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

[0001] This application is a divisional application of the original application with the application number 202380063758.7, the original application date is October 10, 2023, the entire contents of the original application are incorporated herein by reference; and the original application is the Chinese national phase of the PCT application with the application number PCT / CN2023 / 123674, the application date is October 10, 2023, which claims priority to the PCT application with the application number PCT / EP2022 / 082379, the application date is November 18, 2022, and the PCT application with the application number PCT / EP2022 / 078128, the application date is October 10, 2022, the entire contents of which are incorporated herein by reference. TECHNICAL FIELD

[0002] The present disclosure relates to a receiver device and a receiving method for receiving a pulse amplitude modulation (PAM) signal transmitted 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) representing a quality of the PAM signal transmitted by the transmitter device through the channel. BACKGROUND

[0003] The latest generation of high performance optical interconnects used in data communications employs a 4-level PAM format (PAM4). One of the main system level signal quality metrics is TDECQ. Transmitter eye closure quaternary (TECQ) is also used in channels without chromatic dispersion (CD). The difference between these two values provides the CD penalty.

[0004] TDECQ quantifies the penalty of impairments that can or can not be equalized by a reference receiver. TDECQ is a measure of 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 can be equalized with a reference equalizer. The reference receiver and the reference equalizer can be implemented in software, or can be part of an oscilloscope or other receiver device. SUMMARY

[0005] In Figure 1An exemplary optical interconnect is shown in (a) through which a pattern is sent from an optical transmitter through a worst-case optical channel to a TDECQ tester.

[0006] The TDECQ tester includes a reference receiver and a TDECQ algorithm. The reference receiver converts the received optical signal to an electrical signal and filters the electrical signal through a fourth-order Bessel-Thomson (BT4) filter. Then, given the receiver noise with the BT4 shaping, the TDECQ algorithm finds the optimal 5-tap feed-forward equalizer (FFE). Figure 1 (a) also depicts the reference points for adding noise σ G and σ eq and a noise enhancement factor C eq The TDECQ algorithm connected to the reference receiver finds the maximum input reference receiver noise σ G that makes the signal enhancement ratio (SER) equal to a target SER (TSER) of 4.8 x 10 -4 (KP4 forward error correction (FEC) limit).

[0007] As shown in Figure 1 (b), the equalizer samples at two sample points with a distance of 0.1 UI, and the best sample phase (TDECQ is minimal here) is found. There are two sample phases, and the worst TDECQ value is selected. TEDCQ is calculated by the following equation:

[0008]

[0009] where R is the root mean square (RMS) noise that the receiver can add, Q t is 3.414, which is consistent with the bit error rate (BER) and TSER of Gray-coded PAM4. The whole process is done in a blind mode, so that TDECQ is only used to quantify the quality of the transmitter, but not to quantify 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.

[0010] However, the above procedure comes with challenges. For example, high-speed optical interconnects require very powerful digital signal processing (DSP), including a maximum likelihood sequence estimator (MLSE). As another example, more advanced and complex TDECQ calculations are required for a new generation of faster transceivers.

[0011] In view of the above, it is an object of the present disclosure to provide an improved TDECQ calculation.

[0012] These and other objects are achieved by the present disclosure, as specified in the appended independent claims. Advantageous implementations are further defined in the dependent claims.

[0013] A first aspect of the disclosure provides a receiver device for a PAM signal, the receiver device being configured to: obtain a signal, wherein the signal is based on a PAM signal transmitted by a transmitter device to the receiver device over a channel; filter the obtained signal; equalize the filtered signal using an FFE having a plurality of 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 a TDECQ based on the reconstructed signal constellation of the PAM signal.

[0014] The receiver device according to the first aspect provides an improved TDECQ calculation. For example, the receiver device can calculate an accurate TDECQ. The receiver device according to the first aspect does not use the output of the FFE to calculate the TDECQ, but uses the output of the signal (constellation) reconstruction to calculate the TDECQ.

[0015] In an implementation form of the first aspect, the PAM signal transmitted by the transmitter device is an optical signal, wherein the obtained signal is an electrical signal, and wherein the receiver device comprises a photodetector for converting the optical signal to the electrical signal.

[0016] For example, the PAM signal can be a PAM4 signal. The optical channel can be an optical fiber.

[0017] In an implementation form of the first aspect, the receiver device is configured to filter the obtained signal using a low-pass filter.

[0018] The filter can be an H-BT4 filter, but can also be any kind of low-pass filter.

[0019] In an implementation form of the first aspect, the FFE is configured to recover the PAM levels comprised in the PAM signal by equalizing the filtered signal.

[0020] This reduces the distortion in the acquired signal and the filtered signal, thereby improving the performance of the receiver device.

[0021] In an implementation form of the first aspect, the FFE is configured to perform a blind FFE algorithm to equalize the filtered signal.

[0022] The blind FFE algorithm can result in an improved decision at the receiver device. For example, the FFE can find the taps in blind mode. For example, a decision-directed least-means square (DD-LMS) mode can be used in blind mode, but any other blind method can also be used.

[0023] In an implementation form of the first aspect, filtering the equalized signal comprises linearly filtering the equalized signal based on filter coefficients with a 2-tap post filter, wherein the filter coefficients are determined in an iterative manner.

[0024] In an implementation form of the first aspect, the result of applying the maximum log-mapping algorithm to the filtered signal output by the 2-tap post filter comprises a log probability of each PAM level of the PAM signal.

[0025] In an implementation form of the first aspect, the receiver device is configured to reconstruct a signal constellation of the PAM signal based on the log probability.

[0026] In an implementation form of the first aspect, reconstructing the signal constellation of the PAM signal comprises generating a PAM histogram representing the PAM levels of the PAM signal.

[0027] In an implementation form of the first aspect, the receiver device is configured to calculate the TDECQ based on the PAM histogram.

[0028] In an implementation form of the first aspect, the receiver device is configured to calculate the TDECQ further based on a noise, the noise being added to the reconstructed signal constellation of the PAM signal.

[0029] Adding the noise enables to scan the noise-dependent SER and find the amount of noise that achieves the target SER. This amount of noise can be used to calculate the TDECQ.

[0030] In an implementation form of the first aspect, the receiver device is configured to: compute the TDECQ comprises a 2-tap post-filter parameter CeqPF, which is equal to sqrt(1+α 2 ) / (1+α). The introduction of CeqPF can improve the accuracy of the TDECQ computation.

[0031] In an implementation form of the first aspect, the TDECQ is indicative of a quality of the PAM signal transmitted by the transmitter device.

[0032] In an implementation form of the first aspect, the receiver device comprises a sampling oscilloscope configured to: perform equalization of the filtered signal, filter the equalized signal, apply the MLM algorithm, reconstruct the signal constellation, and compute the TDECQ.

[0033] A second aspect of the disclosure provides a receiving method for a pulse amplitude modulation (PAM) signal, the receiving method comprising: obtaining a signal, wherein the signal is based on a PAM signal transmitted by a transmitter device over a channel; filtering the obtained signal; equalizing the filtered signal using a feed-forward equalization having a plurality of taps; filtering the equalized signal using a 2-tap filter, wherein high frequency noise caused by the feed-forward equalization is compressed; applying a 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 computing a TDECQ based on the reconstructed signal constellation of the PAM signal.

[0034] In an implementation form of the second aspect, the PAM signal transmitted by the transmitter device is an optical signal, wherein the obtained signal is an electrical signal, and wherein the receiving method comprises: converting the optical signal to the electrical signal.

[0035] In an implementation form of the second aspect, the receiving method comprises: filtering the obtained signal using a low-pass filter.

[0036] In an implementation form of the second aspect, the feed-forward equalization recovers PAM levels comprised in the PAM signal by equalizing the filtered signal.

[0037] In an implementation form of the second aspect, the feed-forward equalization comprises: performing a blind feed-forward equalization algorithm to equalize the filtered signal.

[0038] In an implementation form of the second aspect, the 2-tap post-filtering of the equalized signal comprises: linearly filtering the equalized signal based on filter coefficients, wherein the filter coefficients are determined in an iterative manner.

[0039] In an implementation form of the second aspect, the result of applying the MLM algorithm to the filtered signal comprises a log probability of each PAM level of the PAM signal.

[0040] In an implementation form of the second aspect, the receiving method device comprises reconstructing a signal constellation of the PAM signal based on the log probability.

[0041] In an implementation form of the second aspect, reconstructing the signal constellation of the PAM signal comprises generating a PAM histogram representing PAM levels of the PAM signal.

[0042] In an implementation form of the second aspect, the receiving method comprises calculating the TDECQ based on the PAM histogram.

[0043] In an implementation form of the second aspect, the receiving method comprises calculating the TDECQ further based on a noise, the noise being added to the reconstructed signal constellation of the PAM signal.

[0044] In an implementation form of the second aspect, the TDECQ is indicative of a quality of the PAM signal transmitted by the transmitter device.

[0045] In an implementation form of the second aspect, the receiving method is performed using a sampling oscilloscope, the sampling oscilloscope performing the equalizing the filtered signal, the filtering the equalized signal, the applying the MLM algorithm, the reconstructing the signal constellation, and the calculating the TDECQ.

[0046] The method of the second aspect and its implementation forms achieve the same advantages as the receiver device of the first aspect described above.

[0047] A third aspect of the disclosure provides a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method according to the second aspect or any implementation form thereof.

[0048] A fourth aspect of the 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 the implementation forms thereof to be performed.

[0049] Aspects and implementations of the present disclosure differ from other exemplary solutions at least in that 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 can need transmitter quality estimation based on MLSE, as MLSE can handle strong intersymbol interference (ISI).

[0050] The MLM-based TDECQ of the present disclosure includes an FFE and a MLM algorithm for reconstructing the signal constellation of a PAM signal, which will be used for TDECQ computation. In contrast, exemplary solutions directly compute TDECQ from 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.

[0051] The benefit of the solution of the present disclosure is that more advanced algorithms can be used to detect the transmitted signal, and the requirements on the transmitter components can be relaxed (more flexibility, which can eventually reduce system cost). The solution of the present disclosure is also able to compare different transmitters to meet future standards.

[0052] It has to be noted that all devices, elements, units and means described in the present application can be implemented in software or hardware elements or any type of combination thereof. All steps, functions, procedures and / or actions described in the present application can be performed in software or hardware elements or any type of combination thereof. All entities described in the present application performing steps, functions, procedures and / or actions can be implemented in software or hardware elements or any type of combination thereof. The software or hardware elements can be implemented in a single device or a plurality of devices. BRIEF DESCRIPTION OF DRAWINGS

[0053] The specific embodiments described hereinbefore are illustrative of how the above aspects and implementations can be put into effect. In connection with the appended drawings, in which:

[0054] Figure 1 An exemplary scheme for computing TDECQ is shown in (a), and an exemplary PAM4 eye diagram for TDECQ computation is shown in (b).

[0055] Figure 2A receiver device for receiving a PAM signal according to the present disclosure is shown in (a) and another receiver device implemented in an optical transmission system according to the present disclosure is shown in (b).

[0056] Figure 3 An exemplary receiver device implemented in an optical transmission system according to the present disclosure is shown.

[0057] Figure 4 An example of the recovered PAM levels of a PAM signal transmitted by a transmitter device to a receiver device according to the present disclosure is shown.

[0058] Figure 5 Results of a receiver device according to the present disclosure are shown, in particular the histogram levels of three contrast symbol groups 01, 12 and 23.

[0059] Figure 6 Results of a receiver device according to the present disclosure are shown, in particular the histograms of the FFE block and the MLM block.

[0060] Figure 7 Results of a receiver device according to the present disclosure are shown, in particular the histogram of the filtered noise and other histograms.

[0061] Figure 8 Results of a receiver device according to the present disclosure are shown, in particular the noise enhancement after the MLM block.

[0062] Figure 9 Results of a receiver device according to the present disclosure are shown, in particular the results of multiplying the noise and CF histogram bars, summing them, and selecting the noise with SER equal to the target SER.

[0063] Figure 10 Results of a receiver device according to the present disclosure are shown, in particular the histograms after the FFE and MLM for four transmitter cases.

[0064] Figure 11 Results of a receiver device according to the present disclosure are shown, in particular the relationship of SER with EbN0 and TDECQ.

[0065] Figure 12 Results of a receiver device according to the present disclosure are shown, in particular the results of offline data from two different transmitter devices Tx1 and Tx2.

[0066] Figure 13 A method for receiving a PAM signal according to the present disclosure is shown. DETAILED DESCRIPTION

[0067] Figure 2 (a) and Figure 2 (b) illustrates a receiver device 200 according to the present disclosure. Figure 2 (b) illustrates a receiver device 200 according to the present disclosure. Figure 2 (a) illustrates a further improvement of the receiver device 200 and is shown as implemented in an optical transmission system comprising a transmitter device 209. The receiver device 200 of the present disclosure is configured to receive a PAM signal, e.g. a PAM4 signal. The receiver device 200 of the present disclosure can compute a TDECQ of a received signal (received from a channel 208) that is based on a PAM signal (e.g. a PAM4 signal) transmitted by the transmitter device 209 to the receiver device 200 through the channel 208.

[0068] As Figure 2 (a) illustrates, 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 the transmitter device 209. The signal 201 can be an electrical signal, while the PAM signal can be an optical signal.

[0069] The receiver device 200 is further 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 with multiple taps. The receiver device 200 is further 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 high frequency noise caused by the FFE 203.

[0070] The receiver device 200 is further 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 of the PAM signal based on the result of applying the MLM algorithm 205. Furthermore, the receiver device 200 is configured to compute a TDECQ 207 based on the reconstructed signal constellation of the PAM signal acquired using the MLM (e.g. in a signal reconstruction block 206).

[0071] Figure 2 (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 (a) and (b) are labeled with the same reference signs and can act in a similar way. For the receiver device 200 of Figure 2 (b), more optional details are shown.

[0072] As Figure 2 The PAM signal 211 is transmitted by the transmitter device 209, e.g. by an optical transmitter, as shown in (b). Thus, the PAM signal 211 in this case is an optical signal. The PAM signal 211 is transmitted 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.

[0073] The acquired electrical signal 201 can be filtered by an H-BT4 filter of the receiver device 200, and then the filtered signal output by the H-BT4 filter can be equalized by an optimal FFE 203 of the receiver device 200. Then, the equalized signal can be further filtered by an optimal linear filter (as a post filter 204), wherein the filtering is based on filter coefficients a. Then, the filtered signal can be input into an MLM algorithm 205 (e.g. an MLM computation block), and the output of the MLM algorithm 205 is used by a signal reconstruction block 206 for reconstructing the signal constellation of the PAM signal 211. Then, noise 212 can be added to the reconstructed signal constellation of the PAM signal 211, and finally the TDECQ 207 is computed based on the reconstructed signal constellation of the PAM signal 211 with added noise 212.

[0074] The receiver device 200 can comprise a processor or processing circuitry (not shown) configured to perform, conduct or initiate the various operations of the receiver device 200 described herein. The processing circuitry can comprise hardware and / or the processing circuitry can be controlled by software. The hardware can comprise analog circuitry or digital circuitry, or both analog circuitry and digital circuitry. The digital circuitry can comprise components such as application-specific integrated circuits (ASICs), field-programmable arrays (FPGAs), digital signal processors (DSPs), or multi-purpose processors. The receiver device 200 can also comprise memory circuitry storing one or more instructions that can be executed by the processor or by the processing circuitry, in particular under control of software. For example, the memory circuitry can comprise a non-transitory storage medium storing executable software code that, when executed by the processor or the processing circuitry, causes the receiver device 200 to perform various operations. In one implementation, the processing circuitry comprises one or more processors and a non-transitory memory connected to the one or more processors. The non-transitory memory can carry executable program code that, when executed by the one or more processors, causes the receiver device 200 to perform, conduct or initiate the operations or methods described herein.

[0075] Figure 3 A receiver device 200 according to the present disclosure is shown, which is built on Figure 2 (a) and Figure 2 (b) respectively. Identical elements are labeled with identical reference signs and can function similarly or identically.

[0076] Overall, Figure 3 A new MLM-based TDECQ acquisition procedure is proposed. Notably, Figure 3 The receiver device 200 shown can also be based on Figure 1 (a) shown, where the receiver device 200 is extended on the receiver in Figure 1 (a) by at least a 2-tap post-filter 204, an MLM algorithm 205 (simplified BCJR algorithm), a signal reconstruction block 206 and a TDECQ computation 207 based on the output of the signal reconstruction block 206.

[0077] It is worth noting that the receiver device 200 can be used for any PAM modulation format, but the present disclosure focuses on PAM4 specifically because PAM4 is likely to be the modulation format used in next generation high speed optical transceivers. The TDECQ 207 is used to quantify the quality of the PAM4 transmitter device 209, but it can also be referred to as a transmitter quality parameter including any transmission scenario and any modulation format. The value of the TDECQ 207 can indicate the transmitter quality. Thus, the transmitter quality can be quantified by the TDECQ 207 and it can be checked whether this value is below a maximum allowed value to be defined by a standard (e.g., TDECQmax).

[0078] The optical signal 213 (e.g., received as a channel 208 from an optical fiber) is received by a photodetector 210 (e.g., implemented by a photodiode) of the receiver device 200. The signal xi (corresponding to Figure 2 (a) and Figure 2 (b) shown) acquired after the photodetector 210 is an electrical signal xi that is captured (e.g., sampled and stored) by an instrument 300 such as a sampling oscilloscope.

[0079] The captured signal xi (e.g., several million samples) can be processed by a software program running in the receiver device 200. The signal xi (e.g., its stored samples) is low pass filtered (by the H-BT4 filter 202) in the receiver device 200 of Figure 3 to remove out-of-band noise because the oscilloscope can have a large bandwidth and sampling rate.

[0080] The signal x2 after the H-BT4 filter 202 is equalized by the FFE 203, which can have N taps. The signal x2 can be distorted, especially in a histogram based on the signal x2, where clear PAM levels cannot be seen. However, the signal x3 after the FFE 203 is clear, e.g., four PAM4 levels can be seen as Figure 4 indicated. It is worth noting that after the FFE 203, the FFE 203 can use a blind FFE algorithm to obtain better decisions.

[0081] The signal x3 after the FFE 203 is filtered by a 2-tap linear post filter 204. The post filter is defined by its transfer function 1 + aD, where D denotes a delay of a symbol period and a is the filter coefficient. The value of the filter coefficient a can be derived in an iterative manner. After the post filter 204 (which can also be referred to as a noise decorrelation filter), the signal x4 is processed by an MLM block (performing an MLM algorithm 205) to obtain an improved decision. This MLM block can generate log probabilities 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 + aD + bD2D, where D 2 denotes a 2-symbol period delay. 2 The post filter can include more taps. For example, a 3-tap post filter involving three FFE output samples is defined by 1 + aD + bD2D, where D

[0082] The signal x5 can include four log probability values, and these values are used to generate a PAM histogram representing the PAM levels of the PAM signal, e.g., the PAM4 levels 400 of the PAM signal 211 shown in Figure 4 That is, reconstructing the signal constellation of the PAM signal 211 at the signal reconstruction block 206 can include generating a PAM histogram representing the PAM levels of the PAM signal 211. The signal x6 includes the reconstructed signal constellation, e.g., which can be used to represent the samples of the PAM signal with PAM levels.

[0083] The receiver device 200 of the present disclosure can then use the output signal x6 of the signal reconstruction block 206 to compute the TDECQ 207. Since the signal x6 is similar to the signal x3, the computation of the TDECQ can be similar to the exemplary TDECQ computation shown in Figure 1 (a). The TDECQ algorithm used in Figure 1 (a) can be modified. Furthermore, noise 212 can be defined in front of the TDECQ computation block. The signal x7 is the signal x6 to which the noise 212 is added. The TDECQ 207 is then computed on the signal x7, i.e., based on the reconstructed signal constellation x6 to which the noise 212 is added. The TDECQ value can be output as a signal x8.

[0084] In the following, further exemplary implementation details of the receiver device 200 as shown in Figure 2 (a), Figure 2 (b), and Figure 3 are described.

[0085] FFE 203 can use N linear taps to recover the PAM4 levels of the received PAM4 signal 213 from the ISI channel 208. N can be an odd number, with N=7 being exemplarily used in the rest of this disclosure. For N=7, the starting FFE tap can be c=0001000, i.e., all taps can be set to 0, with the center tap (N-l) / 2+1 set to 1. Then, FFE 203 can follow the steps below:

[0086] 1. The signal x2 before FFE 203 is normalized to , dc=mean(x2), to enable fast FFE acquisition. FFE 203 converts the unipolar signal to a bipolar signal to avoid low frequency component suppression. The parameter g is chosen to enable fast acquisition and low FFE output noise.

[0087] 2. FFE 203 finds the taps c(i), i=0, 1,..., N-l, in blind mode. A gradient algorithm quantizes the output signal to levels l=-3, -1, 1, 3 and thresholds t=-2, 0, 2 to adjust the taps by using decisions in a decision-directed least-mean square (DD-LMS) mode. However, DD-LMS can be replaced by other blind methods.

[0088] 3. After the FFE taps are stabilized, the PAM4 output levels are found by histogram analysis. The new levels are l(i), i=0, 1, 2, 3, and the new thresholds are t(i), i=0, 1, 2.

[0089] 4. FFE 203 runs with the new levels. Steps 3 and 4 can be repeated a few times until the taps become stable.

[0090] 5. After the FFE taps are stabilized, the output signal x3 is adjusted by the following equation:

[0091] .

[0092] 6. The output signal histogram is analyzed to find the levels l and thresholds t. Note that, for example, OMA=l3.

[0093] The post-filter 204 converts the FFE output signal x3 to signal x4 by the following equation:

[0094] .

[0095] The parameter a is calculated by the following equation:

[0096] ,

[0097] where error = qsym - y, and qsym is the quantized symbol with threshold t and level l. The error is computed by using the FFE output, which can be unreliable, and the alpha (a) estimate can not be as accurate at high BER values. Since the FFE 302 acts as a high pass filter, the post filter 204 compresses the high frequency FFE noise caused by FFE noise enhancement.

[0098] The MLM algorithm 205 can provide a more reliable decision. The MLM algorithm 205 can be run multiple times to obtain a more accurate a value to be used in the final MLM run. The MLM outputs PAM4 symbol log probabilities. The best symbol can be selected to compute the error. The MLM output symbol x5 can include symMLM and error = l(symMLM) - x3.

[0099] In particular, the MLM algorithm computes the log probability of the 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: and Rodica Stoian, “The Decision Reliability of MAP, Log-MAP, Max-Log-MAP and SOVA Algorithms”, INTERNATIONAL JOURNAL OF COMMUNICATIONS, Issue 1, Volume 2, 2008, where the branch probability is bp(I,k) = (w(i) - m(k)) 2 (Euclidean distance). The signal x4 is:

[0100] ,

[0101] where sl is the transmitted symbol level (sl = l(n), n = 0, 1, 2, 3) and nx3 is the filtered noise.

[0102] When considering a single grid level and the 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 decide the s(i) or s(i+1) symbol, one can get a histogram with the maximum level at the position ll(i) = ± [l(i+1) - l(i)] 2 with threshold 0 and standard deviation of the noise .

[0103] In general, the MLM algorithm 205 uses long sequences to obtain the lp values, and the histogram will have values that are slightly different from the values obtained by single grid level prediction. For the three sets of symbols 01, 12, and 23 as shown in FIG. 3, the final histogram levels (values with the highest probability) will be ±L(i), I = 0, 1, 2. Figure 5 In general, the MLM algorithm 205 uses long sequences to obtain the lp values, and the histogram will have values that are slightly different from the values obtained by single grid level prediction. For the three sets of symbols 01, 12, and 23 as shown in FIG. 3, the final histogram levels (values with the highest probability) will be ±L(i), I = 0, 1, 2.

[0104] The preceding histogram (llp(i) = lp(i) - lp(i+1)) is obtained by choosing lp where the symbol s(i) or the symbol s(i+1) is the best symbol. To calculate the TDECQ 207, it is necessary to obtain the PAM4 histogram after the MLM block based on the lp values. The FFE output levels are l(i), I = 0, 1, 2, 3. First, it is necessary to obtain the normalization factors nf for the three sets of histograms described previously. The nf values can be calculated by nf(i) = [l(i+1) - l(i)] / 2 / L(i) so that the new levels are [l(i+1) - l(i)] / 2.

[0105] Now, for the first column values indicating the symbol at position i where the best symbol is, the three sets of positions can be selected using the ordering matrix b(i,j):

[0106] • Set 1 - all positions p0 where [b(i,0) = 0 and b(i,1) = 1] or [b(i,0) = 1 and b(i,1) = 0]

[0107] • Set 2 - all positions p1 where [b(i,0) = 1 and b(i,1) = 2] or [b(i,0) = 2 and b(i,1) = 1]

[0108] • Set 3 - all positions p2 where [b(i,0) = 2 and b(i,1) = 3] or [b(i,0) = 3 and b(i,1) = 2]

[0109] In the next step, the llr vector is constructed by:

[0110] •

[0111] •

[0112] •

[0113] The signal reconstruction block 296 generates a signal x6 that is similar to the FFE output signal x3. The levels and thresholds are the same as for the FFE output signal x3, but the amount of noise is slightly different. The FFE histogram and the MLM histogram can be in the same Figure 6The effect of the MLM on the BER is visible as the bins are represented to visualize the effect of these bins.

[0114] The normalization based on the single grid analysis needs to be normalized 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 is some offset in the MLM histogram because the MLM histogram is composed of three sets of llrs. This is not related to the TDECQ accuracy because the offset is located around the PAM4 levels. Moreover, the histogram can be normalized such that OMA=3 without changing the final result.

[0115] The post filter 204 shapes the FFE output noise by [1 a] coefficients. The histogram of the filtered noise is shown in Figure 7 . The noise after signal reconstruction (i.e. after the MLM) can be a little smaller than the filtered noise (i.e. before the MLM) as shown in Figure 7 . The MLM curve in Figure 7 . There are three SER values to be computed (three thresholds). Therefore, for each SER computation, a different noise is used, i.e. the white additive noise is corrected by Ceqand nwf(i).

[0116] It can be noticed that there is some deviation between the histograms at high histogram values (bars close to 0; small noise area). These deviations are not related to the TEDCQ computation because the “strong” bars have a negligible contribution to the SER.

[0117] The TDECQ computation part follows the computation described in the IEEE Ethernet standard IEEE Std. 802.3, 2018. The difference is that the CeqMLSE parameter is computed using the FFE Ceq(CeqFFE) and nwf. The resulting CeqMLSE is , i=0, 1, 2.

[0118] In one implementation, the resulting CeqMLSE is , i=0, 1, 2. The 2-taps post filter parameter CeqPF is equal to sqrt(1+ a 2 ) / (1+ a). As can be seen from Figure 8 , the noise enhancement after the MLM block is very small.

[0119] Three cumulative functions (CFs) are acquired by the method described in IEEE Ethernet standard IEEE Std. 802.3, 2018. The noise and CF histogram bins are multiplied, summed, and the noise with SER equal to the target SER is selected, as shown in Figure 9

[0120] Select SER_target and apply a sigma (σ) search to find the sigma value that gives SER = SER_target:

[0121] .

[0122] or in one implementation

[0123]

[0124] The MLM histogram consists of 2K bins of width Δx. The value σ t TDECQ is calculated by the following equation:

[0125]

[0126] where qfuncinv denotes the inverse Q function.

[0127] Four transmitter cases with narrow system bandwidth (a ~ 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 Figure 10 The MLM improves the performance (the histogram after MLM is better). The MLM signal reconstruction block provides a histogram that shows a bit of irregular behavior around the signal level. However, this is not relevant to the TDECQ accuracy because the offset is around the PAM4 levels (contribution to SER is small).

[0128] Figure 11 The first plot in Figure 11 The second plot in

[0129] Offline data Tx1 and Tx2 from two different transmitter devices 209 are processed, as in Figure 12 ​Both data have a pattern dependence behavior, but Tx2 performs better. The TDECQ values are shown (below the markers). TDECQ clearly distinguishes the two transmitter devices without knowing the SER. In the same figure Figure 12 In the same figure, the TDECQ values of the transmitter of case 4 (TDECQ at SER = 3e-4; the Pin values do not correspond to the EbN0 values; this is just for visualization) are added. This transmitter device is not affected by the pattern dependence and has a better (lower) TDECQ value at a higher SER (3e-4) compared to Tx2 even at SER = 2e-4. This means that Tx2 will suffer more loss in the presence of noise than the transmitter of case 4.

[0130] It is worth noting that the receiver device 200 and the 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.

[0131] Figure 13 A method 1300 of reception of a PAM signal according to the present disclosure is shown. The method 1300 can be performed by the receiver device 200 and can be used to receive a PAM4 signal.

[0132] The method 1300 comprises a step 1301 of acquiring a signal 201, x1; wherein the signal 201, x1 is based on a PAM signal 211 transmitted by a transmitter device 209 over a channel 208. The method 1300 further comprises a step 1302 of filtering the acquired signal 201, x1; the method 1300 further comprises a step 1303 of equalizing the filtered signal x2 using a feed forward equalization (FFE 203) with multiple taps. The method 1300 further comprises a step 1304 of filtering the equalized signal x3 using a 2-tap filtering (2-tap filter 204), wherein high frequency noise caused by the feed forward equalization is compressed. Then, the method 1300 comprises a step 1305 of applying an MLM algorithm 205 to the 2-tap filtered signal x4; then the method 1300 comprises a step 1306 of 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 computing 1307 a TDECQ 207 based on the reconstructed signal constellation x6 of the PAM signal 211.

[0133] The present disclosure has been described in connection with various embodiments as examples and in connection with implementations. However, other variations can be understood and implemented by those skilled in the art upon study of the drawings, the present disclosure and the independent claims. In the claims, as well as in the specification above, all transitional phrases such as "comprising," "including," "carrying," "having," "containing," "holding," "composed of," and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases "consisting of and "consisting essentially of shall be closed or semi-closed transitional phrases, respectively, meaning that the claims contain only those elements listed in the claim or those elements plus sub-elements of the essential elements listed in the claim. No transitional phrase is to be construed to be limiting in any way.

Claims

1. A receiver device (200) for a pulse amplitude modulated, PAM, signal, the receiver device (200) being configured to: acquiring a signal (xl), wherein the signal (xl) being based on a PAM signal (211) transmitted by a transmitter device (209) to the receiver device (200) over a channel (208); filtering the acquired signal (xl); 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 multi-tap post filter (204); based on the filtered signal, reconstructing a signal constellation (x6) of the PAM signal (211); and based on the reconstructed signal constellation (x6) of the PAM signal (211), calculating a transmitted chromatic dispersion eye closure quadrature, TDECQ, (207).

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

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

4. The receiver device (200) of claim 1, wherein, the FFE (203) being configured to recover PAM levels (400) comprised in the PAM signal (211) by equalizing the filtered signal (x2).

5. The receiver device (200) of claim 1, wherein, the FFE (203) being configured to perform a blind FFE algorithm to equalize the filtered signal.

6. The receiver device (200) of claim 1, wherein, filtering the equalized signal (x3) comprises linearly filtering the equalized signal (x3) based on a filter coefficient a using the multi-tap post filter (204), wherein the filter coefficient a is determined in an iterative manner.

7. The receiver device (200) according to any one of claims 1 to 6, the receiver device being particularly configured to: apply a maximum log-mapping, MLM, algorithm (205) to the filtered signal; based on a result (x5) of applying the MLM algorithm (205), reconstruct a signal constellation (x6) of the PAM signal (211).

8. The receiver device (200) according to claim 7, wherein the result (x5) of applying the MLM algorithm (205) to the filtered signal (x4) comprises a log-probability of each PAM level (400) of the PAM signal (211).

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

10. The receiver device (200) of claim 8, wherein, the reconstruction of the signal constellation (x6) of the PAM signal (211) comprises generating a PAM histogram representing PAM levels (400) of the PAM signal (211).

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

12. The receiver device (200) according to any one of claims 1 to 6, configured to compute the TDECQ (207) further based on a noise (x7, 212) added to a reconstructed signal constellation (x6) of the PAM signal (211).

13. The receiver device (200) according to claim 6, wherein, The number of taps of the multi-tap post filter is 2, the TDECQ (207) is calculated to include a 2-tap post filter parameter CeqPF, which is equal to sqrt(1+α 2 ) / (1+α).

14. The receiver device (200) according to any of claims 1 to 6, wherein, The TDECQ (207) is indicative of a quality of transmission of the PAM signal (211) by the transmitter device (209).

15. The receiver device (200) according to any one of claims 1 to 6, comprising a sampling oscilloscope (300) configured to perform equalizing the filtered signal (x2), filtering the equalized signal (x3), applying the maximum log-mapping algorithm (205), reconstructing the signal constellation (x6), and computing the TDECQ (207).

16. The receiver device (200) according to any of claims 1 to 6, wherein The number of taps of the multi-tap post-filter is 2 or 3.

17. A reception method (1300) for a pulse amplitude modulation, PAM, signal, the reception method (1300) comprising: obtaining (1301) a signal (xl), wherein the signal (xl) is based on a PAM signal (211) transmitted by a transmitter device (209) over a channel (208); filtering (1302) the obtained signal (xl); equalizing (1303) the filtered signal (x2) using a feed-forward equalizer, FFE, (203) having a plurality of taps; filtering (1304) the equalized signal (x3) using a multi-tap post-filter (204); reconstructing (1306) a signal constellation (x6) of the PAM signal (211) based on the filtered signal; and computing (1307) a TDECQ (207) based on the reconstructed signal constellation (x6) of the PAM signal (211).

18. The receiving method (1300) of claim 17, wherein, The reconstructing the signal constellation of the PAM signal based on the filtered signal specifically comprises: applying a maximum log-mapping, MLM, algorithm (205) to the filtered signal; reconstructing the signal constellation of the PAM signal based on a result (x5) of applying the MLM algorithm (205).

19. The receiving method (1300) of claim 17 or 18, wherein, The number of taps of the multi-tap post-filter is 2 or 3.

20. A computer program product comprising instructions which, when executed by a computer, cause the computer to carry out the method (1300) according to any one of claims 17-19.

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