Receiver device for pulse amplitude modulated signal

Abstract

The present disclosure relates to a receiver device for a pulse amplitude modulation (PAM) signal. The receiver device computes a transmit dispersion eye pattern closed four-phase (TDECQ). The receiver device first acquires a signal, where the signal is based on a PAM signal transmitted by the transmitter device over a channel to the receiver device, and filters the acquired signal. Further, the transmitter device equalizes the filtered signal using an FFE having a plurality of taps, and filters the equalized signal output by the FFE using a 2-tap post-filter in which high-frequency noise caused by the FFE is compressed. The receiver device applies a maximum logarithm mapping (MLM) algorithm to the filtered signal output by the 2-tap post-filter, reconstructs a signal constellation of the PAM signal based on a result of the MLM algorithm, and calculates a TDECQ based on the reconstructed signal constellation.

Description

Technical Field

[0001] The present disclosure relates to a receiver device and a receiving method for receiving a pulse amplitude modulation (PAM) signal sent by a transmitter device through a channel. The receiver device and the receiving method of the present disclosure are configured to obtain a transmitter dispersion eye closure quaternary (TDECQ), which indicates the quality of the PAM signal transmitted by the transmitter device through the channel. Background Art

[0002] The latest generation of high-performance optical interconnects used in data communications uses a 4-level PAM format (PAM4). One of the main system-level signal quality metrics is TDECQ. In channels without chromatic dispersion (CD), transmitter eye closure quaternary (TECQ) is also used. The difference between these two values ​​provides the CD penalty.

[0003] TDECQ utilizes a reference receiver to quantify the penalty of impairments that can or cannot be equalized. TDECQ is a measure of the vertical eye closure of an optical transmitter when transmitting a PAM signal through a worst-case optical channel. TDECQ can be measured by an optical to electrical converter (O / E) and an oscilloscope with a combined frequency response, and TDECQ can be equalized with a reference equalizer. The reference receiver and reference equalizer can be implemented in software or can be part of an oscilloscope or other receiver device. Summary of the invention

[0004] exist Figure 1 An exemplary optical interconnect is shown in (a) through which a pattern is sent from an optical transmitter to a TDECQ tester through a worst-case optical channel.

[0005] The TDECQ tester includes a reference receiver and a TDECQ algorithm. The reference receiver converts the received optical signal into an electrical signal and filters the electrical signal through a fourth-order Bessel-Thomson (BT4) filter. Then, given the BT4-shaped receiver noise, the TDECQ algorithm finds the optimal 5-tap feed-forward equalizer (FFE). Figure 1(a) also depicts the noise σ G and σ eq and the noise enhancement factor C eq The TDECQ algorithm connected to the reference receiver finds the maximum input reference receiver noise σ G , which makes the signal enhancement ratio (SER) equal to 4.8x 10 -4 The target SER (targetSER, TSER) (KP4 forward error correction (FEC) limit).

[0006] like Figure 1 As shown in (b), the equalizer samples at two sampling points with a distance of 0.1UI, and the best sampling phase (TDECQ is the smallest here) is found. There are two sampling phases, and the TDECQ with the worst value is selected. TEDCQ is calculated by the following formula:

[0007]

[0008] Where R is the root mean square (RMS) noise that the receiver can add, and Q t is 3.414, which is consistent with the bit error rate (BER) and TSER of Gray-coded PAM4. The whole process is performed in blind mode, so that TDECQ is only used to quantify the quality of the transmitter, not the BER or SER. For example, in the IEEE standard for Ethernet (IEEE Std.802.3, 2018), the calculation of R is described. The optical modulation amplitude (OMA) is the highest amplitude level.

[0009] However, the above process brings challenges. For example, high-speed optical interconnects require very powerful digital signal processing (DSP), which includes maximum likelihood sequence estimators (MLSE). As another example, for new generations of higher-speed transceivers, more advanced and complex TDECQ calculations are required.

[0010] In view of the above, an object of the present disclosure is to provide an improved TDECQ calculation.

[0011] These and other objects are achieved by the present disclosure, as set out in the attached independent claims. Advantageous implementations are further defined in the dependent claims.

[0012] A first aspect of the disclosed content provides a receiver device for a PAM signal, the receiver device being configured to: acquire a signal, wherein the signal is based on a PAM signal sent by a transmitter device to a receiver device through a channel; filter the acquired signal; equalize the filtered signal using an FFE having multiple taps; filter the equalized signal output by the FFE using a 2-tap post-filter, wherein high-frequency noise caused by the FFE is compressed; apply a maximum log-map (MLM) algorithm to the filtered signal output by the 2-tap post-filter; reconstruct a signal constellation of the PAM signal based on a result of applying the MLM algorithm; and calculate TDECQ based on the reconstructed signal constellation of the PAM signal.

[0013] The receiver device according to the first aspect provides an improved TDECQ calculation. For example, the receiver device can calculate accurate TDECQ. The receiver device according to the first aspect does not use the output of FFE to calculate TDECQ, but uses the output of signal (constellation) reconstruction to calculate TDECQ.

[0014] In an implementation of the first aspect, the PAM signal sent by the transmitter device is an optical signal, wherein the acquired signal is an electrical signal, and wherein the receiver device includes a photodetector for converting the optical signal into an electrical signal.

[0015] For example, the PAM signal may be a PAM4 signal. The optical channel may be an optical fiber.

[0016] In an implementation of the first aspect, the receiver device is configured to filter the acquired signal using a low-pass filter.

[0017] The filter can be an H-BT4 filter or any other type of low pass filter.

[0018] In an implementation of the first aspect, the FFE is configured to restore a PAM level included in the PAM signal by equalizing the filtered signal.

[0019] This reduces distortion in the acquired and filtered signals, thereby improving the performance of the receiver device.

[0020] In one implementation of the first aspect, the FFE is configured to perform a blind FFE algorithm to equalize the filtered signal.

[0021] The blind FFE algorithm can result in improved decisions at the receiver device. For example, FFE can find taps in a blind mode. For example, a decision-directed least-meansquare (DD-LMS) mode can be used in the blind mode, but any other blind method can also be used.

[0022] In an implementation of the first aspect, filtering the equalized signal includes: using a 2-tap post filter to linearly filter the equalized signal based on filter coefficients, wherein the filter coefficients are determined in an iterative manner.

[0023] In one implementation of the first aspect, a result of applying a maximum logarithmic mapping algorithm to a filtered signal output by the 2-tap post-filter includes a logarithmic probability of each PAM level of the PAM signal.

[0024] In an implementation of the first aspect, the receiver device is configured to reconstruct a signal constellation of the PAM signal based on logarithmic probabilities.

[0025] In an implementation manner of the first aspect, reconstructing a signal constellation of the PAM signal includes: generating a PAM histogram representing a PAM level of the PAM signal.

[0026] In an implementation of the first aspect, the receiver device is configured to calculate TDECQ based on a PAM histogram.

[0027] In an implementation of the first aspect, the receiver device is configured to calculate the TDECQ further based on noise, which is added to the reconstructed signal constellation of the PAM signal.

[0028] Adding noise enables scanning the noise-dependent SER and finding the amount of noise that achieves the target SER. This amount of noise can be used to calculate TDECQ.

[0029] In an implementation of the first aspect, the receiver device is configured to: calculate TDECQ including a 2-tap post-filter parameter CeqPF, where CeqPF is equal to sqrt(1+α 2 ) / (1+α). The introduction of CeqPF can improve the accuracy of TDECQ calculation.

[0030] In an implementation manner of the first aspect, TDECQ indicates the quality of a PAM signal transmitted by the transmitter device.

[0031] In one implementation of the first aspect, a receiver device includes a sampling oscilloscope configured to perform equalization of a filtered signal, filtering of the equalized signal, applying an MLM algorithm, reconstructing a signal constellation, and calculating a TDECQ.

[0032] A second aspect of the disclosure provides a receiving method for a pulse amplitude modulation (PAM) signal, the receiving method comprising: acquiring a signal, wherein the signal is based on a PAM signal sent by a transmitter device through a channel; filtering the acquired signal; equalizing the filtered signal using a feedforward equalizer with multiple taps; filtering the equalized signal using a 2-tap filter, wherein high-frequency noise caused by the feedforward equalization is compressed; applying an MLM algorithm to the 2-tap filtered signal; reconstructing a signal constellation of the PAM signal based on a result of applying the MLM algorithm; and calculating TDECQ based on the reconstructed signal constellation of the PAM signal.

[0033] In an implementation manner of the second aspect, the PAM signal sent by the transmitter device is an optical signal, wherein the acquired signal is an electrical signal, and wherein the receiving method includes: converting the optical signal into an electrical signal.

[0034] In an implementation manner of the second aspect, the receiving method includes: filtering the acquired signal using a low-pass filter.

[0035] In an implementation manner of the second aspect, the feedforward equalization restores the PAM level included in the PAM signal by equalizing the filtered signal.

[0036] In an implementation of the second aspect, the feedforward equalization includes: executing a blind feedforward equalization algorithm to equalize the filtered signal.

[0037] In an implementation of the second aspect, the 2-tap post-filtering of the equalized signal includes linearly filtering the equalized signal based on filter coefficients, wherein the filter coefficients are determined in an iterative manner.

[0038] In an implementation of the second aspect, the result of applying the MLM algorithm to the filtered signal includes a log probability of each PAM level of the PAM signal.

[0039] In an implementation manner of the second aspect, the receiving method device includes: reconstructing a signal constellation of the PAM signal based on logarithmic probability.

[0040] In an implementation manner of the second aspect, reconstructing a signal constellation of the PAM signal includes: generating a PAM histogram representing a PAM level of the PAM signal.

[0041] In an implementation manner of the second aspect, the receiving method includes: calculating TDECQ based on a PAM histogram.

[0042] In an implementation of the second aspect, the receiving method includes: further calculating TDECQ based on noise, where the noise is added to the reconstructed signal constellation of the PAM signal.

[0043] In an implementation manner of the second aspect, TDECQ indicates the quality of a PAM signal transmitted by the transmitter device.

[0044] In an implementation of the second aspect, the receiving method is performed using a sampling oscilloscope, which performs equalization of the filtered signal, filtering of the equalized signal, application of the MLM algorithm, reconstruction of the signal constellation, and calculation of the TDECQ.

[0045] The method of the second aspect and its implementation manner achieve the same advantages as the receiver device of the first aspect described above.

[0046] A third aspect of the present disclosure provides a computer program comprising instructions, which, when executed by a computer, causes the computer to perform the method according to the second aspect or any implementation thereof.

[0047] A fourth aspect of the present disclosure provides a non-transitory storage medium storing executable program code, which, when executed by a processor, causes the method according to the second aspect or any of its implementations to be performed.

[0048] Various aspects and implementations (solutions) of the present disclosure differ from other exemplary solutions in at least the following aspects. The exemplary solutions typically use a simple DSP consisting of a linear FFE. This equalizer structure is even preferred in commercial systems. The FFE can have more taps, including nonlinear taps, to improve performance. However, the next generation of high-speed transceivers will include MLSE, and transmitter quality estimation may need to be performed based on MLSE because MLSE can handle strong intersymbol interference (ISI).

[0049] The MLM-based TDECQ of the present disclosure includes FFE and MLM algorithms for reconstructing the signal constellation of the PAM signal, which will be used for TDECQ calculation. In contrast, the exemplary solution calculates TDECQ directly based on the FFE output. The present disclosure can perform transmitter quality estimation for various PAM systems (e.g., PAM4 systems). The PAM signal can be a PAM4 signal.

[0050] The solution of the present disclosure brings the benefit that more advanced algorithms can be used to detect the transmitted signal and the requirements on the transmitter components can be relaxed (more flexible, which can ultimately reduce system costs). The solution of the present disclosure also enables comparison of different transmitters to meet future standards.

[0051] It must be noted that all devices, elements, units and means described in this application can be implemented in software or hardware elements or any type of combination thereof. All steps performed by various entities described in this application and the functions described to be performed by various entities are intended to indicate that the corresponding entities are suitable for or configured to perform the corresponding steps and functions. Although in the description of the following specific embodiments, the specific functions or steps to be performed by the external entity are not reflected in the description of the specific detailed elements of the entity performing the specific steps or functions, it should be clear to the technician that these methods and functions can be implemented by corresponding software or hardware elements or any combination thereof. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In conjunction with the accompanying drawings, the specific embodiments described below illustrate the above aspects and implementation methods. In the drawings:

[0053] Figure 1 An exemplary scheme for calculating TDECQ is shown in (a), and an exemplary PAM4 eye diagram for TDECQ calculation is shown in (b).

[0054] Figure 2 In (a) a receiver device for receiving a PAM signal according to the present disclosure is shown, and in (b) another receiver device implemented in an optical transmission system according to the present disclosure is shown.

[0055] Figure 3 An exemplary receiver device implemented in an optical transmission system according to the present disclosure is shown.

[0056] Figure 4 An example of a recovered PAM level of a PAM signal sent by a transmitter device to a receiver device according to the present disclosure is shown.

[0057] Figure 5 Results for a receiver device according to the present disclosure are shown, in particular the histogram levels of three contrasting symbol groups 01 , 12 and 23 .

[0058] Figure 6 Results of a receiver device according to the present disclosure are shown, in particular histograms of FFE blocks and MLM blocks.

[0059] Figure 7Results of a receiver device according to the present disclosure are shown, in particular a histogram of filtered noise and other histograms.

[0060] Figure 8 Results for a receiver device according to the present disclosure are shown, particularly the noise enhancement after the MLM block.

[0061] Fig. 9 Results for a receiver device according to the present disclosure are shown, particularly the result of multiplying the noise and CF histogram bins, summing them, and selecting the noise for which the SER is equal to the target SER.

[0062] Fig.10 Results for a receiver device according to the present disclosure are shown, in particular histograms after FFE and MLM for four transmitter cases.

[0063] Fig.11 Results for a receiver device according to the present disclosure are shown, particularly SER versus EbN0 and TDECQ.

[0064] Fig.12 Results of a receiver device according to the present disclosure are shown, in particular results of offline data from two different transmitter devices Tx1 and Tx2.

[0065] Fig.13 A method for receiving a PAM signal according to the present disclosure is shown. DETAILED DESCRIPTION

[0066] Figure 2 (a) and Figure 2 (b) shows a receiver device 200 according to the present disclosure. Figure 2 The receiver device 200 shown in (b) is Figure 2 (a) is a further improvement of the receiver device 200 shown, and is shown to be implemented in an optical transmission system including a transmitter device 209. The receiver device 200 of the present disclosure is configured to receive a PAM signal, such as a PAM4 signal. The receiver device 200 of the present disclosure can calculate the TDECQ of a received signal (received from a channel 208) based on a PAM signal (e.g., a PAM4 signal) sent by the transmitter device 209 to the receiver device 200 through the channel 208.

[0067] like Figure 2 As shown in (a), the receiver device 200 of the present disclosure is configured to acquire a signal 201, wherein the signal 201 is based on a PAM signal transmitted by a transmitter device 209. The signal 201 may be an electrical signal, and the PAM signal may be an optical signal.

[0068] The receiver device 200 is also configured to filter the acquired signal 201 by using a filter 202 (e.g., using a low-pass filter). Then, the receiver device 200 is configured to equalize the filtered signal by using an FFE 203 having a plurality of taps. The receiver device 200 is also configured to filter the equalized signal output by the FFE by using a 2-tap post-filter 204. The 2-tap post-filter 204 is configured to compress the high-frequency noise caused by the FFE 203.

[0069] The receiver device 200 is also configured to apply an MLM algorithm 205 to the filtered (equalized) signal output by the 2-tap post-filter 204. Then, the receiver device 200 is configured to reconstruct a signal constellation 206 of the PAM signal based on the result of applying the MLM algorithm 205. In addition, the receiver device 200 is configured to calculate TDECQ 207 based on the reconstructed signal constellation of the PAM signal obtained using MLM (e.g., in the signal reconstruction block 206).

[0070] Figure 2 The receiver device 200 of (b) is based on Figure 2 The receiver device 200 of (b) is configured and can perform the same steps. Figure 2 (a) and Figure 2 The same elements in (b) are marked with the same reference numerals and may serve similar functions. Figure 2 (b) Receiver device 200 showing more optional details.

[0071] like Figure 2 As shown in (b), the PAM signal 211 is sent by a transmitter device 209, for example, by an optical transmitter. Therefore, the PAM signal 211 in this case is an optical signal. The PAM signal 211 is sent through a channel 208, which can be considered as a worst-case optical channel. After the channel 208, the optical signal 213 is received by a PIN-based photodetector 210 of the receiver device 200, which is configured to convert the optical signal 213 (corresponding to the optical PAM signal 211 after the channel 208) into an acquired signal 201, which is an electrical signal. The electrical signal can be processed in the receiver device 200.

[0072] The acquired electrical signal 201 may be filtered by the H-BT4 filter of the receiver device 200, and then the filtered signal output by the H-BT4 filter may be equalized by the optimal FFE 203 of the receiver device 200. The equalized signal may then be further filtered by an optimal linear filter (as a post filter 204), wherein the filtering is based on the filter coefficient α. The filtered signal may then be input into an MLM algorithm 205 (e.g., an MLM calculation block), and the output of the MLM algorithm 205 is used by a signal reconstruction block 206 to reconstruct a signal constellation of a PAM signal 211. Noise 212 may then be added to the reconstructed signal constellation of the PAM signal 211, and finally TDECQ 207 may be calculated based on the reconstructed signal constellation of the PAM signal 211 to which the noise 212 is added.

[0073] The receiver device 200 may include a processor or processing circuit system (not shown) configured to perform, conduct or initiate various operations of the receiver device 200 described herein. The processing circuit system may include hardware and / or the processing circuit system may be controlled by software. The hardware may include an analog circuit system or a digital circuit system, or both an analog circuit system and a digital circuit system. The digital circuit system may include components such as an application-specific integrated circuit (ASIC), a field-programmable array (FPGA), a digital signal processor (DSP) or a multi-purpose processor. The receiver device 200 may also include a memory circuit system that stores one or more instructions that can be executed by a processor or by a processing circuit system (specifically, executed under the control of software). For example, the memory circuit system may include a non-transitory storage medium storing executable software code that, when executed by a processor or a processing circuit system, enables the receiver device 200 to perform various operations. In one embodiment, the processing circuit system includes one or more processors and a non-transitory memory connected to one or more processors. The non-volatile memory may carry executable program code that, when executed by one or more processors, causes the receiver device 200 to perform, perform, or initiate the operations or methods described herein.

[0074] Figure 3 A receiver device 200 according to the present disclosure is shown, which is constructed in Figure 2 (a) and Figure 2 (b) The receiver device 200 is shown separately. The same elements are marked with the same reference numerals and may perform similar or identical functions.

[0075] Overall, Figure 3 A new MLM-based TDECQ acquisition process is proposed. It is worth noting that Figure 3 The receiver device 200 shown may also be based on Figure 1 (a) shows a system in which a receiver device 200 is implemented by at least a 2-tap post filter 204, an MLM algorithm 205 (a simplified BCJR algorithm), a signal reconstruction block 206, and a TDECQ calculation 207 based on the output of the signal reconstruction block 206. Figure 1 The expansion is performed on the receiver in (a).

[0076] It is worth noting that the receiver device 200 can be used for any PAM modulation format, but the present disclosure focuses specifically on PAM4 because PAM4 is likely to be the modulation format used in the next generation of high-speed optical transceivers. TDECQ 207 is used to quantify the quality of the PAM4 transmitter device 209, but it can also be called a transmitter quality parameter that includes any transmission scenario and any modulation format. The value of TDECQ 207 can indicate the transmitter quality. Therefore, the transmitter quality can be quantified by TDECQ 207, and it can be checked whether the value is lower than the maximum allowed value (e.g., TDECQmax) that will be defined by the standard.

[0077] The optical signal 213 (eg, received from an optical fiber as channel 208) is received by a photodetector 210 (eg, implemented by a photodiode) of the receiver device 200. The signal x1 (corresponding to Figure 2 (a) and Figure 2 The acquired signal 201) shown in (b) is an electrical signal x1 that is captured (eg, sampled and stored) by an instrument 300 such as a sampling oscilloscope.

[0078] The captured signal x1 (e.g., millions of samples) can be processed by a software program running in the receiver device 200. The signal x1 (e.g., its stored samples) is Figure 3 The oscilloscope is low-pass filtered (via H-BT4 filter 202) in the receiver device 200 to remove out-of-band noise because the oscilloscope can have a larger bandwidth and sampling rate.

[0079] The signal x2 after the H-BT4 filter 202 is equalized by the FFE 203, which may have N taps. The signal x2 may be distorted, especially in the histogram based on the signal x2, no clear PAM level can be seen. However, the signal x3 after the FFE 203 is clear, for example, as can be seen Figure 4It is worth noting that after FFE 203, FFE 203 may use a blind FFE algorithm to obtain better decisions.

[0080] The signal x3 after FFE 203 is filtered by a 2-tap linear post-filter 204. The post-filter is defined by its transfer function 1+αD, where D represents the delay in symbol periods and α is the filter coefficient. The value of the filter coefficient α can be derived in an iterative manner. After the post-filter 204 (which can also be called a noise decorrelation filter), the signal x4 is processed by an MLM block (executing the MLM algorithm 205) to obtain improved decisions. This MLM block can generate a logarithmic probability for each PAM level. The result of the MLM algorithm 205 is a signal x5. The post-filter can include more taps. For example, a 3-tap post-filter involving three FFE output samples is defined by 1+αD+βD 2 Definition, where D 2 Indicates a 2-symbol period delay.

[0081] The signal x5 may include four log-probability values, and these values ​​are used to generate a PAM histogram representing the PAM levels, e.g. Figure 4 PAM4 levels 400 of PAM signal 211 are shown. That is, reconstructing the signal constellation of PAM signal 211 at signal reconstruction block 206 may include generating a PAM histogram representing PAM levels of PAM signal 211. Signal x6 includes the reconstructed signal constellation, which may be used to represent samples of the PAM signal using PAM levels, for example.

[0082] Then, the receiver device 200 of the present disclosure can use the output signal x6 of the signal reconstruction block 206 to calculate TDECQ 207. Since the signal x6 is similar to the signal x3, the calculation of TDECQ can be similar to Figure 1 (a) shows an exemplary TDECQ calculation. The TDECQ algorithm is used to calculate TDECQ 207. Thus Figure 1 The TDECQ algorithm used in (a) may be modified. In addition, noise 212 may be defined in front of the TDECQ calculation block. Signal x7 is signal x6 with noise 212 added. Then, TEDCQ 207 is calculated on signal x7, i.e., based on the reconstructed signal constellation x6 with noise 212 added. The TDECQ value may be output as signal x8.

[0083] In the following, it is described as Figure 2 (a) Figure 2 (b) and Figure 3 Further exemplary implementation details of receiver device 200 are shown.

[0084] FFE 203 may use N linear taps to recover the PAM4 level of the received PAM4 signal 213 from the ISI channel 208. N may be an odd number, and N=7 is used exemplarily in the remainder of this disclosure. For N=7, the starting FFE taps may be c=0001000, i.e., all taps may be set to 0, and the center tap (N-1) / 2+1 may be set to 1. Then, FFE 203 may follow the following steps:

[0085] 1. The signal x2 before FFE 203 is normalized to x=g*(x2-dc), dc=mean(x2) to enable fast FFE acquisition. FFE 203

[0086] Convert unipolar signals to bipolar signals to avoid low frequency component suppression. Select parameter g to enable fast acquisition and low FFE output noise.

[0087] 2. FFE 203 finds taps c(i) in blind mode, i = 0, 1, ..., N-1. The gradient algorithm quantizes the output signal to levels l = -3, -1,

[0088] 1, 3 and thresholds t = -2, 0, 2 to use decision-directed least-mean square (DD-

[0089] However, DD-LMS can be replaced by other blind methods.

[0090] 3. After the FFE taps are stabilized, the PAM4 output level is found by histogram analysis. The new level is l(i), i=0, 1, 2, 3, and the new threshold is t(i), i=0, 1, 2.

[0091] 4. The FFE 203 operates with the new level. Steps 3 and 4 may be repeated several times until the taps become stable.

[0092] 5. After the FFE tap is stabilized, the output signal x3 is adjusted by the following formula:

[0093] x3=x3+g*dc*sum(c).

[0094] 6. Analyze the output signal histogram to find the level l and threshold t. Note that, for example, OMA = l3.

[0095] The post filter 204 converts the FFE output signal x3 into a signal x4 by the following formula:

[0096] x4(k)=x3(k)+α*x3(k-1).

[0097] The parameter α is calculated by the following formula:

[0098] α=-mean(error(1:end-1).*error(2:end)) / mean(error.^2),

[0099] Where error = qsym - y, and qsym is a quantized symbol with threshold t and level l. By using the FFE output to calculate the error, the FFE output may be unreliable, and at high BER values, the alpha (α) estimate may not be very accurate. Since the FFE 302 acts as a high-pass filter, the post filter 204 compresses the high-frequency FFE noise caused by the FFE noise enhancement.

[0100] The MLM algorithm 205 can provide a more reliable decision. The MLM algorithm 205 can be run multiple times to obtain a more accurate α value to be used in the final MLM run. The MLM outputs the PAM4 symbol log probability. The best symbol can be selected to calculate the error. The MLM output symbol x5 can include symMLM and error=l(symMLM)-x3.

[0101] Specifically, the MLM algorithm calculates the logarithmic probability of symbol time i for each of the four PAM4 symbol candidates lp(i, j), j = 0, 1, 2, 3. For example, the MLM algorithm can use the algorithm described in the following document: Lucian Andrei and Rodica Stoian, “The Decision Reliability of MAP, Log-MAP, Max-Log-MAP and SOVA Algorithms”, INTERNATIONAL JOURNAL OF COMMUNICATIONS, No. 1, Vol. 2, 2008, where the branch probability is bp(I,k) = (w(i) - m(k)) 2 (Euclidean distance). The signal x4 is:

[0102] x4(k)=x3(k)+α*x3(k-1)=(1+α)*sl(k)+n(k)+α*n(k-1)=x3 0 (k)+nx3(k),

[0103] Wherein sl is the transmitted symbol level (sl=l(n), n=0, 1, 2, 3), and nx3 is the noise after filtering.

[0104] When considering a single trellis level and two symbols s(i) and s(i+1), i=0, 1, 2, 3 and s(i)=i, the log-likelihood ratio llr is equal to llp(i)=lp(i)-lp(i+1). By collecting the events that determine the symbol s(i) or s(i+1), we can obtain the probability that the probability at position ll(i)=±[l(i+1)-l(i)] 2 The histogram with the maximum level is found at (the positive histogram and the negative histogram are combined into a single histogram), the threshold is 0, and the standard deviation of the noise is σ(i)=2*[l(i+1)-l(i)].

[0105] Typically, the MLM algorithm 205 uses a long sequence to obtain lp values, and the histogram will have slightly different values ​​than those predicted by a single grid level. Figure 5 For the three contrast symbol groups 01, 12 and 23 shown in , the final histogram levels (the values ​​with the highest probability) will be ±L(i), I=0, 1, 2.

[0106] The previous histogram (llp(i) = lp(i) - lp(i+1)) is obtained by selecting lp where symbol s(i) or symbol s(i+1) is the best symbol. In order to calculate TDECQ 207, it is necessary to obtain the PAM4 histogram after the MLM block based on the lp value. The FFE output level is l(i), I = 0, 1, 2, 3. First, it is necessary to obtain the normalization factor nf of the three sets of histograms described above. The nf value can be calculated by nf(i) = [l(i+1)-l(i)] / 2 / L(i), so that the new level is [l(i+1)-l(i)] / 2.

[0107] Now, for the symbol at position i where the first column value indicates the best symbol, three sets of positions can be selected using the sorting matrix b(i,j):

[0108] Group 1 - all positions p0 where [b(i,0)=0 and b(i,1)=1] or [b(i,0)=1 and b(i,1)=0]

[0109] Group 2 - all positions p1 where [b(i,0)=1 and b(i,1)=2] or [b(i,0)=2 and b(i,1)=1]

[0110] Group 3 - all positions p2 where [b(i,0)=2 and b(i,1)=3] or [b(i,0)=3 and b(i,1)=2]

[0111] In the next step, the llr vector is constructed by:

[0112] ·llr(p0)=nf(0)*[lp(p0,0)-lp(p0,1)]+t(0)

[0113] ·llr(p1)=nf(1)*[lp(p1,1)-lp(p1,2)]+t(1)

[0114] ·llr(p2)=nf(2)*[lp(p2,2)-lp(p2,3)]+t(2)

[0115] Signal reconstruction block 296 generates signal x6 similar to FFE output signal x3. The levels and thresholds are the same as those of FFE output signal x3, but the amount of noise is slightly different. FFE histograms and MLM histograms can be generated in the same Figure 6 , to visualize the effect of these blocks. The impact of MLM on BER is obvious.

[0116] Normalization based on a single grid analysis requires normalization by nfST(i)=0.5 / [l(i+1)-l(i)], but the present disclosure normalizes by nf(i)=[l(i+1)-l(i)] / 2 / L(i). There are some offsets in the MLM histogram because the MLM histogram consists of three groups of llrs. This is not related to TDECQ accuracy because the offset is near the PAM4 level. In addition, the histogram can be normalized so that OMA=3 without changing the final result.

[0117] The post filter 204 shapes the FFE output noise through [1α] coefficients. The histogram of the filtered noise is as follows: Figure 7 The noise after signal reconstruction (i.e. after MLM) can be compared to the noise after filtering ( Figure 7 MLM curves in TDECQ; MLM uses a grid search, which further improves the noise statistics) a little bit. To achieve a more accurate TDECQ calculation, noise can be added to the TDECQ calculator and the noise is additionally normalized by a factor nwf(i) = (l(i+1) - l(i)) / sqrt(L(i)) that is usually less than 1. After normalization, the MLM noise is very close to the filtered noise ( Figure 7 There are three SER values ​​to be calculated (three thresholds). Therefore, for each SER calculation, a different noise is used, i.e., white additive noise is corrected by Ceq and nwf(i).

[0118] It can be noticed that there are some deviations between the histograms at high histogram values ​​(bins close to 0; smaller noise areas). These deviations are not relevant for the TEDCQ calculation, since the contribution of the “strong” bins to the SER is negligible.

[0119] The TDECQ calculation part follows the calculation described in the IEEE Ethernet standard IEEE Std.802.3, 2018. The difference is that the CeqMLSE parameter is calculated using FFE Ceq (CeqFFE) and nwf. The obtained CeqMLSE is CeqMLSE(i) = CeqFFE*nwf(i), i = 0, 1, 2.

[0120] In one implementation, the obtained CeqMLSE is CeqMLSE(i)=CeqFFE·CeqPF·nwf(i), i=0, 1, 2. The 2-tap post-filter parameter CeqPF is equal to sqrt(1+α 2 ) / (1+α). Figure 8 As can be seen in Fig. 1, the noise enhancement obtained after the MLM block is very small.

[0121] The three cumulative functions (CF) are obtained by the method described in the IEEE Ethernet standard IEEEStd.802.3, 2018. The noise and CF histogram bars are multiplied and summed, and the noise whose SER is equal to the target SER is selected, such as Fig. 9 as shown in .

[0122] Select SER_target and apply a sigma(σ) search to find the value of sigma that gives SER = SERtarget:

[0123]

[0124] Or in one implementation

[0125]

[0126] The MLM histogram consists of 2K bars of width Δx. The value σ corresponding to the SER_target value t Used to calculate TDECQ using the following formula:

[0127]

[0128] Where qfuncinv represents the inverse Q function.

[0129] Four transmitter cases with narrow system bandwidth (α ∼ 0.35; EbN0 = 17 dB, ER = 10 dB) are simulated. The target SER is set to 4e-3. The histograms after FFE and MLM are shown in Fig.10MLM improves the performance (the histogram after MLM is better). The MLM signal reconstruction block provides the following histogram, which shows a somewhat irregular behavior near the signal level. However, this is not relevant to TDECQ accuracy because the offset is near the PAM4 level (which contributes little to SER).

[0130] Fig.11 The first sub-figure in Figure 2 shows the relationship between SER and EbN0, while Fig.11 The second sub-figure in FIG shows TDECQ 207. The MLM-based TDECQ clearly distinguishes between better channels and worse channels. As expected, better channels have smaller TDECQ. This proves that the new TDECQ 207 can be used to blindly estimate the quality of the transmitter device 209.

[0131] Processing offline data Tx1 and Tx2 from two different transmitter devices 209, such as Fig.12 Both data have pattern-dependent behavior, but Tx2 performs better. TDECQ values ​​are shown (below the mark). TDECQ clearly distinguishes the two transmitter devices without knowing the SER. Fig.12 In Figure 1, the TEDCQ values ​​of the transmitter of Case 4 are added (TDECQ at SER = 3e-4; the Pin values ​​do not correspond to the EbN0 values; this is just for visualization). This transmitter device is not affected by the pattern dependency, and even at SER = 2e-4, it has a better (lower) TDECQ value at a higher SER (3e-4) compared to Tx2. This means that Tx2 will suffer more losses than the transmitter of Case 4 in the presence of noise.

[0132] It is worth noting that the receiver device 200 and scheme of the present disclosure can be used for measurement devices to characterize the quality of optical transmitters. The present disclosure can support standardization and optical transmitter selection.

[0133] Fig.13 A method 1300 for receiving a PAM signal according to the present disclosure is shown. The method 1300 may be performed by the receiver device 200 and may be used to receive a PAM4 signal.

[0134] The method 1300 includes step 1301: acquiring a signal 201, x1; wherein the signal 201, x1 is based on a PAM signal 211 transmitted by a transmitter device 209 through a channel 208. The method 1300 also includes step 1302: filtering the acquired signal 201, x1; the method 1300 also includes step 1303: equalizing the filtered signal x2 using a feedforward equalization (FFE 203) with a plurality of taps. The method 1300 also includes step 1304: filtering the equalized signal x3 using a 2-tap filter (2-tap filter 204), wherein high-frequency noise caused by the feedforward equalization is compressed. Then, the method 1300 includes step 1305: applying the MLM algorithm 205 to the 2-tap filtered signal x4; then, the method 1300 includes step 1306: reconstructing a signal constellation x6 of the PAM signal 211 based on the result x5 of applying the MLM algorithm 205. Finally, the method 1300 comprises a step 1308 of calculating 1307 the TDECQ 207 based on the reconstructed signal constellation x6 of the PAM signal 211 .

[0135] The present disclosure has been described in conjunction with various embodiments as examples and in conjunction with implementations. However, from a study of the drawings, the present disclosure and the independent claims, a person skilled in the art will be able to understand and implement other variations when implementing the claimed subject matter. In the claims as well as in the specification, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. A single element or other unit may fulfil the functions of several entities or items described in a claim. The fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.

Claims

1. A receiver device (200) for a pulse amplitude modulation (PAM) signal, the receiver device (200) being configured to: Get the signal (201, x1), where The signal (201, x1) is based on a PAM signal (211) transmitted by a transmitter device (209) to the receiver device (200) through a channel (208); Filtering (202) the acquired signal (201); equalizing the filtered signal (x2) using a feed-forward equalizer (FFE) (203) having a plurality of taps; filtering the equalized signal (x3) output by the FFE (203) using a 2-tap post filter (204), wherein high frequency noise caused by the FFE (203) is compressed; Applying a maximum logarithmic mapping (MLM) algorithm (205) to the filtered signal (x4) output by the 2-tap post-filter (204); reconstructing a signal constellation (x6, 206) of the PAM signal (211) based on the result (x5) of applying the MLM algorithm (205); and Based on the reconstructed signal constellation (x6) of the PAM signal (211), a transmit dispersion eye closure four-phase TDECQ (207) is calculated.

2. The receiver device (200) according to claim 1, wherein The PAM signal (211) transmitted by the transmitter device (209) is an optical signal, wherein the acquired signal (201, x1) is an electrical signal, and wherein the receiver device (200) comprises a photodetector (210) for converting the optical signal into an electrical signal.

3. The receiver device (200) according to claim 1 or 2, configured to filter the acquired signal (201, x1) using a low pass filter (202).

4. The receiver device (200) according to one of claims 1 to 3, wherein The FFE (203) is configured to restore the PAM level (400) included in the PAM signal (211) by equalizing the filtered signal (x2).

5. The receiver device (200) according to one of claims 1 to 4, wherein The FFE (203) is configured to perform a blind FFE algorithm to equalize the filtered signal.

6. The receiver device (200) according to one of claims 1 to 5, wherein Filtering the equalized signal (x3) includes linearly filtering the equalized signal (x3) based on a filter coefficient (α) using the 2-tap post-filter (204), wherein the filter coefficient (α) is determined in an iterative manner.

7. The receiver device (200) according to one of claims 1 to 6, wherein The result (x5) of applying the MLM algorithm (205) to the filtered signal (x4) output by the 2-tap post-filter (204) includes the logarithmic probability of each PAM level (400) of the PAM signal (211).

8. The receiver device (200) according to claim 7, configured to reconstruct a signal constellation (x6, 206) of the PAM signal (211) based on the logarithmic probability.

9. The receiver device (200) according to claim 7 or 8, wherein The reconstruction of the signal constellation (x6, 206) of the PAM signal (211) includes generating a PAM histogram representing the PAM levels (400) of the PAM signal (211).

10. The receiver device (200) of claim 9, configured to calculate the TDECQ (207) based on the PAM histogram.

11. The receiver device (200) according to one of claims 1 to 10, configured to calculate the TDECQ (207) further based on noise (x7, 212), which is added to the reconstructed signal constellation (x6) of the PAM signal (211).

12. The receiver device (200) according to one of claims 1 to 11, wherein The TDECQ (207) is calculated including the 2-tap post-filter parameters CeqPF, which is equal to sqrt(1+α 2 ) / (1+α).

13. The receiver device (200) according to one of claims 1 to 12, wherein: The TDECQ (207) indicates the quality of the PAM signal (211) transmitted by the transmitter device (209).

14. A receiver device (200) according to one of claims 1 to 13, comprising a sampling oscilloscope (300), which is configured to: perform equalization of the filtered signal (x2), filter the equalized signal (x3), apply the maximum logarithmic mapping algorithm (205), reconstruct the signal constellation (x6, 206) and calculate the TDECQ (207).

15. A method (1300) for receiving a pulse amplitude modulation (PAM) signal, the receiving method (1300) comprising: Acquiring (1301) a signal (201, x1), wherein the signal (x1) is based on a PAM signal (211) transmitted by a transmitter device (209) through a channel (208); Filtering (1302) the acquired signal (201, x1); equalizing (1303) the filtered signal (x2) using a feed-forward equalization (203) having a plurality of taps; filtering (1304) the equalized signal (x3) using a 2-tap filter (204), wherein high frequency noise caused by the feed-forward equalization (203) is compressed; Applying (1305) the MLM algorithm (205) to the 2-tap filtered signal (x4); reconstructing (1306) a signal constellation (x6, 206) of the PAM signal (211) based on a result (x5) of applying the MLM algorithm (205); and The TDECQ (207) is calculated (1307) based on the reconstructed signal constellation (x6) of the PAM signal (211).

16. A computer program comprising instructions which, when executed by a computer, cause the computer to perform the method (1300) according to claim 14.

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