WO2022113200A1

WO2022113200A1 - Waveform equalizer, waveform equalization method, and waveform equalization program

Info

Publication number: WO2022113200A1
Application number: PCT/JP2020/043803
Authority: WO
Inventors: Nikolaos-Panteleimon DIAMANTOPOULOS; Shinji Matsuo
Original assignee: Nippon Telegraph And Telephone Corporation
Priority date: 2020-11-25
Filing date: 2020-11-25
Publication date: 2022-06-02
Also published as: JP7556459B2; JP2023543270A

Abstract

A waveform equalizer (10) of this invention includes a delay tap (11) configured to perform delay processing for an input signal, a first-order sub-filter (12) configured to perform linear processing for the signal output from the delay tap (11), a second-order sub-filter (13) configured to perform first nonlinear processing based on a second-order Volterra series for the signal output from the delay tap (11), a third-order sub-filter (14) configured to perform second nonlinear processing based on a third-order term of a nonlinear polynomial for the signal output from the delay tap (11), and an adding unit (15) configured to add the signal output from the first-order sub-filter (12), the signal output from the second-order sub-filter (13), and the signal output from the third-order sub-filter (14). Hence, the waveform equalizer of this invention can provide simplified nonlinear equalization processing for improving signal quality.

Description

WAVEFORM EQUALIZER, WAVEFORM EQUALIZATION METHOD, AND WAVEFORM EQUALIZATION PROGRAM

The present invention relates to a waveform equalization device, a waveform equalization method, and a waveform equalization program configured to eliminate a waveform distortion of an optical signal caused by nonlinearity of an optical fiber or the like.

Internet traffic is expected to grow in data centers and access networks, and 400-Gb Ethernet using a wavelength multiplexing technique and direct detection (DD) is being put into practical use. Conventionally, to increase the capacity of a core network, phase modulation and coherent reception have been used as the means of multi-valuing. On the other hand, in short-range communication, an intensity modulation/direct detection (IM/DD) technique has received attention from the viewpoint of cost reduction and power consumption reduction. The IM/DD technique uses PAM-M (Multi-level Pulse-Amplitude Modulation) which has a high energy efficiency and whose cost and complexity are low.

In the IM/DD system using PAM, particularly, in a 100-GBaud modulation by the limited bandwidth of an electric/photoelectronic device, a linear effect and a nonlinear effect degrade signal quality and lower the bit-error rate (BER) characteristic of an optical link. To compensate for these distortions, a digital nonlinear equalizer (NLE) is used for digital signal processing (DSP) of a receiver.

Japanese Patent Laid-Open No. 2020-88495

J. Tsimbinos and K. V. Lever, "Computational complexity of Volterra based nonlinear compensators", Electronics Letters, vol. 32, no. 9, pp. 852-854, 1996.

A PAM-M scheme is a modulation format, and a waveform amplitude is modulated by M different amplitude levels. In each modulation pulse, a waveform generated as a result carries log₂(M) bits. Here, the width of the modulation pulse is T = 1/R. In addition, R is a symbol or a Baud rate, and its unit is GHz or GBaud.

In the IM/DD transmission system, a nonlinear distortion occurs in a PAM waveform due to the following reasons.
-Nonlinearity associated with modulation and demodulation
-Signal-signal beat interference (SSBI) caused by direct detection
-Optical fiber nonlinearity
-Influence of fiber dispersion

Details of these nonlinear distortions will be described below.

Nonlinearity associated with modulation and demodulation will be described first. Nonlinearity associated with modulation and demodulation is generated by an RF electric device or a photoelectronic device, for example, a signal generator, an electric amplifier, a driver, an optical modulator, a direct modulation laser, a filter, a light receiver, or the like. In particular, the nonlinearity is enhanced in a case of a signal or waveform having a high peak-to-average power ratio (PAPR), like a majority carrier format or a high-level PAM signal.

Most general distortions in such a signal or waveform are the relationship of modulation between nonlinear input and output and a delay depending on the intensity/power.

The former is static nonlinearity and normally exists in an optical modulator and an RF device. On the other hand, the latter is dynamic nonlinearity and exists in a direct modulation laser. Especially, in PAM signals, the former generates different eye patterns in correspondence with different amplitude levels. On the other hand, the latter generates a skew depending on an amplitude in an entire PAM waveform. Figs. 10A and 10B show examples of eye patterns in a case in which a nonlinear distortion does not exist and in a case in which a nonlinear distortion exists, respectively.

A signal-signal beat interference (SSBI) caused by direct detection will be described next. The SSBI is a quadratic term generated by square detection of a normal photodiode. The SSBI is another nonlinear distortion derived from the receiver structure of a direct detection system. The SSBI has received a great deal of attention, and several mitigation techniques and linearization techniques have been proposed mainly based on an approach of single-sideband (SSB) modulation.

Optical fiber nonlinearity will be described next. The optical fiber nonlinearity is mostly caused by the nonlinear effect of a silica fiber and depends on a launch power and a transmission distance. Most of IM/DD systems that have attracted interests in the 400-Gb/s Ethernet and application techniques thereof are used in a range of several ten km, normally a range up to 100 km. Here, the contribution of whole nonlinear distortions can be neglected in single channel transmission. However, in a WDM signal, the combined effect of four-wave mixing and cross/self-phase modulation could cause a serious distortion.

The influence of fiber dispersion will be described at last. Especially in a C-band communication window, chromatic dispersion of a single mode optical fiber generates a memory effect in a nonlinear distortion related to modulation by conspicuously acting with the nonlinear chirp of an optical modulation pulse, although it is originally a linear process. Also, when coupling with square detection, chromatic dispersion causes zero in a modulation spectrum and generates a storing power fading effect.

To compensate for the above-described nonlinear distortions, a Volterra series is used as nonlinear equalization processing by digital signal processing (DSP) (non-patent literature 1).

In conventional equalization processing using a Kth-order Volterra series, letting x be an input signal to a waveform equalization device, and L_k be the memory length in the kth order, an mth output y(m) is given by

In equation (1), w_k(n₁, n₂,..., n_k) is the weight of the kth-order tap for equalization processing. In addition, the memory length L_k is the kth-order memory length, and is the storage length of the input signal data x necessary for performing waveform equalization correction.

The equalization technique (VNLE) (Volterra-based Nonlinear Equalization) using the Volterra series is effective in many cases. However, since the arithmetic processing amount increases, there is a problem in real-time processing.

Patent literature 1 discloses a technique capable of simplifying, using the Volterra series, equalization processing for a signal in which nonlinearity exists.

However, in the simplified equalization processing technique using the Volterra series, the BER characteristic needs to be further improved.

In order to solve the above-described problem, according to the present invention, there is provided a waveform equalizer comprising a delay tap configured to perform delay processing for an input signal, a first-order sub-filter configured to perform linear processing for the signal output from the delay tap, a second-order sub-filter configured to perform first nonlinear processing based on a second-order Volterra series for the signal output from the delay tap, a third-order sub-filter configured to perform second nonlinear processing based on a third-order term of a nonlinear polynomial for the signal output from the delay tap, and an adding unit configured to add the signal output from the first-order sub-filter, the signal output from the second-order sub-filter, and the signal output from the third-order sub-filter.

According to the present invention, there is also provided a waveform equalization method comprising a step of performing delay processing for an input signal, a step of performing linear processing for the signal that has undergone the delay processing, a step of performing first nonlinear processing based on a second-order Volterra series for the signal that has undergone the linear processing, a step of performing second nonlinear processing based on a third-order term of a nonlinear polynomial for the signal that has undergone the first nonlinear processing, and a step of adding the signal that has undergone the linear processing, the signal that has undergone the first nonlinear processing, and the signal that has undergone the second nonlinear processing.

According to the present invention, there is also provided a waveform equalization program configured to cause a waveform equalizer including a delay tap, a first-order sub-filter, a second-order sub-filter, a third-order sub-filter, and an adding unit and configured to perform equalization processing for an input signal to function, characterized by causing the waveform equalizer to execute processing comprising a step of causing the delay tap to perform delay processing for the input signal, a step of causing the first-order sub-filter to perform linear processing for the signal that has undergone the delay processing, a step of causing the second-order sub-filter to perform first nonlinear processing based on a second-order Volterra series for the signal that has undergone the linear processing, a step of causing the third-order sub-filter to perform second nonlinear processing based on a third-order term of a nonlinear polynomial for the signal that has undergone the first nonlinear processing, and a step of causing the adding unit to add the signal that has undergone the linear processing, the signal that has undergone the first nonlinear processing, and the signal that has undergone the second nonlinear processing.

According to the present invention, it is possible to provide a waveform equalizer, a waveform equalization method, and a waveform equalization program, which can improve signal quality using simplified linear processing and nonlinear processing.

Fig. 1 is a schematic view showing the arrangement of a waveform equalizer according to the first embodiment of the present invention; Fig. 2 is a block diagram showing the arrangement of the waveform equalizer according to the first embodiment of the present invention; Fig. 3 is a view for explaining the effect of the waveform equalizer according to the first embodiment of the present invention; Fig. 4 is a schematic view showing the arrangement of an optical communication system according to the second embodiment of the present invention; Fig. 5 is a view showing the experimental system of an optical communication system according to the first embodiment of the present invention; Fig. 6 is a view showing the BER characteristic of the experimental system of the optical communication system according to the first embodiment of the present invention; Fig. 7 is a view showing the BER characteristic of the experimental system of the optical communication system according to the first embodiment of the present invention; Fig. 8 is a view showing the arrangement of a receiver in the optical communication system according to the second embodiment of the present invention; Fig. 9 is a view showing an example of the arrangement of a computer according to the embodiment of the present invention; Fig. 10A is a view for explaining a signal characteristic in a conventional technique; and Fig. 10B is a view for explaining a signal characteristic in a conventional technique.

(First Embodiment)
A waveform equalizer according to the first embodiment of the present invention will be described with reference to Figs. 1 to 3.

(Arrangement of Waveform Equalizer)
Fig. 1 is a schematic view showing the arrangement of a waveform equalizer 10. An input signal is input to a waveform processing unit 11, and the waveform processing unit 11 performs linear processing (LE: W1) and nonlinear processing (NLE: W2, and NLE: W3), and outputs an output signal.

A training unit 12 can repetitively update the coefficients of all filters of NLE used in the waveform equalizer 10 based on a known adaptive algorithm such as a least-squares method. The training unit 12 is not always necessary to execute waveform equalization processing according to this embodiment. For example, it is not necessary when the coefficients are already determined and when the waveform equalizer is stable.

Fig. 2 shows the detailed arrangement of the waveform processing unit 11 in the waveform equalizer 10. The waveform processing unit 11 includes a delay tap 111, a first-order linear sub-filter 112, a second-order nonlinear sub-filter 113, a third-order nonlinear sub-filter 114, and an adding unit 115.

First, an input signal x is input to the delay tap 111. The delay tap 111 has an array structure including a plurality of delay taps 111. A signal output from each delay tap 111 is input to each sub-filter (to be described later).

The array of the delay taps 111 perform delay processing for the input signal x, and the signal that has undergone the delay processing is input to the three

different sub-filters

112, 113, and 114. A delayed input signal x_m corresponding to an mth equalized output signal y_m is given, using a vector, by

Here, T represents a linear transposition. 2N_max = 2max(N₁, N₂, N₃), and this represents the maximum number of taps. 2N_i, for which i = {1, 2, 3}, defines the number of taps corresponding to each of the three

sub-filters

112, 113, and 114. A length L_max of x_m is given by L_max = 2N_max + 1 = max(L₁, L₂, L₃), and Li = 2N_i + 1.

In addition, L_max is the maximum memory length, and L₁, L₂, and L₃ are the memory lengths of the first-order term, the second-order term, and the third-order term, respectively.

Next, the delayed input signal x_m is input to the first-order linear sub-filter 112, the second-order nonlinear sub-filter 113, and the third-order nonlinear sub-filter 114. Next, signals output from the sub-filters are added by the adding unit 115, thereby obtaining the output signal y(m) that has undergone the equalization processing.

The mth equalized output signal y(m) of the NLE according to this embodiment is given by

Here, y_i, for which i = {1, 2, 3}, defines the output of each of the three

sub-filters

112, 113, and 114.

y₁(m) is the first-order linear term.

y₂(m) is the second-order term that is a P-VNLE (Pruned VNLE) term with a memory effect. The P-VNLE term is a second-order Volterra series with reduced computational complexity (J. Tsimbinos and K.V. Lever, "Computational complexity of Volterra based nonlinear compensators", Electronics Letters, vol. 32, no. 9, pp. 852-854, 1996.). In addition, y₂(m) is formed by a self-beating term (p = 0) and four cross-beating terms (p = 1, 2, 3, 4).

y₃(m) is the third-order term (to be referred to as "the third-order term of a polynomial" hereinafter) in a nonlinear polynomial and has a memory effect. In addition, y₃(m) is formed only by a self-beating term (p = 0) and does not include a cross-beating term. Here, the nonlinear polynomial represents the nonlinear output signal y by the polynomial of the input signal x. The output signal y is represented by the sum of the input signals x multiplied by nonlinear coefficients.

The first-order linear term y₁(m), the P-VNLE term y₂(m) of the second-order term, and the third-order term y₃(m) of the polynomial are represented by

The sub-filter 113 of the second-order term is formed by a self-beating term (p = 0) and four cross-beating terms (p = 1, 2, 3, 4).

The sub-filter 114 of the third-order term is formed only by a self-beating term (p = 0) and does not include a cross-beating term.

Using the vector expression of equation (2) and equations (4) to (6), equation (3) can be rewritten as

Here, the first term in the sum of the right side of equation (7) represents processing by the linear sub-filter 112, the second term represents processing by the P-VNLE sub-filter 113, and the third term represents processing by the third-order sub-filter 114. To implement this scheme in an electronic circuit, only nonzero coefficients are taken into consideration.

Computational complexity is a parameter that is important in NLE and defines important parameters such as cost, power consumption, and size. From the viewpoint of the number of multiplications, the computational complexity of the entire NLE is represented by equations (11) to (14) (non-patent literature 1).

Where h₂ is the total number of cross-beating terms considering the P-VNLE sub-filter 113.

Fig. 3 shows computational complexity in a case in which the filters in the waveform equalizer 10 according to this embodiment are used in comparison with cases in which a simple linear filter, a filter by a nonlinear polynomial, and a filter by a full Volterra series are used. Here, L = L₁ = L₂ = L₃ < 100. Here, the full Volterra series is represented by equation (1).

In Fig. 3, "LinEQ" shows a case in which a simple linear filter is used, "PolyEQ-x" shows a case in which a filter by an xth-order nonlinear polynomial is used, "fullVNLE-x" shows a case in which a filter by an xth-order full Volterra series is used, and "prunedVNLE-2" shows a case in which a filter by P-VNLE is used.

The computational complexity of NLE according to this embodiment is higher by five to six times than in cases in which nonlinear polynomials up to a third-order term are used, and is slightly higher than that of P-VNLE. On the other hand, the computational complexity of NLE according to this embodiment exhibits a value smaller by one or two orders of magnitude as compared to a case in which a second-order full Volterra series is used and a case in which a third-order full Volterra series is used. These results show that the computational complexity of NLE according to this embodiment falls within an implementable range.

In this embodiment, an example in which the second-order term y₂(m) is formed by a self-beating term (p = 0) and four cross-beating terms (p = 1, 2, 3, 4) has been described. However, the number of cross-beating terms is not limited to this. However, if five or more cross-beating terms are used, the computational complexity increases, but no great effect of reducing BER can be obtained.

In this embodiment, an example in which the third-order term y₃(m) does not include a cross-beating term has been described. This is because if the third-order term y₃(m) includes a cross-beating term, the computational complexity remarkably increases.

According to the waveform equalizer 10 of this embodiment, it is possible to suppress computational complexity of nonlinear processing for compensating for a nonlinear distortion of a PAM signal and simplify the processing.

(Second Embodiment)
The second embodiment of the present invention will be described with reference to Fig. 4.

(Arrangement of Optical Communication System)
Fig. 4 shows the arrangement of a receiver and an optical communication system according to this embodiment. In the optical communication system 20, an optical transmitter 21 generates an optical signal and transmits it to an optical transmission path 22. In the present invention, an intensity-modulated PAM (IM-PAM) signal and an optical signal corresponding to an optical channel are transmitted through a standard single mode fiber (SSMF) within a range up to 10 km. The distance of 10 km is a normal distance in a short-range interconnect and a data center network. At the end of transmission, the signal is detected by an optical receiver 23. Here, detection based on direct detection is considered.

In the receiver 23, a waveform equalizer 10 according to the first embodiment is used. An input optical signal is converted into an electric waveform by a direct detection unit 231. Next, the signal is sampled by an analog/digital conversion unit 232 and input to a time recovery unit 233. Next, the output signal from the time recovery unit 233 is input to the waveform equalizer 10. In the equalization process by the waveform equalizer 10, the signal is down-sampled to one sample/symbol, and data is recovered by a data recovery unit 234. The data recovery unit 234 also performs demodulation of the symbol of the PAM signal.

According to the receiver and the optical communication system of this embodiment, as will be shown in the first example to be described later, it is possible to suppress computational complexity of nonlinear processing for compensating for a nonlinear distortion of a PAM signal and simplify the processing, and also improve the BER characteristic and improve signal quality.

(First Example)
The first example of the present invention will be described with reference to Figs. 5 to 7. This example is an example of validating the effects of the waveform equalizer, the receiver, and the optical communication system according to the present invention. Fig. 5 shows an experimental system 30 used in this example.

On the transmitting side, four pulse pattern generators 301 generate four independent data streams. These data streams are formed by an NRZ (Non-Return to Zero) of 1/Ts = 64 GBaud.

Next, a PAM4-MUX (multiplexer) 302 is used to generate a 256-Gbit/s (128-GBaud) PAM symbol. An inset (a) in Fig. 5 shows the eye pattern of the PAM4 signal. Using a linear RF amplifier 303 having a gain of 22 dB and a bandwidth of 60 GHz, a bias-tee 304, and an RF probe 305, a direct modulation laser (DML) 306 is driven by a 27.2-mA DC bias current and a 1.6 Vp-p modulation voltage.

The DML 306 is a membrane laser of III-V compound semiconductor on an SiC substrate, and operates at a stage control temperature of 25 degrees Celsius with a 3-dB bandwidth up to 108 GHz and a fiber coupling output at 27 mA (N. Kaneda, et al., "Nonlinear Equalizer for 112-Gb/s SSB-PAM4 in 80-km Dispersion Uncompensated Link", Optical Society of America, Optical Fiber Communications Conference and Exhibition, pp. 19-23, 2017.) The fiber coupling output under the operation conditions is -2 dBm, and the oscillation wavelength is about 1,286 nm. The signal is coupled with a 2-km standard single mode fiber (SSMF) 307 using a lens fiber. The loss coefficient in the O band of the SSMF is 0.34 to 0.4 dB/km, and the chromatic dispersion coefficient is -2.4 ps/km/nm at a wavelength of about 1,286 nm.

To detect light, a uni-travelling-carrier (UTC) photodiode (PD) module 310 having a bandwidth larger than 67 GHz in the O band is used. Received optical power (ROP) in the preceding stage of the UTC-PD module 310 is controlled by a praseodymium-doped fiber amplifier (PDFA) 308 and a variable optical attenuator (VOA) 309. The ROP is measured by a power meter (PM) 311 via a 20-dB coupler. The signal received by the UTC-PD module 310 is stored at 256 GSa/s by offline processing using a 110-GHz digital sampling oscilloscope (DSO) 312.

In DSP 313 of the receiver, first, re-sampling (314) and time recovery (315) are executed. Next, NLE (316) by the waveform equalizer 10 according to the embodiment of the present invention is executed at 2 SpS (Samples per Symbol) using 101 input taps for linear terms and 61 input taps for nonlinear terms including second- and third-order terms. The number of taps increases along with the Baud rate. Computational complexity according to this example is calculated by equations (11) to (14), and 874 is obtained as an actual multiplication count. Insets (b) and (c) in Fig. 5 show the eye patterns of the PAM4 signal before and after the NLE (316).

In the NLE, a signal is down-sampled at 1 SpS. Also, the NLE is trained and adapted by a decision-directed LMS algorithm. Finally, a bit error is measured, and the BER is evaluated (317).

Figs. 6 and 7 show BER results by equalization processing using different methods in optical BTB (Back-To-Back) transmission and 2-km transmission, respectively.

In the BTB transmission and the 2-km transmission, in all ROPs, the BER characteristic is improved as compared to a case of linear equalization (LinEQ) regardless of used nonlinear equalization processing (NLE). When equalization processing (PolyEQ-2 or PolyEQ-3) by second- or third-order nonlinear polynomial is used, the BER exhibits a value equal to or more than a threshold of Hard Decision-Forward Error Correction (HD-FEC) to which an 7% overhead is added.

On the other hand, the HD-FEC threshold is achieved in both the BTB transmission and the 2-km transmission by processing including four second-order Volterra cross-beating terms (prunVNLE-2 and nonlinear equalization processing according to the embodiment).

The NLE according to this example includes a third-order term of a polynomial and improves a power margin by about 0.76 in the BTB transmission and by about 0.35 dB in the 2-km transmission, as compared to NLE that does not include a third-order term of a polynomial. It is considered that in all cases, the 2-km transmission exhibits a slightly better BER value as compared to the BTB transmission by negative dispersion of a fiber.

As described in this example, according to the receiver and the optical communication system of the second embodiment, it is possible to suppress computational complexity of nonlinear processing for compensating for a nonlinear distortion of a PAM signal and simplify the processing, and also improve the BER characteristic and improve signal quality.

In other words, when the waveform equalizer according to the present invention is applied to the receiver and the optical communication system, it is possible to suppress computational complexity of nonlinear processing and simplify the processing, and also improve the BER characteristic and improve signal quality.

(Second Example)
A receiver in an optical communication system according to the second example of the present invention is almost the same as the receiver in the optical communication system according to the second embodiment.

A receiver 43 in the optical communication system according to this example uses a waveform equalizer 10 according to the first embodiment, and includes a direct detection unit 431, an analog/digital conversion unit 432, the waveform equalizer 10, and a data recovery unit 433, as shown in Fig. 8. In the receiver 43, the data recovery unit 433 includes an accurate time recovery algorithm that is executed after NLE according to the second embodiment.

Fig. 9 shows an example of the arrangement of a computer in the waveform equalizer according to the embodiment of the present invention. The waveform equalizer 10 can be implemented by a computer 50 including a CPU (Central Processing Unit) 53, a storage device (storage unit) 52, and an interface device 51, and a program configured to control these hardware resources. The CPU 53 executes processing according to the embodiment of the present invention in accordance with a waveform equalization program stored in the storage device (storage unit) 52. The waveform equalization program thus causes the waveform equalizer to function.

In the storage device (storage unit) according to the embodiment of the present invention, the computer may be provided in the device, or at least some of the functions of the computer may be implemented using an external computer. Additionally, as the storage unit, a storage medium 54 outside the device may be used or a signal generation program stored in the storage medium 54 may be read out and executed. The storage medium 54 includes various kinds of magnetic recording media, opto-magnetic recording media, CD-ROM, CD-R, and various kinds of memories. The signal generation program may be supplied to the computer via a communication network such as the Internet.

In the embodiment of the present invention, an example of the structures, dimensions, materials, and the like of the constituent parts is shown concerning the arrangement, manufacturing method, and the like of the waveform equalizer. However, the present invention is not limited to this. Any parts capable of exhibiting the functions of the waveform equalizer and obtaining the effect can be used.

The present invention can be applied to an optical communication system and a device such as a receiver or a waveform equalizer in the optical communication system.

10...waveform equalizer, 111...delay tap, 112...first-order sub-filter, 113...second-order sub-filter, 114...third-order sub-filter, 115...adding unit

Claims

A waveform equalizer comprising:
a delay tap configured to perform delay processing for an input signal;
a first-order sub-filter configured to perform linear processing for the signal output from the delay tap;
a second-order sub-filter configured to perform first nonlinear processing based on a second-order Volterra series for the signal output from the delay tap;
a third-order sub-filter configured to perform second nonlinear processing based on a third-order term of a nonlinear polynomial for the signal output from the delay tap; and
an adding unit configured to add the signal output from the first-order sub-filter, the signal output from the second-order sub-filter, and the signal output from the third-order sub-filter.
The waveform equalizer according to claim 1, characterized in that
the linear processing is performed using equation (1),
the first nonlinear processing is performed using equation (2), and
the second nonlinear processing is performed using equation (3):

wherein x is the input signal, y₁, y₂ and y₃ are the output signals, p is the number of cross-beating terms, N₁, N₂ and N₃ are the numbers of the delay taps, and w₁, w₂ and w₃ are weight coefficients.
The waveform equalizer according to claim 1 or 2,
characterized by comprising a training unit configured to update coefficients of all the sub-filters.
A receiver sequentially comprising:
a direct detection unit;
an analog/digital conversion unit;
a time recovery unit;
a waveform equalizer described in any one of claims 1 to 3; and
a data recovery unit.
The receiver according to claim 4,
characterized in that the data recovery unit executes an accurate time recovery algorithm.
An optical communication system comprising:
an optical transmitter;
an optical transmission path; and
a receiver described in claim 4 or 5.
A waveform equalization method comprising:
a step of performing delay processing for an input signal;
a step of performing linear processing for the signal that has undergone the delay processing;
a step of performing first nonlinear processing based on a second-order Volterra series for the signal that has undergone the linear processing;
a step of performing second nonlinear processing based on a third-order term of a nonlinear polynomial for the signal that has undergone the first nonlinear processing; and
a step of adding the signal that has undergone the linear processing, the signal that has undergone the first nonlinear processing, and the signal that has undergone the second nonlinear processing.
A waveform equalization program configured to cause a waveform equalizer including a delay tap, a first-order sub-filter, a second-order sub-filter, a third-order sub-filter, and an adding unit and configured to perform equalization processing for an input signal to function, characterized by causing the waveform equalizer to execute processing comprising:
a step of causing the delay tap to perform delay processing for the input signal;
a step of causing the first-order sub-filter to perform linear processing for the signal that has undergone the delay processing;
a step of causing the second-order sub-filter to perform first nonlinear processing based on a second-order Volterra series for the signal that has undergone the linear processing;
a step of causing the third-order sub-filter to perform second nonlinear processing based on a third-order term of a nonlinear polynomial for the signal that has undergone the first nonlinear processing; and
a step of causing the adding unit to add the signal that has undergone the linear processing, the signal that has undergone the first nonlinear processing, and the signal that has undergone the second nonlinear processing.