according to claim 1 or 2, wherein the decoder is configured to calculate soft metrics, for decoding the equalized signal, based on the equalized signal and on the gain correction.

8. The receiver according to claim 1 or 2, wherein the decoder, the equalizer or the processor is configured to adjust a feedback signal, which is fed back from the decoder to the equalizer for adapting the equalizer, responsively to the gain correction.

9. The receiver according to claim 1 or 2, wherein the processor is configured to estimate the gain correction by estimating an offset between at least one nominal constellation point and a corresponding histogram of the signal.

10. A method for communication, comprising:receiving a signal;equalizing the signal by an adaptive equalizer;estimating a gain correction, which compensates for attenuation of the equalized signal by the equalizer due to noise present in the signal; anddecoding the equalized signal,wherein at least one of (i) equalizing the signal and (ii) decoding the equalized signal, is based on the gain correction.

11. The method according to claim 10, wherein estimating the gain correction comprises estimating a reciprocal of a Signal-to-Noise Ratio (SNR) of the signal.

12. The method according to claim 10 or 11, further comprising scaling the equalized signal responsively to the gain correction prior to providing the equalized signal for decoding.

13. The method according to claim 10 or 11, wherein decoding the equalized signal comprises amplifying the equalized signal in a decoder responsively to the gain correction prior to decoding the equalized signal.

14. The method according to claim 10 or 11, wherein decoding the equalized signal comprises scaling-down one or more nominal constellation points, used for decoding the equalized signal, responsively to the gain correction.

15. The method according to claim 10 or 11, wherein decoding the equalized signal comprises scaling-down one or more decision thresholds, used for decoding the equalized signal, responsively to the gain correction.

16. The method according to claim 10 or 11, wherein decoding the equalized signal comprises calculating soft metrics, for decoding the equalized signal, based on the equalized signal and on the gain correction.

17. The method according to claim 10 or 11, and comprising adjusting a feedback signal, which is fed back from a decoder to the equalizer for adapting the equalizer, responsively to the gain correction.

18. The method according to claim 10 or 11, wherein estimating the gain correction comprises estimating an offset between at least one nominal constellation point and a corresponding histogram of the signal.

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