阅读说明：本技术 针对在50 gbps和更大值的pamn光收发器中使用的模拟电子光纤色散和带宽预补偿（edpc）的装置和方法 (Apparatus and method for analog electronic fiber dispersion and bandwidth precompensation (EDPC) for use in 50GBPS and larger PAMN optical transceivers ) 是由 温斯顿·I·卫 雷格哈芬卓拉·V·朱路里 康斯坦丁·珍纳迪耶维雀·库斯明 于 2019-08-02 设计创作，主要内容包括：本发明提出了具有成本效益的高数据速率光学数据收发器,其包括电子模拟横向滤波器,同时为传输的光信号提供带宽补偿和前向减损补偿中的一个或多个。这些设备可以包括模拟横向滤波器电路,被配置为调节来自PAM处理器的模拟调制器信号。该调节可以涉及近似希尔伯特变换、色散预补偿或其两者。(The present invention proposes a cost-effective high data rate optical data transceiver that includes an electronic analog transversal filter while providing one or more of bandwidth compensation and forward impairment compensation for the transmitted optical signal. The apparatus may include an analog transversal filter circuit configured to condition the analog modulator signal from the PAM processor. The adjustment may involve an approximate hilbert transform, dispersion pre-compensation, or both.)

1. An optical transceiver module for n-level pulse amplitude modulated (PAMn) optical symbologies, where n ≧ 2, the optical transceiver module providing an interface between electronic data signals on a host and optical symbologies transmitted at a baud rate through an optical communication device, the optical transceiver module comprising:

a receiver section including at least one photoelectric receiver to convert a received optical signal into an analog electrical signal;

a PAMn digital signal processing DSP circuit which at least provides a logic interface with electronic host data, a Forward Error Correction (FEC) function, performs analog-to-digital conversion on an electric signal from an optical receiver, performs digital adaptive filtering on a converted received signal, and reconstructs the filtered received signal into data;

a transmitter section comprising at least one laser and at least one interference modulator; and

an analog transversal filter circuit configured as an electronic dispersion pre-compensator EDPC for filtering the PAMn transmit signal provided by the PAMn DSP,

wherein the filtered signal transmitted from the EDPC is connected to a signal input of an interference modulator.

2. The optical transceiver module of claim 1, wherein the EDPC filter circuit comprises: a finite impulse response filter comprising at least three taps, an amplifier/attenuator for adjusting the tap weights, and an electrical combiner for combining the signals from the taps.

3. The optical transceiver module of claim 2, wherein the at least three taps are 5 taps, 7 taps, or 9 taps.

4. An optical transceiver module as claimed in claim 2 or 3, wherein the amplifier/attenuator is field programmable.

5. The optical transceiver module of any of claims 2-4, wherein the EDPC further comprises an integrated driver for the output from the electrical synthesizer, wherein a driver output power rating is sufficient to directly drive the jammer modulator.

6. The optical transceiver module of any of claims 1-5, wherein the EDPC performs an approximate Hilbert transform on the analog signal.

7. The optical transceiver module of any of claims 1-6, wherein the EDPC implements distortion pre-correction based on predicted distortion corresponding to a multiple of half of a maximum correction length provided by the receiver.

8. The optical transceiver module of claim 7, wherein the distortion pre-correction is selected from a set of pre-stored tap weights, wherein members of the set represent different multiples of half of a maximum correction length.

9. An optical transceiver module as claimed in claim 7 or claim 8, wherein the EDPC further implements an approximate hilbert transform.

10. The optical transceiver module of any of claims 1-9, wherein the PAMn DSP is a PAM4 chip designed for the MSA standard of table 1.

11. The optical transceiver module of any of claims 1-10 wherein the PAM optical signal carries a data stream of m x50 Gbps/wavelength x channel, m ≧ 1, and the module is functionally housed in a standard QSFP28, DD-QSFP, OSFP, CFP2, or CFP8 pluggable package.

12. An optical transceiver module as claimed in any one of claims 1 to 11, wherein the interference modulator is a DDMZM, and wherein two modulator signals are provided from the EDPC to two DDMZM arms.

13. The optical transceiver module of any of claims 1-11, wherein the interference modulator is an IQ nested MZM, and wherein four modulator signals are provided from the EDPC to four MZM arms of the IQ nested MZM.

14. The optical transceiver module of claim 1, further comprising: a fixed dispersion compensation module for providing a range of applicable distances, a maximum distance of the applicable distances being longer than a span of the range.

15. A method for extending transmission distance using readable symbols of an optical transmitter operating with PAMn modulation, the method comprising:

conditioning the analog modulator signal from the PAMn processor using an analog transversal filter circuit to perform an approximate hilbert transform, a dispersion pre-compensation, or both the approximate hilbert transform and the dispersion pre-compensation to form a conditioned modulator signal; and

an optical laser is modulated using an optical interferometric modulator based on the adjusted modulator signal.

16. The method of claim 15, wherein the PAMn processor comprises a PAM4 DSP configured within a transceiver module.

17. The method of claim 15 or claim 16, wherein the analog transversal filter circuit approximates a hilbert transform using at least three taps.

18. The method of any one of claim 15 or claim 16, wherein the analog transversal filter circuit implements dispersion pre-compensation by setting tap weights.

19. The method of claim 18, wherein the analog transversal filter further implements an approximate hilbert transform.

20. The method of claim 18, wherein the tap weights are operably selected from a predetermined set of tap weights, wherein members of the set provide compensation for different dispersion accumulations.

21. The method of any of claims 15 to 20, wherein the optical interferometric modulator performing the modulation is an IQ-nested MZM, and wherein four modulator signals are provided to four MZM arms of the IQ-nested MZM.

22. The method of any of claims 15 to 20, wherein the optical interferometric modulator performing the modulation is a DDMZM, and wherein two modulator signals are provided to two arms of the DDMZM.

23. A method for determining tap weights for an analog transversal filter circuit configured to adjust an analog modulator signal from a PAMn processor to perform an approximate hilbert transform, dispersion pre-compensation, or both, to form an adjusted modulator signal, the method comprising:

tap weights are iteratively corrected to improve dispersion for a composite range of various fiber lengths.

24. The method of claim 23, wherein the iterative correction is performed by error vector magnitude measurements of optical receivers located at a target distance for each fiber length.

25. The method of claim 23 or claim 24, wherein tap weight settings are determined for a plurality of different fiber length composite ranges and the settings for each length composite range are stored in a digital memory of the optical transceiver as a member of a set for operational selection.

Technical Field

The technical field of the present invention relates to optical data transceivers, and more particularly to optical fiber-type optical transceiver modules that provide greater than or equal to 50 gigabits per second ("Gbps") per wavelength in high-throughput, medium-short-range optical fiber-type optical communication links (e.g., in access networks, data centers, data center interconnects, and campus networks).

Background

Conventional optical fiber-type optical communication links directly transmit binary data as a binary, e.g., sending a "power on" burst to represent a binary "1" or sending a "power off" burst to represent a binary "0". This type of coding is referred to in various ways by various alternatives and, in most cases, can be described uniformly as on-off keying ("OOK") in view of certain discretion. "bits" are transmitted at a bit rate of 1/T bits per second or "bps". For contemporary high-speed optical fiber-type optical links, the bit rate is typically expressed in "giga" (10)⁹) Every second or "Gbps", accordingly, T (bit period) will be expressed in picoseconds or "ps". For example, 10Gbps links with 100ps bit periods are almost ubiquitous. Following the terminology developed for communication and control theory, the physical communication link and medium from the transmitter to the receiver or vice versa is commonly referred to as a communication "device".

With the advancement of other technologies and the increasing demand for transmitting more data, significant challenges arise because the available communication devices cannot reliably support OOK for data rates significantly greater than 10Gbps per optical wavelength. Complex optical link systems utilizing coherent optical technology with high performance Digital Signal Processing (DSP) control have emerged to provide 100 Gbps/wavelength and higher bit rates, which are suitable for high end applications and have high costs compared to existing communication equipment. However, there are many valuable applications that require more than 10Gbps but do not have the requirements of such "high-end applications", but attempting to use coherent systems for such less demanding applications does not alleviate the "high cost" associated with coherent technology. Therefore, there is a need to establish a more cost-effective method to provide increased data capacity in important applications using communication devices that do not meet high-end requirements. This is common, for example, where many individual interconnections are required and the length of the fiber optic equipment is in a medium range, such as from as little as several hundred meters to about 40-80km (sometimes referred to simply as "short haul"). This situation is encountered in many valuable applications such as access networks, data centers, data center interconnects and campus networks.

One key method of particular success is to convert from OOK to multi-level signaling, transmitting more than 1 bit of binary data per cycle T. In this case, the optical transmission per period T is a more densely valued "symbol", rather than just a bit. In that case, the term physical transmission rate changes from "bits per second" to a symbol rate, commonly referred to as the baud ("Bd") rate. E.g. 25 x10⁹The symbol per second (about) is referred to as "25 GBd" which has a corresponding symbol period T of 40 ps. Such links are also commonly referred to in terms of effective bit rates, so a 25GBd system may support, for example, 50Gbps (2 bits per symbol) or 100Gbps (4 bits per symbol), but in any case, the symbol period T remains 40 ps.

Coherent systems apply this dense symbol approach to practical extremes, such as 600Gbps at a single wavelength (where a portion of the data is siphoned to improve quality) by using 64GBd and 12 bits per symbol. The methods described herein employ less extreme, but generally more cost-effective methods. Perhaps the most basic and widely sought improvement is to replace OOK with 4-level pulse amplitude modulation (PAM4) so that 2 bits are provided per symbol. The same principle can easily be applied to consider PAM8(3 bits per symbol), PAM16(4 bits per symbol) or any corresponding quadrature amplitude modulation (QAMn), but PAM4 has many supporting techniques and is therefore of particular interest for application.

Disclosure of Invention

For the present invention we propose a new approach that exploits the technical finding that adding an analog linear equalizer chip in the transceiver, for example, using a short-haul 100Gbps PAM4 DSP chip (converting 4x25Gbps or 2x50Gbps on the host side to 2x50Gbps on the line side), can improve performance in edge applications or inaccessible applications for this data rate. The added analog chip can provide electronic dispersion pre-compensation (EDPC), while PAM4 DSP can provide electronic dispersion post-compensation for distances up to 40km or more, as well as other filter enhancement functions, without any optical dispersion compensation. The enhancements provided in this manner are significantly more efficient in size, cost and power consumption than corresponding upgrades in DSP performance or the addition of fixed or tunable optical dispersion compensators. The EDPC chip may provide any of the following enhancements: (a) approximating the hilbert transform of the PAM4 signal to transform it to a single sideband (PAM4-SSB) signal, along with additional fiber dispersion pre-compensation; and (b) dispersion pre-compensation for conventional double sideband (PAM4-DSB) PAM4 signals. A conventional commercial digital PAM4 chip for a transceiver is responsible for host-side interface, FEC, and a powerful line-side post-compensation equalizer. This principle of operation applies to both 50Gbps per wavelength and 100Gbps per wavelength supported by current transceiver standards, and may be equally applicable to higher data rates that will occur in future transceivers. To increase the transmission distance to SSMF over 40km, the number of equalizer taps in the EDPC can be increased (limited by the power consumption of the pluggable module) and/or a simple passive optical dispersion compensator can be further added to keep the residual fiber dispersion range within a 40km window. Passive (fixed) dispersion compensating elements are known in the art and are commercially available from Proximion AB. In this case, since the distance will be greater than 40km, there will necessarily be one or two optical amplifiers which may additionally be used to compensate for the losses caused by the passive optical dispersion compensator.

Many OSSB schemes for binary data transmission have been proposed to use analog hilbert converters (note that digital hilbert converters may also be used, but a new DSP chip is required). For example, [ 8, 9 ] for baseband 10Gbps NRZ signals, [ 10 ] for microwave sub-carrier 2.5Gbps NRZ signals.

In a first aspect, the present invention is directed to an optical transceiver module for n-level pulse amplitude modulation (PAMn) optical symbols to provide an interface between electronic data signals on a host and optical symbols transmitted at a baud rate through an optical communication device, where n ≧ 2, the transceiver comprising: a receiver section, a PAMn Digital Signal Processing (DSP) circuit, a transmitter section, and an analog transversal filter circuit. The receiver section may comprise at least one optical receiver to convert the received optical signal into an analog electrical signal. The PAMn DSP circuitry may generally provide at least a logical interface to the electronic host data, Forward Error Correction (FEC) functionality, analog-to-digital conversion of the electrical signal from the optical receiver, digital adaptive filtering of the converted received signal, and reconstruction of the filtered received signal into data. The transmitter section typically includes at least one laser and at least one interference modulator. The analog transversal filter circuit is configured as an electronic dispersion pre-compensator (EDPC) to filter a multi-level transmission signal, such as a PAMn signal provided by a PAMn DSP, wherein the filtered signal emitted from the EDPC is connected to a signal input of the interference modulator. In a variant of this aspect, the current required to drive the modulator electrodes according to the filtered signal voltage may be provided by an electronic amplifier external to the EDPC, or the current may be provided directly by an amplifier integrated within the EDPC.

In another aspect, the present invention relates to a method for extending transmission distance using readable symbols of an optical transmitter operating with PAMn modulation, wherein the method comprises: conditioning the analog modulator signal from the PAMn processor using an analog transversal filter circuit to perform approximate hilbert transform, dispersion pre-compensation, or both, to form a conditioned modulator signal; and modulating the optical laser using the optical interferometric modulator based on the adjusted modulator signal.

In another aspect, the invention relates to a method for determining tap weights for an analog transversal filter circuit configured to adjust an analog modulator signal from a PAMn processor to perform an approximate hilbert transform, dispersion pre-compensation, or both, to form an adjusted modulator signal, wherein the method comprises iteratively correcting the tap weights to improve dispersion for a composite range of lengths of a variety of fiber optic equipment.

Drawings

Fig. 1A depicts an analog transversal filter schematic that approximates a hubert transform using a one symbol period delay cell.

Fig. 1B depicts an analog transversal filter schematic that approximates a hilbert transform using a delay cell with a two-thirds sampling period.

FIG. 2A depicts an optical Mach-Zehnder modulator configuration for providing SSB modulation using dual drive capability, where d₁And d₂Are independent.

FIG. 2B depicts an optical Mach-Zehnder modulator configuration for providing SSB modulation using IQ drive capability, where d_1a＝-d_1b，d_2a＝-d_2bAnd d is₁And d₂Are independent.

Fig. 3A depicts a block diagram of an optical transceiver module that provides a 100Gbps link using two 50Gbps wavelength PAMs 4.

Fig. 3B depicts a block diagram of an optical transceiver module that provides a 100Gbps link using one 100Gbps wavelength PAM 4.

Fig. 4A shows an optical configuration of a dual wavelength emitter whose optical outputs are combined on a single optical fiber.

Fig. 4B shows an optical configuration of a dual wavelength emitter whose optical outputs are kept separate on separate output fibers.

Fig. 5A shows an optical configuration of a dual wavelength receiver having optical inputs presented in combination on a single optical fiber.

Fig. 5B shows an optical configuration of a dual wavelength receiver having optical inputs presented separately on separate input fibers.

Fig. 6A depicts a block diagram of an optical transceiver module that provides a 400Gbps link using eight 50Gbps wavelengths of PAM 4.

Fig. 6B depicts a block diagram of an optical transceiver module that provides a 400Gbps link using four 100Gbps wavelengths of PAM 4.

Fig. 7 depicts a communication device for determining optimal tap weighting parameters for an optical data link.

Fig. 8 presents a flow chart of a preferred optimization process for the communication device of fig. 7.

Fig. 9A depicts a simulated optical eye diagram transmitted by a transmitter with EDPC tap weights obtained by a calculated convolution of the hilbert transform and dispersion pre-compensation of a 10km fiber.

Fig. 9B depicts the received signal level of the transmit signal of fig. 9A prior to processing by the DSP.

Fig. 9C depicts a simulated optical eye diagram emitted by an emitter with EDPC tap weights optimized via the algorithm of fig. 8.

Fig. 9D depicts the received signal level of the transmit signal of fig. 9C before being processed by the DSP.

FIG. 10A is a graph of experimental results for one of the 50Gbps wavelengths for the embodiment shown in FIG. 3A.

FIG. 10B is a graph of experimental results of the optical signal-to-noise ratio as a function of one of the 50Gbps wavelengths for the embodiment shown in FIG. 3A.

Detailed Description

An optical data transceiver is described herein that also includes an electronic analog transversal filter to provide critical signal conditioning functions in converting PAMn formatted (n ≧ 2) digital data into a properly modulated optical signal emanating from the transceiver's optical transmitter. The electronic analog transversal filter circuit will be referred to herein as an Electronic Dispersion Precompensator (EDPC). The following signal conditioning methods may be equally applicable to the C, L and O optical bands as well as any other practically useful optical band in an optical fiber link. The transceiver with EDPC described herein may provide a very efficient method to extend transmission distance while also providing a smaller footprint for incorporating standard module formats that should be followed for incorporation into conventional systems. The description and examples herein will distinguish parallel optical data streams according to "per wavelength". For transceivers using parallel fibers, "per wavelength" herein may be equivalently understood as "per fiber," even if the wavelengths are not different between fibers. The present invention accommodates parallel wavelength/parallel fibers by simple integration and/or discrete replication. It should be assumed that the description herein applies to any reasonable number of parallel wavelengths and/or parallel fibers supported by the fiber optic equipment.

In general, the transceivers herein are suitable for various PAMn modulation formats and other directly detected multi-bit symbol formats, but since PAM4 is widely adopted in existing deployments, the discussion focuses on PAM 4for a more detailed description. PAM4 modulation has been widely used in short haul transmission systems as shown in table 1 below. Table 1 refers to the IEEE standard or multi-source agreement (MSA) standard relating to PAM4 modulation. All entries, except the last entry, use a 1.3 μm wavelength to avoid fiber dispersion in Standard Single Mode Fiber (SSMF). However, operating at 1.3 μm wavelength can cause certain other problems, such as (a) higher optical fiber transmission loss (< 0.35dB/km) than at 1.55 μm (< 0.20 dB/km), and (b) not providing DWDM (dense wavelength division multiplexing) wavelengths for 1.3 μm to increase the number of supported wavelengths, and therefore not the total transmission per fiber.

TABLE 1

("DC" ═ data center; "CO" ═ central office, e.g., access network, EML ═ external modulated laser, DML ═ direct modulated laser, SiPho ═ silicon photonic device)

As a result, a commercial 100Gbps optical transceiver module [ 6 ] has emerged that uses two 1.55 μm wavelengths to carry 100Gbps data for Data Center Interconnect (DCI). Each of the two wavelengths in the transceiver module is modulated based on PAM4 to carry approximately 50Gbps at 25 GBd. However, the 50Gbps PAM4 wavelength is very sensitive to fiber dispersion inherent to fiber optic equipment. It cannot even tolerate the dispersion of SSMF of only a few kilometers, thus requiring tunable Optical Dispersion Compensators (ODCs) in the transmission link. Such actively tunable ODCs are complex and management intensive items of optical hardware, which makes optical network operations very complex and cumbersome. To solve this problem, intensive studies [ 7 ] have been made to propose to cancel the dispersion compensation of the optical fiber for transmission of 50Gbps or 100Gbps PAM4 per wavelength. However, almost all proposals are associated with new Digital Signal Processing (DSP) algorithms, which would require significant investment in manufacturing, acquiring and operating custom DSP ASICs.

Another application where short-range dispersion (CD) compensation is required is 100 Gbps/wavelength with 1.3 μm CWDM wavelength spread over 10 km. The calibration wavelengths defined in 400G-LR4 [ 1 ] were 1271, 1291, 1311 and 1331nm, each with a drift/tolerance of ± 6.5 nm. Many typical optical transmitters exhibit "chirp," and the optical wavelength is slightly skewed when the transmitter level is changed to a new symbol. When the optical transmitter has such a chirp, a larger dispersion loss is brought about. The dispersion loss is also not uniform for all channels, and if the chirp is positive, the dispersion loss will be greater for longer wavelengths (e.g., 1331nm), and if the chirp is negative, the dispersion loss will be greater for shorter wavelengths (e.g., 1271 nm). It is proposed to increase the number of CWDM wavelengths to 8, which will make the parallax larger.

Another application that requires CD compensation at 50 Gbps/wavelength or 100 Gbps/wavelength in the 10-20 km range is the forward and backhaul links feeding wireless/mobile networks. For service areas with an insufficient number of fibers, CWDM or DWDM is required to support the required data bandwidth, and the fiber CD may cause significant system performance loss. In this case, it is actually necessary to recognize the electronic CD compensation method.

PAM4 (or PAMn) OSSB

4-level pulse amplitude modulated (PAM4) data symbols may be transmitted on an Optical Single Sideband (OSSB) optical carrier using known data formats and optical modulation techniques. As is well known, this compresses the optical bandwidth of the transmission, thereby reducing the dispersion impairments that accumulate as the signal propagates along the length of the fiber. A general description of a PAM4 based transceiver can be found in U.S. patent 7,380,993 entitled "optical transceiver for 100 gigabit/second transmission," which is incorporated herein by reference. Embodiments of the transceiver described herein may configure the EDPC to approximate the hilbert transform of the electrical PAM4 data to condition the electrical signal applied to the optical modulator for PAM4 OSSB transmission. Corresponding processing may be performed on the PAMn data symbols by summarizing the discussion in this section to account for the corresponding data symbols.

The optical SSB signal can be mathematically represented as

Where m (t) is a modulation signal (which may be a wideband digital signal or a narrowband microwave signal),is its Hilbert transform, and ω_cIs the optical carrier frequency. In this embodiment, m (t) may be a PAM4 signal at 50Gbps or 100Gbps, or may be easily at higher data rates, such as PAMn (n ≧ 4), where other elements of the optical link may support such higher rates. The hilbert transformer is an all-pass filter that provides a-90 degree phase shift at all positive frequencies and a +90 degree phase shift at all negative frequencies. Compared to conventional Optical Double Sideband (ODSB) signals, the central motivation for OSSB is to remove half of the spectral components, i.e., to suppress the spectral components on the positive or negative frequency side of the optical carrier as much as possible. This in turn enables:

a) reducing cumulative fiber dispersion effects including signal fading and signal-to-signal difference frequency interference after square-law detection, an

b) Post-detection compensation of accumulated dispersion in the electrical domain is supported.

The analog hilbert transformer may be approximated with a finite impulse response Filter (FIR) based on a tapped delay line, the FIR having a finite number of taps [ 9, 11 ]. Finite impulse filters based on tapped delay lines are an alternative name for analog transversal filters. Because of the limited number of taps, sideband suppression is not ideal. The fewer taps, the more residual power remains in the suppressed sidebands. According to [ 11 ], tap weights in the analog hilbert transformer are as follows:

for integer sample delay:

for any delay:

where n corresponds to the nth tap relative to the center tap (the n values of the taps from the center tap to the input are negative) and τ is the tap delay in the sample. Typically, the number of taps in the analog circuit is at least three, in other embodiments at least five, and in other embodiments 5 to 25. The center tap has a weight of +1 or-1, as described further below. In a simpler symmetrical circuit, the number of taps is odd, although contemplated configurations include configurations having an even number of taps. Those of ordinary skill in the art will appreciate that other ranges of tap numbers within the explicit ranges are contemplated and are encompassed within the present disclosure.

FIGS. 1A and 1B depict an EDPC circuit configuration to approximate a Hilbert transform and generate a filtered signal for an optical modulatorThe adder portion of the EDPC actually provides two coordinated outputs, one for eachIn that(center tap +1.0 coefficient), the other for(center tap is-1.0 coefficient). Fig. 1A utilizes a finite impulse response filter 101 having a unit delay period of T, where taps 103 have tap weights obtained from equation (2). T is the symbol rate. The output from tap 103 goes to amplifier/attenuator 105, and amplifier/attenuator 105 sums at output unit 107 to send the summed transform signal (equation (4) below) to output 109. An alternative central amplifier/attenuator may be provided to the further output 113, the negative value of the original signal being added to the hilbert transform (equation 5 below) for driving the modulator, as described below. An alternative central amplifier/attenuator may be provided by having a single tap weighted amplifier/attenuator providing positive and negative outputs. The amplifier/attenuator 105 determines tap weights, shown from left to right, -2/(3 pi) (n ═ -3), -2/pi (n ═ -1), 1 or-1 (n ═ 0), 2/pi (n ═ 1) and 2/(3 pi) (n ═ 3). It is pointed out from equation (2) that even if the tap weights are set to zero, in this example, the outer two tap weight amplifiers/attenuators are each assigned a delay of ± 3T to maintain five non-negligible tap weights. The n-0 tap is set to provide an untransformed input that has been added to the transformed signals of equations 2 and 3. Similarly, fig. 1B depicts EDPC circuit configuration 121 based on a unit delay of (2/3) T and taps 123 from equation (3) to derive tap weights to generate corresponding filtered signals. The output from tap 123 goes to amplifier 125, which is summed with the transformed signal at 127 (equation (4) below) for output 129. For this embodiment, the tap weights are determined by equation (3) using a delay unit of 2T/3. Also, an alternative central amplifier/attenuator may be provided to the further output 131, the hilbert transform being added to the negative signal of the original signal (equation 5 below) for driving the modulator, as described below. Signal bandwidth, tap delay interval, and decimation for reasons and results described subsequently hereinThe preferred balance between the number of heads varies depending on the nature of the application. For example, the configuration shown in FIG. 1B has been used to demonstrate excellent transmission performance at DWDM wavelengths and distances up to 40km, for 50 Gbps/wavelength, with further modifications to the tap weights (as described below), as will be described below.

The filtered signal is only part of the conversion of PAM4 data to a PAM4 OSSB optical signal. It is further desirable to provide an optical carrier with in-phase and quadrature phase modulation according to equation (1). Preferably, the modulation is provided by driving an interferometric optical modulator, in particular a Mach-Zehnder type optical modulator (MZM), using signals from the EDPC.

This can be achieved by using a dual drive base MZM (ddmzm)201 or an IQ nested MZM 203, as shown in fig. 2A (see [ 9 ]) and fig. 2B, respectively. The IQ nesting MZM 203 comprises an I MZM 205 and a Q MZM 207, which themselves serve to nest the respective arms 209, 211 of their MZMs. The base MZM 201 of FIG. 2A is generally preferred in appropriate applications due to its simplicity. The IQ nested MZM 203 of fig. 2B may provide a better range of signal integrity for applications that might otherwise be marginal, but such an embodiment would typically involve an additional inverting amplifier for the EDPC signal, with greater power requirements. The MZM modulator includes a semiconductor optical waveguide that interacts with an RF electrode. While lithium niobate-based modulators are commercially available and other semiconductor/electro-optic modulator types may be used, indium phosphide (InP) -based MZMs are particularly desirable in view of size, efficiency and performance. InP-based IQ MZMs are available from NeoPnics, Inc. and are found in their high bandwidth coherent driver modulator (HB-CDM) product. Further, note that the electrical signal amplitude required to drive the passive electrode 213 of the MZM is substantially less than the conventional OOK or PAM4 signal. This is because OSSB signals require a higher ratio of optical carrier to signal beat frequency than signal to signal beat frequency. As a result, the MZM may be directly driven using the amplified output signal from the EDPC (as shown in FIG. 1) without the need for an additional driver amplifier.

The output of the EDPC chip may include a base amplifier suitable for directly driving the MZM electrode. In an alternative embodiment, an analog electrical amplifier is used to amplify the output of the EDPC chip to provide the drive current to the MZM electrode. The modulator signal from the EDPC is reflected in the following equations, where equations (4) and (5) are used for fig. 2A, and equations (6) and (7) are used for fig. 2B:

the configuration of the EDPC chip relative to the MZM eliminates the need for an otherwise required transmitter driver amplifier, further reducing the associated cost, size and significant power consumption. Although multiple FIR elements may be used in a single chip or multiple chips, a single FIR may be configured to generate d as shown in FIGS. 1A and 1B₁And d₂The output of both. With respect to equations (6) and (7), the EDPC chip may further include a buffer amplifier for receiving the output of the summing unit to direct the signal to the output. The buffer amplifier can be easily configured to output either a positive output or a negative output or both, or can be used as an integrated driver. The output units (107 in fig. 1A and 127 in fig. 1B) may include a summing unit and a buffer amplifier, and for suitable embodiments, the buffer amplifier may output a positive output and a negative output, as indicated by the dashed lines in fig. 1A and 1B.

Dispersion (CD) precompensation

To further improve transmission distance, we describe the inclusion of a portion of the fiber in an analog EDPCAn alternative embodiment of dispersion pre-compensation. Since the actual length of the transmission link is usually not available to the transceiver, the CD at the receiver end must be estimated or adaptively compensated. This estimation is unlikely to be used in practice, since additional power consumption would be involved in making the estimation. The power consumption limited number of taps in a receiver adaptive equalizer provided by a short-range PAM4 chip limits the maximum dispersion that can be adaptively compensated. For the purposes of illustration, it can now be assumed that the adaptive equalizer of the receiver is capable of compensating for the CD corresponding to the maximum transmission length L. Due to the symmetry of adaptive equalization, this means that the CD range that can be compensated by the adaptive equalizer of the receiver is-CD_LAnd + CD_LIn the meantime. We have found that by pre-compensating the dispersion corresponding to a fixed equivalent of the transmission distance L at the transmitter side, the meaningful optical transmission range can be effectively extended, thereby doubling the transmission distance.

For the purpose of elaboration, the proposed pre-compensation method is considered in two extreme cases:

1) the transmission distance is zero: at the transmitter side, with dispersion (-CD) of opposite sign_L) Will be applied to the signal. Since this value is within its compensation range, it can be processed by the adaptive equalizer of the receiver.

2) The transmission distance is 2L. On the transmitter side, the dispersion (-CD) corresponding to the transmission length L has an opposite sign_L) Will be applied to the signal again so as to pre-compensate half the transmission length. After a distance of 2L of propagation in the fiber, the residual CD will be equal to the CD at the receiver end_L. Since the value is still within its compensation range, it can be processed again by the adaptive equalizer of the receiver.

Thus, in these embodiments, the analog EDPC is designed to provide both combined hilbert transform and dispersion pre-compensation. This is achieved by convolving the tap weights of the hilbert transformer with the tap weights of the dispersion pre-compensation FIR. Tap weights for CD pre-compensation FIRs can be obtained by calculating the inverse fourier transform of the conjugate of the dispersive fiber transfer function h (f) for the fiber plant length L [ 8 ].

Where D is the fiber dispersion parameter, L is the length of the fiber, λ is the wavelength of the signal, f is the low pass equivalent frequency, and c is the speed of light.

The method based on the optical fiber CD pre-compensation with Hilbert transform (hereinafter referred to as "HT + CD") is shown in FIGS. 3A (block 301) and 3B (block 303)^-1") EDPC, for 2 λ x50Gbps and 1 λ x100Gbps, respectively. While both fig. 3A and 3B are contemplated for use as a 100G QSFP28 module, the optical module may be implemented in a pluggable package according to the QSFP28, DD-QSFP, OSFP, CFP2, or CFP8 standards under the industry MSA. The dual wavelength 2x50G optical transceiver 301 in fig. 3A can be easily reduced to a single wavelength 50Gbps QSFP or SFP optical transceiver module for wireless fronthaul or mid-stream or Passive Optical Network (PON) applications.

Referring to fig. 3A, the optical transceiver module 301 includes a 2x50Gbps PAM4 DSP 311, the PAM4 DSP 311 connected on the receive side to a 2-wavelength Receiver Optical Subassembly (ROSA) 313, the 2-wavelength ROSA receiving two wavelength separated optical signals from a demultiplexer 315, the demultiplexer 315 connected to an optical input 317 into the module. The ROSA 313 typically includes a photodetector (e.g., a PIN diode or APD (avalanche photodiode)) and a transimpedance amplifier (TIA) for each wavelength, and converts the optical signal into an electrical signal. Demultiplexer 315 may include an optical grating, a filter, and/or a 1: 2 mach-zehnder interferometer based demultiplexer. The transmit signal from the PAM4 DSP 311 is directed to a 2x analog EDPC 321, which may be two analog circuits, as shown in fig. 1A and 1B. From the 2x analog EDPC to the 2x MZM 323 pre-compensation signal, the 2x MZM 323 receives optical inputs from the λ 1 laser 325 and the λ 2 laser 327, which are modulated and directed to an output 329.

Referring to fig. 3B, the optical transceiver module 303 includes a 1x100 Gbps PAM4 DSP 331 that is connected on the receive side to a 1-wavelength ROSA 333, the 1-wavelength ROSA 333 receiving a wavelength optical signal from an optical input 335 into the module. The ROSA 333 typically includes a photodetector (e.g., PIN or APD) and TIA for converting an optical signal at a wavelength to an electrical signal. The transmit signal from the PAM4 DSP 331 is directed to a 1x analog EDPC 341, which may be an analog circuit, as shown in fig. 1A or fig. 1B. From the 1x analog EDPC 341 to the 1x MZM 343 pre-compensation signal, the 1x MZM 343 receives an optical input from the λ 1 laser 345, which is modulated and directed to an output 349.

In order to apply the CD pre-compensation together with the hilbert transform, equations 9 to 12 below replace the equations based only on the hilbert transform of fig. 2. For the two λ embodiment of FIG. 3A, d is used₁、d₂、d₃And d₄For one λ embodiment of FIG. 3B, only d is used₁And d₂。

F^-1Inverse Fourier transform

By adjusting the attenuation output from each tap of two FIR elements (one FIR of equations (9) and (10) and one FIR of equations (11) and (12)) within the analog chip, the analog circuit can be designed to approximately perform the desired transformation in equations 9 through 12. In transceiver embodiments that support multiple simultaneous transmit wavelengths and/or transmission fibers,preferably, the analog EDPC chip may include multiple FIR banks for filtering multiple signal streams simultaneously. For example, in the above example, an analog EDPC may have two parallel FIR banks, one for each signal m₁Solving equations (9) and (10), the other for the signal m₂Equations (11) and (12) are solved. In particular, the response of the FIR can be written as:

wherein c (t) is set equal to d₁、d₂、d₃And d₄And delta denotes the Dirac trigonometric function, where c_nAre the tap weights and τ is the delay period of the analog filter, e.g., T (fig. 1A) or 2T/3 (fig. 1B) (or other suitable delay), T being the symbol rate. 2N +1 equals the number of taps. This relationship may be evaluated by simulation for a set number of taps, or may be corrected empirically. The general theory of correcting communication distortion with electronic filters is described in Rudin "automatic equalization with transversal filters" (IEEE Spectrum, 1 month 1967, pages 53-59), which is incorporated herein by reference.

As shown in fig. 4A and 4B, one of two alternative structures 403, 405 of a dual wavelength transmitter may be present within the optical transceiver module 301 (fig. 3A). The first configuration (FIG. 4A) has an integrated optical combiner 407, so the output is connected to a single optical fiber 409, which in turn can be connected to 40 with 100GHz spacing⁺A channel DWDM multiplexer or by dark fiber to a remote receiver. The second structure 405 (FIG. 4B) has two transmitter output fibers 411, 413 that can be connected to 80 with 50GHz spacing⁺Two input ports of a channel DWDM multiplexer. 80⁺Channel DWDM multiplexers are typically made up of two 40's with even and odd (ITU-T) channels, respectively⁺The channel DWDM multiplexer components may be combined by an interleaver.

Similarly, as shown in fig. 5A and 5B, the dual of optical transceiver modules 301 (fig. 3A)The wavelength light receiver may have one of two different alternative configurations corresponding to the two emitter configurations. The structure of fig. 5A corresponds to the structure shown in fig. 3A. E.g. from 40⁺The optical input fibers 505 of the channel DEMUX are received by a two-channel DEMUX 507 corresponding to the demultiplexer 315 of fig. 3. The λ 1 output of the two-channel DEMUX 507 is directed to the ROSA 509 and the λ 2 output of the two-channel DEMUX 507 is directed to the ROSA 511. Referring to fig. 5B, separate optical fibers 521, 523 carrying inputs at λ 1 and λ 2, respectively, direct their respective inputs to ROSA 525 and ROSA 527. The input fibers 521, 523 may be from 80, for example⁺Channel DEMUX, which is typically composed of two 40⁺Channel DWDM demultiplexer composition, two 40⁺The channel DWDM demultiplexers have even and odd ITU-T channels, respectively, which can be combined by an interleaver.

The module concept in fig. 3A and 3B can be extended to a 400Gbps DD-QSFP (or OSFP, CFP2, CFP8) transceiver module by quadrupling the number of wavelengths, PAM4 channels, and analog hilbert converters, as shown in fig. 6A and 6B. Specifically, the embodiments of FIGS. 3A and 3B are based on having a Hilbert transform and fiber CD pre-compensation (hereinafter referred to as "HT + CD^-1") EDPC may be extended to 400Gbps, for 8x50Gbps and 4x100Gbps, respectively. While fig. 6A and 6B are each particularly contemplated for use as a 400G QSFP28 module, the optical module may be implemented in a pluggable package in accordance with QSFP28, DD-QSFP, OSFP, CFP2, or CFP8 standards under the industry MSA.

Referring to fig. 6A, an optical transceiver module 601 includes an 8x50Gbps PAM4 DSP 611 that is connected on the receive side to an 8 wavelength Receiver Optical Subassembly (ROSA)613, the ROSA 613 receiving 8 wavelength separated optical signals from a demultiplexer 615, the demultiplexer 615 being connected to an optical input 617 into the module. The ROSA 613 typically includes a photodetector for each wavelength and converts the optical signal to an electrical signal. Demultiplexer 615 may include a grating, an interference filter, and/or an AWG-based demultiplexer. The transmit signal from the PAM4 DSP 611 is directed to an 8x analog EDPC 621, which may be eight analog circuits, as shown in fig. 1A and 1B. From the 8x analog EDPC to the pre-compensation signal of the 8x MZM 623, the 8x MZM 623 receives optical inputs from a laser bank 625 of eight (λ 1.. λ 8) lasers, which are modulated by an eight-channel multiplexer 627 and directed to an output 629. Similar multiplexing elements may be used for the description of the demultiplexing function.

Referring to fig. 6B, the optical transceiver module 603 includes a 4x100Gbps PAM4 DSP 631 connected on the receive side to a 4-wavelength ROSA 633 that receives a wavelength optical signal from an optical input 635 into the module. The ROSA 633 typically includes a photodetector (e.g., PIN or APD) and TIA for converting an optical signal of one wavelength into an electrical signal. The transmit signal from the PAM4 DSP 631 is directed to a 4x analog EDPC 641, which may be an analog circuit, such as shown in fig. 1A and 1B. From the 4x analog EDPC 641 to the pre-compensation signal of the 4x MZM 643, the 4x MZM 643 receives optical inputs from a laser group consisting of four (λ 1.. λ 4) lasers 645, which are modulated by a four-channel multiplexer 647 and directed to an output 649.

N in the figure: 1 multiplexer and 1: the N demultiplexer is only an example of a variety of possible configurations. Also, there are passive (fixed) dispersion compensating elements in the optical path after the multiplexer. For the purposes of the figures, passive dispersion compensating elements may be considered within the block of the multiplexer, although in actual devices they may be packaged separately. Also, for embodiments where the multiplexer is not shown, there may be a passive dispersive element located in the optical path substantially at the location of the multiplexer without multiplexing functionality. Mx1 couplers and L: 1 multiplexer/demultiplexer combination to perform the same function. In the case of DWDM applications, multiple TX and RX fibers may also be used, as well as MPO (multi-fiber push-in) connectors.

In the block representation of the figure, all PAM4 DSP chips may be originally designed for short distances (≦ 10km) and low power consumption, and typically include host side SERDES (serializer/deserializer), line side Forward Error Correction (FEC) encoder/decoder, line side equalizers (e.g., CTLE, feedforward and decision feedback equalizers), MSB/LSB amplitude and skew adjustment, digital-to-analog converters (DAC) and analog-to-digital converters (ADC), and many other functions. It is envisioned that these PAM4 DSP chips could further be replaced by simpler analog-based implementations that do not require DACs and ADCs. However, the number of feed-forward equalizer taps in an analog PAM4 chip may not be sufficient to obtain sufficient post-compensation for chromatic dispersion for the required transmission distance. Likewise, analog PAM4 chips typically do not contain FEC. Although we know that the higher the FEC coding gain, the stronger the equalizer (e.g., more taps), the longer the transmission distance. Given the maturity of existing DSP-based PAM4 chips, it appears to be generally more suitable for use in the transceiver modules described herein.

Iterative tap weight optimization

Use of HT + CD as shown in formulas (5) to (8)^-1The driving signals for the tap weights are based on theoretical calculations. In practice, the bandwidth of the transmitter and receiver also affects performance. Therefore, we can compute HT + CD based on configurable FIR filter^-1Tap weights are used as initial conditions and improved tap weights are sought which can also compensate for both transmitter and receiver bandwidth limitations through a convergence process. Adjustment of the amplifier/attenuator output is used to adjust the tap weights. When the actual distance differs from the optimization goal, the performance of tap weights optimized for a certain target distance may degrade rapidly. In order to obtain a set of tap weights that operate over a wide range of transmission distances, it is proposed herein to perform a process of joint optimization for a plurality of transmission distances (or fiber lengths) within a desired range. Note that this process can also be used to optimize a single transmission distance.

The search algorithm is used in transmitting test signal with a length L₁，..L_N. The weighted sum of EVM (error vector magnitude) obtained after a set of fibers as optimization metric J.

Wherein w_nIs adjustable to achieve the desired EVM and distance distributionArbitrary weight of (a). A schematic diagram of the architecture of a system 701 for implementing iterative tap weight optimization is depicted in fig. 7. The transmitter 703 may be one of the transmitter components of the transceiver described herein. The transmitter 703 then outputs light from the fiber set 705 into each fiber and then transmits the light to the receiver 707. The receiver 707 calculates the EVM using a suitable processor and transmits the EVM to a controller 709 that is coupled to both the transmitter 703 and the receiver 707. For convenience, the controller 709 may be used in preparation for the manufacture/configuration of the transceiver and may be an analog circuit, a digital processor, or a combination of both. The controller 709 may be used to configure the FIR and is not typically used by the end user, although the controller 709 may be used to reconfigure the FIR during a subsequent time after a period of use.

Note that in a production line, a programmable dispersion compensator can be used to simulate a CD instead of a length L₁..L_NA set of physical fiber links. For a description of a programmable dispersion compensator, see, for example, U.S. patent 6,879,426 to Weiner, entitled "system and method for programmable polarization independent phase compensation of an optical signal," which is incorporated herein by reference. For an EDPC with n taps, the best tap search is an n-dimensional optimization problem that can be solved, usually by a known search method (e.g., steepest descent). In a practical plant, the number of taps may be small, n ≦ 5, and its value must be specified as an integer within a limited range (in the experimental plant described later, its value is an integer between-100 and 100). For this case, it is likely that the simplified search process shown in the flowchart of fig. 8 will be used.

It is convenient to consider the tap weights as a vector h which is formed by concatenating the separately generated signals d₁(formula (9)) and d₂(equation (10)) required tap weights. For example, consider an EDPC with five analog taps. Then, a signal d is generated₁Has a tap weight of [ I₁ I₂ I₃ I₄ I₅]And generates a signal d₂Has a tap weight of [ Q ]₁ Q₂ Q₃ Q4 Q₅]. Then, the vector h is [ I ]₁ I₃ I₂ I₄ I₅ Q₁ Q₂ Q₃ Q₄ Q₅]. It is observed that a change in tap weights in the middle has a greater impact on EDPC performance than a change in tap weights outside. Therefore, it is preferable to adjust the tap weights in order of their importance. For this reason, it is convenient to sort the vectors h in descending order of importance, h ═ I₃ Q₃ I₂ Q₂ I₄ Q₄ I₁ Q₁ I₅ Q₅]Then adjust the elements of h from beginning to end. The best tap is iteratively searched. Initially, the controller loads the EDPC with the tap weight that is analytically calculated as a convolution of the hilbert transform and a CD pre-compensation weight corresponding to one of the target fiber lengths L. The signal is then subsequently transmitted to each fiber in the optimization target set of fibers, and the EVM value is obtained from the receiver by the controller. The optimization cost function is calculated by the controller according to equation (14).

A similar iterative process can be used, whether from programmable dispersion compensator simulation J or using a set of fiber lengths connected to an optical receiver for measurement. Referring to the iterative process 801 in FIG. 8, a set of fiber lengths (L) within a desired range is specified (803)₁，...，L_N) And its importance (w)₁，...，w_N) As described above in formula (14). Initial tap weights are then specified (805) in step size s (selectable by the user as a reasonable initial value) in the order of importance indicated in the previous paragraph. Like most stochastic convergence optimization processes, the initial value of the step size affects the balance between convergence speed and convergence quality towards obtaining the best results. For a given setting, it is often necessary to evaluate different initial step sizes depending on the desired quality to determine a preferred value or range. Will vector h₀Load (807) to the EDPC. For each L, a signal is transmitted (809) to obtain an EVM₁，...，EVM_N. Using these values, a cost function J is calculated (811)₀(h₀) Is started.

At each iteration k (813 of fig. 8), the controller generates two sets h of test tap weights by increasing and decreasing, respectively, one of the tap weights by a value designated as a step size s⁺And h^-. The tap weight vector is then loaded into the EDPC for each fiber length L_1..NTransmitting test signals and summing the obtained EVMs according to equation (14) to obtain sum vectors h, h⁺And h^-Corresponding three cost functions J, J⁺And J^-. Next, the cost function values are compared and the smallest function value with a corresponding h is selected for the next iteration. The iteration will continue until the cost function stops decreasing. The iteration separately traverses each tap, with parameter "i" counting the taps. In this case, the step size s will be halved and the iteration will continue. This loop continues until the step size equals 1.

The proposed search procedure has been validated by simulating the final EDPC in the optical link.

Fig. 9A shows a simulated transmit optical eye diagram generated by a transmitter with EDPC tap weights obtained by a calculated convolution of a hilbert transform and dispersion pre-compensation on 10km of fiber with a target transmission distance of 20km (i.e., without iterative optimization). Since the deterministic filter is calculated for 10km, an open eye pattern can be seen after 10km transmission even without an Rx adaptive equalizer. Thus, fig. 9B shows an eye diagram of the received signal level before DSP processing, and it can be seen that the eye is almost absent, but still open. Note that if the same pre-compensated optical signal is transmitted over 20km of fiber, no open eye is seen before the DSP, since the transmitted signal is only pre-compensated for half the distance, and therefore the remaining 10km of dispersion washes out the open eye. Fig. 9C and 9D show the transmitted and received eye diagrams when optimized taps (obtained by the search algorithm in fig. 8) are used. We can see a significant improvement in the eye diagram over fig. 9A and 9B.

Based on the above, short PAM4 DSP chip can be used to find applicationsA set of tap weights for any distance within 40km (when only 5 EDPC taps are used). By setting L20 km and based on Hilbert transform and CD precompensation (HT + CD)^-1) And then the set of tap weights may be found by the iterative search to find an optimized set of weights. If the use of this set of tap weights would result in poor link performance, we can instead choose to use two sets of tap weights and select the best tap weight as part of the link initialization. In this case, the first tap weight is found by: for example, set L-10 km (refine the actual tap weights as described above) to cover a distance between 0 and 20 km; and similarly determines a second set of tap weights by refining L-30 km or so to cover a distance between 20 and 40 km. These two sets of tap weights may be stored in a transceiver configuration memory and appropriate settings for best performance may be selected when the transceiver is enabled on the actual fiber optic equipment. Depending on power consumption requirements, more taps may be used to further improve link BER performance or increase transmission distance. For example, the 5 taps shown in FIG. 1 may be increased to 7 or 9 taps.

PAM4 ODSB

Above, the described transceiver embodiments are all based on OSSB transmission. For certain considerations, it is preferred to use conventional Optical Double Sideband (ODSB) transmission. For these embodiments, no Hilbert transform is performed. In another embodiment of the transceiver, the EDPC chip may also be advantageously used in ODSB signal transmission. The drive signals to the two MZI electrodes are:

wherein

The same principle can be applied to optical transceivers with line-side optics based on 1x100G, 8x50G, or 4x100G, etc. The process of optimizing the tap weights may still follow the process in fig. 8. In general, an ODSB-PAM4 transceiver may achieve a lower raw error rate than OSSB-PAM4 at a particular distance. However, the optimized tap weights for ODSB-PAM4 cannot cover as wide a transmission distance range as OSSB-PAM 4. As a result, more sets of tap weights for different distance ranges would need to be stored in the transceiver memory, which may be operationally inconvenient for the service provider.

Results of the experiment

Following the optical transceiver configuration shown in fig. 3A, a field experiment was configured, although only one of the two wavelengths was activated to demonstrate the present invention. The experiment used a commercial short-range PAM4 DSP (which converted the host side 4x25Gbps to the line side 2x50 Gbps). The EDP C chip is a simulated transversal filter made with IBM 90nm 9HP SiGe BiCMOS process with a cut-off frequency of 300GHz [ 12 ]. The MZM structure is shown in FIG. 2B.

After a direct 40km fiber link without optical dispersion compensation, we obtained the Bit Error Rate (BER), which is a function of the received optical power, as shown in fig. 10A. We can see in this figure that when the pre-FEC BER threshold is set to 1e-3 (determined by the PAM4 DSP chip used in the experiment), a receiver sensitivity of < -10.5dBm after 40km and < -11dBm after 20/30km can be achieved (the minimum received optical power remains below 10)^-3Raw error rate). Receiver sensitivity can be further improved by replacing the older TIA (spectral noise density of 17pA/√ Hz) in our experiments with the newest TIA (spectral noise density of 12pA/√ Hz).

For DWDM systems with DWDM booster and preamplifier, we also measured the BER performance versus the optical signal-to-noise ratio (OSNR), as shown in fig. 10B. We can see in this figure that when the pre-FEC BER threshold is set to 1e-3 (shown by the black dashed line), the required OSNR < 33dB after 40km and < 32 dB after 20/30km can be achieved.

The references cited above in brackets are incorporated herein by reference:

【1】http：//100glambda.com/specifications

【2】IEEE802.3bsTM/D3.5

【3】 N.Eiselt et al, "Evaluation of Real-Time 8 × 56.25Gbps (400G) PAM-4for Inter-Data Center Application Over 80km of SSMF at 1550nm (evaluated for Real-Time 8 × 56.25Gbps (400G) PAM-4for SSMF applications that exceed 80km at 1550nm between Data centers)," J.Lightwave Tech., 35(4), 955- "962, 2017.

【4】 Yin et al, "100-km DWDM Transmission of 56-Gbps PAM4 per λ via Tunable Laser and 10-Gbps InP MZM (100 km DWDM Transmission per λ 56Gbps PAM4 by Tunable Laser and 10Gbps InP MZM)," photon.

【5】 Us patent 9,722,722B 2, 8 months and 1 days 2017.

【6】 Us patent 9,553,670B 2, 24 months 1 and 2017.

【7】 M.morsy and d.v.plant, "a comparative study of technology options for next generation intra-and inter-data center interconnects (comparative study of intra-and inter-data interconnection technology selection), the fiber optic telecommunications congress of w4e.1, 2018.

【8】 M.Sieben et al, "Optical Single band Transmission at 10Gbps Using one Electrical Dispersion Compensation (Optical Single Sideband Transmission at 10Gbps with Electrical Dispersion Compensation Only)", J.Lightwave Tech., Vol.17, Vol.10, p.1742-.

【9】 U.S. Pat. No. 5,880,870, 3.9.1999.

【10】 Us patent 7,206,520B 2, 4.17.2007.

【11】 L.R. Rabiner and R.W.Schafer, "On the behavior of minimax FIR digital Hilbert transformers (behavior On minimax FIR digital Hilbert transformers)", Bell systems technology J., Vol.53, Vol.2, p.363-.

【12】 Edem Ibragianov et al, "Coherent Analog Low Power, Small Size 400/200/100GB/s Receiver Based on Bipolar SiGe Technology Coherent Analog Low Power consumption, miniature 400/200/100GB/s Receiver", Th1A.5, 2018 optical fiber communications Congress.

The above embodiments are intended to be illustrative and not restrictive. Additional embodiments are within the claims. Additionally, although the present invention has been described with reference to particular embodiments, workers skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention. Any incorporation by reference of documents above is limited such that subject matter contrary to the explicit disclosure herein is not incorporated. To the extent that particular structures, compositions, and/or methods are described herein with components, elements, ingredients, or other dividers unless otherwise specifically stated, it is to be understood that the disclosure herein encompasses specific embodiments, embodiments that include particular components, elements, ingredients, other dividers, or combinations thereof, as well as embodiments that consist essentially of such particular components, ingredients, or other dividers, or combinations thereof, which may include other features that do not alter the basic nature of the subject matter, as suggested in the discussion.