EP3566337A1

EP3566337A1 - Digital pre-distortion for complex modulator based-imdd system

Info

Publication number: EP3566337A1
Application number: EP17702358.7A
Authority: EP
Inventors: Qiang Zhang
Original assignee: Huawei Technologies Co Ltd
Current assignee: Huawei Technologies Co Ltd
Priority date: 2017-01-30
Filing date: 2017-01-30
Publication date: 2019-11-13
Also published as: WO2018137782A1

Abstract

The present invention relates to a digital signal processing module in a transmitter of an optical transceiver. The digital signal processing module performs a bias-related linear transform in order to align, in a vector plane, the vector of an optical carrier signal with the vector of a modulated optical signal that is modulated by a modulator implemented inside the transmitter, and also performs a digital pre-distortion in order to compensate for the nonlinearity of the modulator. The digital pre-distortion method mainly consists in converting a target signal into a pre-distorted signal by subtracting a signal proportional to the distortion signal from the target signal. The non-orthogonality of the modulator is mitigated by an appropriate bias-related linear transform that is selected as to obtain the best quality performance using a scan method or as to obtain a maximum value of cross-correlation using a pilot tone method.

Description

Digital pre-distortion for complex modulator based-IMDD system

TECHNICAL FIELD The present invention relates to the field of wireless communications, and more particularly to an intensity-modulation direct-detection system of an optical transceiver.

BACKGROUND

Intensity-modulation and direct-detection (IMDD) systems are attractive for their low cost and low power requirements in metropolitan networks. However, such systems have significant transmission distance limitations by working, for example, in the C-band, due to high performance degradation caused by power fading.

As a solution to extend the transmission distance, dispersion compensation module (DCM) can be used in the IMDD system to compensate for the chromatic dispersion (CD) in the link. However, this DCM implementation has the disadvantage to increase the cost and size of the system and to be difficult to implement in a real system.

Another solution to extend the reach can consist of a CD pre-compensation or a single sideband modulation, which can be carried out by means of a complex signal modulator such as a dual-drive Mach-Zehnder modulator (dual-drive MZM or DDMZM) and a in- phase/quadrature (IQ) modulator (also known as a single sideband modulator).

Fig. 1 shows a conventional DDMZM in a transmitter (Tx) 100 of an optical transceiver.

Such a conventional DDMZM consists of two independent phase modulators and each phase modulator will induce a phase shift proportional to the applied voltage. As depicted in Fig. 1, the two arms (also designated as upper and lower arms, respectively) of the DDMZM are respectively driven by the two voltage signals di and d₂ (also designated as the drive signals hereafter). Each one of the drive signals di and d₂ comprises two components: a direct current (DC) component and a radio frequency (RF) component. The DC voltages are bias voltages

1 that will induce a constant phase shift (i.e., a constant angle value) between the upper and lower arms in order to adjust the bias point of the DDMZM away from the null point, while the RF signals carry the information to be sent. Thus, the drive signals di and d₂ can be written as follows: d₂ = V_b2 + S₂ (1) where Vbi and Vb₂ are the bias voltages for the respective arms of the DDMZM, and Si and S₂ are the respective RF signals.

The DDMZM output signal Ετχ, which is the electric field at the DDMZM output, is given by the following relationship:

E_TX (t) = E_in cos ( ^diC^t)-¾ (^t))^ _exp ^^(^₂M)) ₍₂₎ where Ei_n is the DDMZM input signal, which is the electric field at the DDMZM input, and ν_π is the voltage needed to induce a π phase shift between the arms of the two phase modulators. From the transfer function Ετχ/Ει_η, it results that the DDMZM can be regarded as an intensity modulator through its cosine part and as a phase modulator through its

exponential part. Thus, the DDMZM can be used to generate a complex signal.

If the target signal (T) is defined by: T = T(x) = |T(x)|exp(j Φ(ί)), then the transfer function Ετχ/Ein of the DDMZM can be inverted and the drive signals can be calculated as follows:

«" = (*⁽^^«1¾ ))

This method of inverting the transfer function has the benefit to fully compensate for the nonlinearity and other distortions of the DDMZM in the case that the bandwidth, the samplin rate and the quantized bits of the digital-to-analog (D/A) converter (DAC) are high enough. However, this method also has several disadvantages. Indeed, the calculated bias point is related to the RF signals being added, which is not acceptable to use in the real product. In addition, it is necessary to sample at a high rate and to quantize bits of the DAC in order to

2 avoid any penalties. Also, due to a pure nonlinearity process, the gain will be reduced or even removed when this process is combined with a bandwidth filtering effect.

When the two arms of the DDMZM are respectively biased with Vbi = ν_π/4 and Vb2 = -VJ4, the DDMZM works at the quadrature point, i.e., at the operating point that is at the center of the quasi-linear region of the DDMZM characteristic and that thereby offers a maximum signal excursion, and the phase shift between the two arms is π/2. In addition, if the RF signal is small, namely if the DDMZM is working under small signal condition, then the DDMZM can be considered as a linear modulator and the DDMZM output signal Ετχ can be written as Eout approximated by the following relationship:

^■•out exp (; ) ^ [l + jS₁ + jS₂)] = A [l - j + (5₂ + jS₁ ] (4) where A

This method based on small signal condition has the benefit to have the DDMZM working at the quadrature bias point. However, this method also has disadvantages. Indeed, the small signal condition leads to a poor performance in terms of optical signal-to-noise ratio (OSNR) and sensitivity. In addition, significant error floor will appear if the drive signal is large.

In the case of a IQ modulator, if the phase shift between the in-phase (I) and quadrature (Q) arms are π/2, then the optical carrier signal can be written in a complex form as (a+bj), where the parameters a and b stand for the optical carrier signal in the respective I and Q arms. If the I and Q arms use the MZM structure in such a manner that the IQ modulator can be referred to as a IQMZM, then the transfer function of each arm is: cos— π (5) where V is the bias voltage added to the arm, ν_π is the voltage needed to induce a π phase shift between the arms of the two phase modulators.

Thus, if the bias voltages of the I and Q arms are respectively V_a and Vb, then the optical carrier signal (i.e., the optical DC carrier signal) in each one of both arms can be respectively expressed by: a = cos— π

2V„

3 b = cos—^v b π

2V_n (6)

Moreover, if the RF signals (kiRFl , k₂RF2) are added to the two arms, then the optical carrier signal can be rewritten from (a, b) to (a', b') according to the following relationships: a' = a+kiRFl b' = b+k₂RF2 (7) where k =—sin— π and k₇ =—sin— π are modulation slopes.

Thus, from the relationships (6) and (7), it can observed that not only the nonlinearity of the modulation, coming from the cosine part of the transfer function, but also the modulation slope will vary with the bias voltage (V_a, Vb).

A solution to this bias-related issue would be to use the method of inverting the transfer function. However, it is not so easy to apply and always leads to penalties. In addition, there will be a non-zero angle denoted β between the vector of the optical carrier signal (a, b) and the vector of the modulated optical signal (Si), as depicted in Fig. 2 showing a vector plane representation of the optical carrier signal (a, b) and the modulation optical signal (Si, S₂). In fact, it is known that the beating process between the optical carrier signal and the modulated optical signal is a dot multiplication process and the non-zero angle (i.e., β) between them will reduce the amplitude by a factor equal to cosP between the optical DC carrier signal and the target signal, which will reduce the detected signal intensity.

SUMMARY

It is therefore an object of the present invention to provide apparatuses and methods capable of optimizing the performance of an optical transceiver by mitigating the non-orthogonality and the nonlinearity of a complex modulator implemented at the transmitter side.

The object is achieved by the features of the independent claims. Further embodiments of the invention are apparent from the dependent claims, the description and the drawings. According to a first aspect, the invention relates to a digital signal processing (DSP) module in a transmitter (Tx) of an optical transceiver. The DSP module is adapted to perform a bias- related linear transform (M_a) in order to align, in a vector plane, the vector of an optical carrier signal with the vector of a modulated optical signal that is modulated by a modulator implemented inside the Tx, and to perform a digital pre-distortion (DPD) in order to compensate for the nonlinearity of the modulator.

Thereby, the performance (e.g., the OSNR) of the optical transceiver can be improved thanks to a bias-related linear transform (M_a) allowing to compensate for the non-orthogonality of the modulator and a digital pre-distortion allowing to mitigate the nonlinearity of the modulator. Indeed, the detected signal intensity can increase due to the vector alignment allowing the cosine of the angle between the vector of the optical carrier signal and the vector of the optical signal modulated by the modulator to increase, and in addition, the nonlinearity of the modulator can be compensated.

According to a first implementation of the DSP module according to the first aspect, the angle (β) between the vector of the optical carrier signal and the vector of the modulated optical signal verifies the relationship: β = π\*π, where m denotes an integer and π denotes an angle expressed in radians.

Thereby, an optimal performance of the optical transceiver can be obtained in response to an optimal compensation of the non-orthogonality of the modulator thanks to the perfect alignment between the vector of the optical carrier signal and the vector of the modulated optical signal.

According to a second implementation of the DSP module according to the first aspect or the first implementation of the first aspect, the bias-related linear transform (M_a) is added to any portion of an existing linear process of the DSP module and is located between the portion of a symbol generation and the portion of the DPD.

Thereby, an easy implementation of the bias-related linear transform (M_a) can be obtained.

The above object is also solved in accordance with a second aspect.

5 According to the second aspect, the invention relates to a transmitter (Tx) comprising the DSP module as claimed in the first aspect or any one of the implementations of the first aspect, and the modulator as specified in the first aspect.

According to a first implementation of the Tx according to the second aspect, the modulator is a dual-drive Mach-Zehnder modulator (DDMZM) or an in-phase/quadrature (IQ) modulator.

The above object is also solved in accordance with a third aspect.

According to the third aspect, the invention relates to an intensity-modulation (IM) direct- detection (DD) system for transmitting and receiving signals in an optical transceiver. The IM DD system comprises the transmitter (Tx) as claimed in the second aspect or the first implementation of the second aspect, and a receiver (Rx).

The above object is also solved in accordance with a fourth aspect.

According to the fourth aspect, the invention relates to a digital pre-distortion (DPD) method for compensating for a nonlinearity of a modulator in a transmitter (Tx) of an optical transceiver. The DPD method comprises the step of obtaining an optical signal (T) modulated by the modulator, the modulated optical signal (T) verifying the relationship: T = S + D, where S denotes a target signal (S) and D denotes a distortion signal (D), the step of decomposing the modulated optical signal (T), the step of deriving the distortion signal (D) from a comparison between the modulated optical signal (T) and the target signal (S), and the step of converting the target signal (S) into a pre-distorted signal (S') by subtracting a signal (D*) proportional to the distortion signal (D) from the target signal (S) according to the relationship: S' = S - D*.

According to a first implementation of the method according to the fourth aspect, the step of deriving the distortion signal (D) is based on decomposing the modulated optical signal (T) in a series of polynomials using a Taylor series. According to a second implementation of the method according to the fourth aspect or the first implementation of the fourth aspect, the modulator is either an in-phase/quadrature (IQ) modulator or a dual-drive Mach-Zehnder modulator (DDMZM). In the case of the IQ modulator, D* equals D. In the case of the DDMZM, the target signal S is split into the respective target signals SI and S2 corresponding to the two drive signals in each arm of the DDMZM and the relationship: S' = S - D* is decomposed into the equation system: S' l = SI

6 - D/2 and S'2 = S2 + D/2, where S' l and S'2 are the pre-distorted signals corresponding to the respective target signals SI and S2, D* = D/2 if related to SI and D* = -D/2 if related to S2.

The above object is also solved in accordance with a fifth aspect. According to the fifth aspect, the invention relates to a method for enhancing a system performance of an optical transceiver. The method comprises the step of performing a bias- related linear transform (M_a) at a transmitter (Tx) of the optical transceiver in order to align, in a vector plane, the vector of an optical carrier signal with the vector of a modulated optical signal that is modulated by a modulator implemented inside the Tx, and the step of performing a digital pre-distortion (DPD) at the Tx in order to compensate for the nonlinearity of the modulator.

The above object is also solved in accordance with a sixth aspect.

According to the sixth aspect, the invention relates to a method for selecting a bias-related linear transform (M_a) inside a digital signal processing (DSP) module in a transmitter (Tx) of an optical transceiver. The method comprises the step of varying the coefficients of the bias- related linear transform (M_a) through a variation of the bias voltage, the step of measuring a quality performance versus the variation of the coefficients, and the step of selecting the bias- related linear transform (M_a) whose coefficients correspond to the best quality performance.

According to a first implementation of the method according to the sixth aspect, the step of measuring the quality performance comprises measuring a signal-to-noise ratio (SNR) or a quality factor (Q-factor) or a bit error rate (BER) or an error vector magnitude (EVM), the SNR and the Q-factor varying in a same direction as the quality performance and the BER and the EVM varying in an opposite direction to the quality performance.

The above object is also solved in accordance with a seventh aspect. According to the seventh aspect, the invention relates to a method for selecting a bias-related linear transform (M_a) inside a digital signal processing (DSP) module in a transmitter (Tx) of an optical transceiver. The method comprises the step of adding a respective pilot signal (si, s2) to each arm of both drive signals (dl, d2) of a modulator implemented inside the Tx in order to have a respective target signal (sl+dl, s2+d2) to be modulated through the modulator, the step of detecting through a photo-detector (PD) the respective modulated

7 target signal (Rx_sl+dl, Rx_s2+d2), the step of comparing the respective modulated target signal (Rx_sl+dl, Rx_s2+d2) and the respective target signal (sl+dl, s2+d2), and the step of selecting the bias-related linear transform (M_a) whose coefficients correspond to the maximum value of cross-correlation (xcorr(Rx_sl+dl, sl+dl), xcorr(Rx_s2+d2, s2+d2)) between the respective modulated target signal (Rx_sl+dl, Rx_s2+d2) and the respective target signal (sl+dl, s2+d2).

According to a first implementation of the method according to the seventh aspect, the PD is located at the Tx side or at the receiver (Rx) side of the optical transceiver.

The above object is also solved in accordance with an eighth aspect. According to the eighth aspect, the invention relates to a computer program comprising a program code for performing the method according to any one of the fourth to seventh aspects and their respective implementations when executed on a computer or with a real time chip.

Thereby, the method can be performed in an automatic and repeatable manner.

The computer program can be run/executed by the above apparatuses. More specifically, it should be noted that the above apparatuses may be implemented based on a discrete hardware circuitry with discrete hardware components, integrated chips or arrangements of chip modules, or based on a signal processing device or chip controlled by a software routine or program stored in a memory, written on a computer-readable medium or downloaded from a network such as the Internet. It shall further be understood that a preferred embodiment of the invention can also be any combination of the dependent claims or above embodiments with the respective independent claim.

These and other aspects of the invention will be apparent and elucidated with reference to the embodiments described hereinafter.

LIST OF ABBREVIATIONS

IMDD intensity-modulation direct-detection

8 DCM dispersion compensation module

CD chromatic dispersion

MZM Mach-zehnder modulator

DDMZM dual-drive MZM

IQ in-phase/ quadrature

Tx transmitter

RX receiver

DC direct current

RF radio frequency

DAC digital-to-analog converter

SNR signal-to-noise ratio

OSNR optical SNR

PD photo detector

DSP digital signal processing

DPD digital pre-distortion

Q-factor quality factor

BER bit error rate

EVM error vector magnitude

BRIEF DESCRIPTION OF THE DRAWINGS

In the following detailed portion of the present disclosure, the invention will be explained in more detail with reference to the exemplary embodiments shown in the drawings, in which:

Fig. 1 shows a conventional DDMZM in a transmitter (Tx) of an optical transceiver;

Fig. 2 shows a vector plane representation of an optical carrier signal (a, b) and a modulation optical signal (Si, S₂); Fig. 3 illustrates the modulation theory of the DDMZM biased at the quadrature point under small signal condition;

Fig. 4 illustrates the modulation theory of the DDMZM biased at a point other than the quadrature point under small signal condition;

Fig. 5 shows a schematic flow diagram describing the scan method for obtaining the appropriate bias-related linear transform, according to an embodiment of the present invention;

Fig. 6 shows a schematic flow diagram describing the pilot tone method for obtaining the appropriate bias-related linear transform, according to an embodiment of the present invention; and

Fig. 7 shows a structure of a digital signal processing (DSP) module 100 implemented in a transmitter (Tx) of an optical transceiver, according to an embodiment of the present invention.

Identical reference signs are used for identical or at least functionally equivalent features.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Referring to Fig. 1, a conventional DDMZM consists of two independent phase modulators. Considering the fact that a phase modulator does not change the intensity of the signal, it is then possible to plot the two modulated optical signals in a same unity circle (i.e., its radius equals unity) and their sum is the output signal of the DDMZM.

Fig. 3 illustrates the modulation theory of the DDMZM biased at the quadrature point under small signal condition, wherein the first circle represents the case of the modulator biased at any bias point, the second circle represents the case of the modulator biased at the quadrature bias point, the third circle depicts the RF signals when the modulator is biased at the quadrature bias point, and the fourth circle depicts the alignment of the sum vector (denoted by DC in Fig. 3) of the two optical DC carrier signals with the target signal that is the component (denoted by a) of the modulated optical signal (a, b). In a direct detection (DD)

10 system, only one dimension of the signal (i.e., the component a of the target signal in the present example) can be detected.

As can been gathered therefrom, when the DDMZM is biased at the quadrature point, the phase shift between its two arms is equal to π/2 (i.e., the two optical DC carrier signals in the respective I and Q arms are orthogonal to each other) (cf. 32 and 33) and the RF signals are also orthogonal to each other (cf. 33). In order to align the component a of the modulated optical signal with the sum vector (DC) of the two optical DC carrier signals, a π/4 rotation is then needed as the angle between each of them usually equals π/4 (cf. 34). Thereby, the maximum beating signal between the sum vector (DC) and the target signal (a) can be obtained.

However, when the phase shift between the two phase modulators of the DDMZM is not π/2 (also denoted by pi/2) anymore but α (≠π/2) as depicted in Fig. 4 wherein the DDMZM is biased at a point other than the quadrature point, it results therefrom that the orthogonality between the two RF signals is broken, and a mere phase rotation as shown in Fig. 3 cannot recover this orthogonality.

Fig. 4 illustrates the modulation theory of the DDMZM biased at a point other than the quadrature point under small signal condition.

Assuming that the target modulated orthogonal signal is given by: a+jb, as disclosed in Fig. 4 on the right, it is then possible to derive the RF signal (denoted by a' and b') from the target modulated orthogonal signal (denoted by a and b) according to the following relationships:

1 -a , b

b' α ^~ α \

² L^cos( - ) sin(---)J (8) which can be otherwise written in a matrix form as follows:

cos ^y-2 -— 2' sin ^y-2 -— 2^J where M_a is a bias-related linear transform related to the a phase shift.

11 Thus, to get an appropriate bias-related linear transform M_a is the first step towards optimizing the performance of the optical transceiver.

Several methods can be used to obtain the coefficients of the bias-related linear transform M_a.

As depicted in Fig. 5, a first method (also named scan method) for selecting an appropriate bias-related linear transform M_a can consist, starting from an initialized value of the phase shift a, in varying the coefficients of the bias-related linear transform M_a through a variation of the bias voltage, measuring a quality performance versus the variation of the coefficients, and selecting the bias-related linear transform M_a whose coefficients correspond to the best quality performance. The quality performance can be related, for example, to a signal-to-noise ratio (SNR), a quality factor (Q-factor), a bit error rate (BER), or an error vector magnitude (EVM), the SNR and the Q-factor varying in a same direction as the quality performance and the BER and the EVM varying in an opposite direction to the quality performance.

As depicted in Fig. 6, another method (also named pilot tone method) for selecting an appropriate bias-related linear transform M_a can consist in adding a respective pilot signal (si, s₂) to each arm of both drive signals (di, d₂) of a modulator (e.g., the DDMZM), each arm having a respective bias- voltage denoted by bi and b₂ and the modulator being implemented inside the transmitter (Tx) of an optical transceiver (as shown, for example, in Fig. 1), in order to have a respective target signal (si+di, s₂+d₂) to be modulated through the modulator. It can further consist in detecting through a photo-detector (PD), which can be located at the Tx side or at the receiver (Rx) side of the optical transceiver, the respective modulated target signal (Rx_si+di, Rx_s₂+d₂), comparing the respective modulated target signal (Rx_si+di,

Rx_s₂+d₂) and the respective target signal (si+di, s₂+d₂), and selecting the bias-related linear transform M_a whose coefficients correspond to the maximum value of cross-correlation (xcorr(Rx_si+di, si+di), xcorr(Rx_s₂+d₂, s₂+d₂)) between the respective modulated target signal (Rx_si+di, Rx_s₂+d₂) and the respective target signal (si+di, s₂+d₂). By using the pilot signals si and s₂, the bias-related linear transform M_a can thus be tracked and not just scanned.

It should be noted that this linear transform M_a is suitable not only for the DDMZM but also for the IQ modulator such as the IQMZM. In a general manner, it is suitable for any modulator whose transfer function has a cosine profile versus the bias voltage, and in particular suitable for a LiNb03 DDMZM.

12 As regards the nonlinearity of the modulator such as the DDMZM and the IQ modulator, the distortion can be viewed as a high order signal, which is rather small with respect to the driven signals, and the nonlinearity of the modulator will be mitigated using a digital pre- distortion (DPD). Referring to Fig. 7, the linear transform M_a and the DPD can be implemented in a transmitter (Tx) of an optical transceiver, and in particular inside a digital signal processing (DSP) module 100 corresponding, for example, to the processor module of Fig. 1. The DSP module 100 is thus adapted to perform the bias-related linear transform (M_a) in order to align, in the vector plane, the vector of the optical carrier signal with the vector of the optical signal that is modulated by the modulator implemented inside the Tx and also adapted to perform the DPD in order to compensate for the nonlinearity of the modulator. The alignment is achieved once the angle (β, as depicted in Fig. 2) between the vector of the optical carrier signal and the vector of the modulated optical signal verifies the relationship: β = π\*π, where m denotes an integer and π denotes an angle expressed in radians. As shown in Fig. 7, the bias-related linear transform (M_a) can be added to any portion ((a), (b), (c)) of an existing linear process of the DSP module between the portion of a symbol generation and the portion of the DPD. Thus, the bias-related linear transform (M_a) can be located either at the rear part (a) of the existing linear process or at the front part (b) thereof or inside (c) thereof. The DPD method for compensating for the nonlinearity of the modulator comprises several steps amongst which the step of obtaining an optical signal (T) modulated by the modulator, the modulated optical signal (T) then verifying the relationship:

T = S + D (10) where S denotes a target signal and D denotes a distortion signal, the step of decomposing the modulated optical signal (T), the step of deriving the distortion signal (D) from a comparison between the modulated optical signal (T) and the target signal (S), and the step of converting the target signal (S) into a pre-distorted signal (S') by subtracting a signal (D*) proportional to the distortion signal (D) from the target signal (S) according to the relationship:

S' S - D* (11)

13 The step of deriving the distortion signal (D) is based on decomposing the modulated optical signal (T) in a series of polynomials using, for example, a Taylor series.

Referring to the relationship (11), D* equals D in the case where the modulator is an IQ modulator. On the other hand, in the case of a DDMZM, the target signal S is split into the respective target signals S 1 and S2 corresponding to the two drive signals in each arm of the DDMZM and S' is then decomposed into the equation system:

S' l = S1 - D/2

S'2 = S2 + D/2 (12) where S' l and S'2 are the pre-distorted signals corresponding to the respective target signals S 1 and S2, D* = D/2 if related to S 1 , and D* = -D/2 if related to S2.

In summary, the present invention relates to a digital signal (DSP) processing module in a transmitter (Tx) of an optical transceiver. The DSP module performs a bias-related linear transform (M_a) in order to align, in a vector plane, the vector of an optical carrier signal with the vector of a modulated optical signal that is modulated by a modulator implemented inside the Tx, and also a digital pre-distortion (DPD) in order to compensate for the nonlinearity of the modulator. The DPD method mainly consists in converting a target signal into a pre- distorted signal by subtracting a signal proportional to the distortion signal from the target signal. The non-orthogonality of the modulator is mitigated by an appropriate bias-related linear transform that is selected as to obtain the best quality performance using a scan method or a maximum value of cross-correlation using a pilot tone method.

While the invention has been illustrated and described in detail in the drawings and the foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive. The invention is not limited to the disclosed embodiments. From reading the present disclosure, other modifications will be apparent to a person skilled in the art. Such modifications may involve other features, which are already known in the art and may be used instead of or in addition to features already described herein.

The invention has been described in conjunction with various embodiments herein. However, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure and the appended claims. In the claims, the word "comprising" does not exclude other elements or

14 steps, and the indefinite article "a" or "an" does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. A computer program may be stored/distributed on a suitable medium, such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.

Although the present invention has been described with reference to specific features and embodiments thereof, it is evident that various modifications and combinations can be made thereto without departing from the spirit and scope of the invention. The specification and drawings are, accordingly, to be regarded simply as an illustration of the invention as defined by the appended claims, and are contemplated to cover any and all modifications, variations, combinations or equivalents that fall within the scope of the present invention.

15

Claims

A digital signal processing, DSP, module in a transmitter, Tx, of an optical transceiver, the DSP module being adapted to perform:

- a bias-related linear transform (M_a) in order to align, in a vector plane, the vector of an optical carrier signal with the vector of a modulated optical signal that is modulated by a modulator implemented inside the Tx; and

- a digital pre-distortion, DPD, in order to compensate for the nonlinearity of the modulator.

The DSP module of claim 1, wherein the angle (β) between the vector of the optical carrier signal and the vector of the modulated optical signal verifies the following relationship (1):

β = ιη*π (1) where m denotes an integer and π denotes an angle expressed in radians.

The DSP module of claim 1 or 2, wherein the bias-related linear transform (M_a) is added to any portion of an existing linear process of the DSP module and is located between the portion of a symbol generation and the portion of the DPD.

A transmitter, Tx, comprising:

- the DSP module as claimed in any one of claims 1 to 3;

- the modulator as specified in claim 1.

The Tx of claim 4, wherein the modulator is a dual-drive Mach-Zehnder modulator, DDMZM, or an in-phase/quadrature, IQ, modulator.

An intensity-modulation, IM, direct-detection, DD, system for transmitting and receiving signals in an optical transceiver, the IM DD system comprising:

- the transmitter, Tx, as claimed in any one of claims 4 to 5; and

- a receiver, Rx.

A digital pre-distortion, DPD, method for compensating for a nonlinearity of a modulator in a transmitter, Tx, of an optical transceiver, the DPD method comprising:

- obtaining an optical signal (T) modulated by the modulator, the modulated optical signal (T) verifying the following relationship (2):

16 T = S + D (2) where S denotes a target signal (S) and D denotes a distortion signal (D);

- decomposing the modulated optical signal (T);

- deriving the distortion signal (D) from a comparison between the modulated

optical signal (T) and the target signal (S); and

- converting the target signal (S) into a pre-distorted signal (S') by subtracting a signal (D*) proportional to the distortion signal (D) from the target signal (S) according to the following relationship (3):

S' = S - D* (3)

The DPD method of claim 7, wherein the step of deriving the distortion signal (D) is based on decomposing the modulated optical signal (T) in a series of polynomials using a Taylor series.

The DPD method of claim 7 or 8, wherein:

- the modulator is either an in-phase/quadrature, IQ, modulator or a dual-drive

Mach-Zehnder modulator, DDMZM;

- in the case of the IQ modulator, D* equals D; and

- in the case of the DDMZM, the target signal S is split into the respective target signals SI and S2 corresponding to the two drive signals in each arm of the DDMZM and the relationship (3) is decomposed into the following equation system (4):

S' l = S1 - D/2

S'2 = S2 + D/2 (4) where S' l and S'2 are the pre-distorted signals corresponding to the respective target signals SI and S2, D* = D/2 if related to SI and D* = -D/2 if related to S2.

A method for enhancing a system performance of an optical transceiver, the method comprising:

- performing a bias-related linear transform (Ma) at a transmitter, Tx, of the optical transceiver in order to align, in a vector plane, the vector of an optical carrier signal with the vector of a modulated optical signal that is modulated by a modulator implemented inside the Tx; and

- performing a digital pre-distortion, DPD, at the Tx in order to compensate for the nonlinearity of the modulator.

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11. A method for selecting a bias-related linear transform (M_a) inside a digital signal processing, DSP, module in a transmitter, Tx, of an optical transceiver, the method comprising:

- varying the coefficients of the bias-related linear transform (Ma) through a

variation of the bias voltage;

- measuring a quality performance versus the variation of the coefficients; and

- selecting the bias-related linear transform (Ma) whose coefficients correspond to the best quality performance.

The method of claim 11 , wherein the step of measuring the quality performance comprises measuring a signal-to-noise ratio, SNR, or a quality factor, Q-factor, or a bit error rate, BER, or an error vector magnitude, EVM, the SNR and the Q-factor varying in a same direction as the quality performance and the BER and the EVM varying in an opposite direction to the quality performance.

A method for selecting a bias-related linear transform (M_a) inside a digital signal processing, DSP, module in a transmitter, Tx, of an optical transceiver, the method comprising:

- adding a respective pilot signal (si, s2) to each arm of both drive signals (dl, d2) of a modulator implemented inside the Tx in order to have a respective target signal (sl+dl, s2+d2) to be modulated through the modulator;

- detecting through a photo-detector, PD, the respective modulated target signal (Rx_sl+dl, Rx_s2+d2);

- comparing the respective modulated target signal (Rx_sl+dl , Rx_s2+d2) and the respective target signal (sl+dl, s2+d2); and

- selecting the bias-related linear transform (Ma) whose coefficients correspond to the maximum value of cross-correlation (xcorr(Rx_sl+dl, sl+dl),

xcorr(Rx_s2+d2, s2+d2)) between the respective modulated target signal (Rx_sl+dl, Rx_s2+d2) and the respective target signal (sl+dl, s2+d2).

14. The method of claim 13, wherein the PD is located at the Tx side or at the receiver, Rx, side of the optical transceiver.

A computer program comprising a program code for performing the method according to any one of claims 10 to 14 when executed on a computer or with a real time chip.

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