Efficiency of nonlinear compensation for WDM-PON based ofdm using optical back propagation

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Ngo Thi Thu Trang, Tran Thuy Binh, Bui Trung Hieu, Nguyen Duc Nhan

EFFICIENCY OF NONLINEAR

COMPENSATION FOR WDM-PON BASED

OFDM USING OPTICAL BACK

PROPAGATION

Ngo Thi Thu Trang , Tran Thuy Binh, Bui Trung Hieu, Nguyen Duc Nhan

Posts and Telecommunications Institute of Technology

^*Abstract: The Kerr nonlinearity is the main obstacle

that limits the performance of the orthogonal frequency

division multiplexing wavelength division multiplexing

(OFDM-WDM) system. Moreover, the nonlinear

compensation method that is feasible and adds no more

complexity to the receiver is very necessary for the long-

range passive optical network (LR-PON) applications. In

this paper, we investigate the nonlinear and dispersion

compensation efficiency in OFDM-WDM system using

an advanced optical back propagation (OBP) approach

based on split-step Fourier method. In the OBP, the real

optical devices such as the high-nonlinear fiber (HNLF),

fiber Bragg grating (FBG) and nonlinear waveguide are

used as a nonlinear operator, a dispersive operator and

phase conjugated media, respectively. The advanced

OBP is located in the transmitter site that is very suitable

for LR-PON applications. The compensation efficiency

of the OBP in OFDM-WDM systems is evaluated by an

analytical model and then Monte-Carlo simulations. The

obtained results from both analytical evaluation and

simulation show that the OBP can improve remarkably

the system performance when the parameters of OBP

such as dispersion and pump power are properly selected.

or higher transmitting power is required to extend the

range of LR-PONs. Therefore, the nonlinear Kerr effects

become a critical concern in these networks, especially in

WDM LR-PONs.

There are many solutions in the digital domain which

have been proposed to compensate the nonlinearity of the

systems [4-8]. Almost these techniques provide a good

PAPR reduction to eliminate the nonlinearity in all parts

of the system, the transmitter, fiber channel and the

receiver. However, each nonlinear compensator can only

applied to each channel so that they make the complexity

and cost of the OFDM-WDM system increase

exponentially.

Nonlinearity in the fiber, especially the Kerr effect,

can be mitigated by mid-span spectrum inversion (MSSI)

method in the optical domain [9]. The MSSI using optical

phase conjugation (OPC) module can reduce significantly

not only Kerr nonlinearities but also group velocity

dispersion in WDM systems [10], [11]. However, this

method requires the OPC module placed in the middle of

transmission link to ensure the power symmetry that is not

feasible in LR-PON. The optical back propagation (OBP)

solution using dispersion compensation fibers (DCFs) and

high nonlinear fibers (HNLFs), proposed by Kumar et al

[12], is placed in the receiver site of the optical systems.

The OBP addresses the main drawback about strict

location requirement of MSSI. Moreover, this solution has

been proposed in the single channel OFDM based LR-

PON that demonstrated its nonlinearity compensation

efficiency [13].

Keywords:

Multiplexing

Orthogonal

(OFDM),

Frequency

Wavelength

Division

Multiplexing (WDM), Nonlinear compensation, Optical

Back Propagation (OBP), Long-range Passive Optical

Network (LR-PON).

I. INTRODUCTION

In this paper, we investigate the efficiency of optical

back propagation technique in nonlinearity compensation

for OFDM-WDM system. The OBP module is located at

the transmitter site that is similar to that proposed in [13].

This OBP consists of HNLFs, fiber Bragg gratings

(FBGs) and an OPC. The HNLF is the nonlinear operator

to compensate the nonlinearity. The FBG is the linear

operator to compensate the dispersion. The signal after

HLNFs and FBGs is conjugated by the OPC to transmit

via the standard single mode fiber to the receiver. A

theoretical analysis model is also used to evaluate the

efficiency of nonlinearity compensation in this study.

Both analytical evaluation and simulation results show

that our proposed OBP technique can improve remarkably

the performance of the OFDM WDM system when the

parameters of OBP module are properly selected. These

The orthogonal frequency division multiplexing

(OFDM) has become the promising solution for the

WDM-based long-range passive optical networks (WDM

LR-PONs) [1], [2]. The OFDM WDM LR-PON can be

extended both the capacity and the range thanks to the

advantages such as highly spectral efficiency, highly

chromatic dispersion tolerance. Moreover, the systems

can get the simple design and cost efficiency when the

intensity modulation and direct-detection (IM-DD)

method is employed [3]. However, a larger power budget

Correspondence: Ngo Thi Thu Trang

Email: [email protected]du.vn

Manuscript communication: received: 10/05/2020, revised:

11/25/2020, accepted: 11/30/2020.

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EFFICIENCY OF NONLINEAR COMPENSATION FOR WDM-PON BASED OFDM USING OPTICAL BACK

PROPAGATION

achieved results also show that the advanced OBP is very

suitable to deploy in OFDM WDM LR-PON.

Nonlinear Kerr effects in the fiber including self-phase

modulation (SPM), cross phase modulation (XPM), and

four-wave mixing (FWM) are the dominant obstacle to

extend the capacity and transmission distance of the

multichannel optical communication systems [14]. In such

systems, all the nonlinear effects such as XPM, SPM are

considered as FWM between all subcarriers. Thus, the

evolution of the FWM field (spectrally located at 휔_퐹)

resulting from the nonlinear wave mixing between three

other optical waves (k, l, m such that 휔_퐹= 휔_푘+ 휔_푙−

휔_푚) can be expressed as [15]

The rest of this paper is organized as follows. Section

2 gives analytical descriptions of nonlinear wave mixing

efficiencies of OFDM WDM systems that influence to the

nonlinearity compensation efficiency of OBP technique.

Simulations are discussed in section 3. Finally, section 4

concludes this paper.

II. THEORETICAL EVALUATION

(

)

−훼+푖∆훽 퐿

푒

푖훽퐿

−1

Optical OFDM Transmitter #N

Optical OFDM Transmitter #2

퐸_퐹(퐿) = 푖 ^훾퐷퐸_푘0 퐸_푙0 퐸_푚0 푒

(1)

∗

( ) ( ) ( )

−훼+푖∆훽

( )

where 퐸_푠푧 is the optical field spectrally located at 휔_푠

measured at distance z, and L is the transmission fiber

length. γ, α and β are nonlinear, attenuation coefficients

and propagation factor of a fiber, respectively. D is the

degeneracy factor of FWM. SPM is considered that three

waves of FWM are coincided, 휔_푘= 휔_푙= 휔_푚, and 퐷 =

1. While XPM is considered as degenerate FWM effect,

in which two of mixing components have the same

frequency, 휔_푘= 휔_푙≠ 휔_푚, and 퐷 = 3. The remaining

case that three mixing components are totally

different, 휔_푘≠ 휔_푙≠ 휔_푚, is called non-degenerate FWM

or simply FWM, and 퐷 = 6. ∆훽 = 훽_푘+ 훽_푙− 훽_푚− 훽_퐹is

the phase mismatch coefficient of the fiber, relates to the

dispersion coefficient 퐷_푐as follows [15]

OBP

Data input

EDFA

MZM

Optical OFDM Transmitter #1

Data output

LPF

OBF

2휋휆

퐷_푐∆푓²(푘 − 푚)(푙 − 푚)

(2)

OFDM

Receiver

∆훽 =

푐

where ∆푓 is channel spacing. It can be obviously seen

from Eq. 1 that the amplitude of FWM field depends

much on channel spacing. To evaluate how the OBP could

compensate the nonlinearity of the OFDM WDM LR-

PON, the powers of FWM field in two cases a link with

OBP and a link without OBP are compared. Thus, Eq. 1

describes the FWM field in case of the OFDM WDM LR-

PON link without OBP. The total power of nonlinear

Figure 1. Block diagram of IM-DD OFDM WDM system

using OBP as pre-compensation.

Fig. 1 shows the schematic of IM-DD optical OFDM

WDM system where the OBP module is located at the

transmitter site. The OBP module consists of steps of

HLNF and FBG, an OPC module and an Erbium Doped

Fiber Amplifier (EDFA) as described in details in [13].

With the advantages of system design and cost efficiency,

the IM-DD OFDM WDM is the good solution for LR-

PON applications. For the sake of simplicity, we assume

that insertion loss of all components of the LR-PON is

ignored. Here, our OBP plays a role as pre-compensation

in optical domain of the LR-PON. The OFDM transmitted

signals are multiplexed in wavelength domain before they

propagates via the OBP section, and then it is phase

conjugated before propagating in the transmission fiber

link. The nonlinear and dispersion distortions of the OBP

section are based on the split-step Fourier method in the

optical domain [14]. The FBG is used as dispersive step

because of its pros such as negligible nonlinearity and

insertion loss, very compact size, and dispersive

tunability. The HNLF is used as nonlinear step due to its

very low dispersion distortion and negligible loss. The

OPC using the nonlinear waveguide produces the

conjugated signal by four-wave mixing (FWM) process to

transmit along the single mode fiber (SMF) to the receiver

site. The EDFA is used to control the signal input power

of the SMF link. By using real photonic device, our OBP

overcomes the cons of digital back propagation (DBP)

method including the computational complexity and less-

flexible configuration [8].

product 퐸_퐹(퐿) ²with assumption that the signal powers

in all channels are equal can be written as [16]

훼²퐿²_푒푓푓

훼²+ ∆훽²

퐷²훾²

4푒^−훼퐿푠푖푛²(∆훽퐿/2)

푃³[

] [1 +

]

( )

푃_퐹퐿 =

(1 − 푒^−훼퐿

)

(3)

where P is the power of each mixing component

−αL

(

)

/α is the

launched into the fiber and L_eff= 1 − e

effective length.

We next consider the nonlinear Kerr power in OBP-

assisted OFDM WDM LR-PON link. The link can be

divided into two segments, OBP segment and SMF

segment. The OFDM signal first is sent through the OBP

segment, phase conjugated at OPC and then transmitted

via the SMF segment. The nonlinearity arisen in the OBP

segment will be compensated in the SMF segment. Given

that after two segments all dispersion effect are

compensated, so the total FWM field in this case will be

∗

푖훽퐿

[

]

퐸_퐹(퐿) = 퐸_퐹(푆푀퐹) + 퐸_퐹(푂퐵푃) 푒

(4)

Applying the Eq. 1 for the OBP segment, the nonlinear

field can be obtain as

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Figure 2 demonstrates the dependent of nonlinear Kerr

퐸_퐹(푂퐵푃) =

(−훼+푖∆훽

푂퐵푃 푂퐵푃

−1

)퐿

power in the OBP-assisted OFDM WDM LR-PON link

on the factor K with the channel spacing of 12.5 GHz and

the fiber link length of 80 km. As can be seen from the

figure, when K is small, the phase mismatch of the OBP is

small that makes the nonlinear effect arisen by OBP

become too strong. At the value of K is smaller than 5, the

nonlinear power in the link with OBP evenly exceeds that

in the link with our OBP. When K increases, the nonlinear

Kerr power of the OBP reduces remarkably. However,

under the asymmetry power condition, the OBP cannot

compensate perfectly the nonlinearity of the SMF. That’s

why the residual nonlinear FWM power in the case of

using OBP become saturation when K is very large

although this value is always smaller than the FWM

power in the case of not using OBP. Consequently, there

is an optimum value of K where the nonlinear Kerr power

in the link with OBP is minimum.

퐷

푒

푖 ^훾

푂퐵푃

∗

푖훽

퐿

푂퐵푃 푂퐵푃

( ) ( ) ( )

퐸_푘0 퐸_푙0 퐸_푚0 푒

−훼+푖∆훽

푂퐵푃

(5)

In the OBP segment, both the loss of HLNFs and

FBGs is negligible so that the attenuation coefficient of

OBP can be omitted. To ensure that the dispersion arisen

in the OBP segment is fully compensated in the SMF

segment, 훽_푂퐵푃퐿_푂퐵푃= 훽퐿 or 훽_퐹퐵퐺퐿_푂퐵푃= 훽퐿 . For more

convenient in calculation, we define 퐾 = 훽_퐹퐵퐺/훽. Hence,

the nonlinear field from the OBP segment can be reduced

푖훽퐿

퐸_퐹(푂퐵푃) = 푖 ^훾

(6)

퐷

푒

푖훽퐿

−1

퐻퐿푁퐹

∗

( ) ( ) ( )

퐸_푘0 퐸_푙0 퐸_푚0 푒

푖퐾∆훽

By the end of the OBP segment, the mixing fields (k, l

and m) are phase shifted due to the accumulation of

(

)

퐿

dispersion along the OBP segment 푒^{푖 ∆훽}

+훽

푂퐵푃

푂퐵푃 푂퐵푃

푒

^{푖(∆훽+훽)퐿}. Then they are conjugated to propagation via the

SMF segment that results the following nonlinear field

w/o OBP

w OBP

(

)

−훼+푖∆훽 퐿

푒

−1

퐸_퐹(푆푀퐹) = 푖 ^훾퐷퐸 0 퐸 0 퐸_푚0 푒

^∗( ) ^∗( ) ( )

−푖∆훽퐿

-10

-20

-30

-40

-50

-60

푘

푙

−훼+푖∆훽

(7)

Substituting Eq. (6) and Eq. (7) into Eq. (4), we can

obtain the total nonlinear field generated by the OBP-

assisted OFDM WDM LR-PON link as follow

(

)

−훼+푖∆훽 퐿

퐷

푒

−1

^∗( ) ^∗( ) ( )

−푖∆훽퐿

퐸_퐹(퐿) = 푖 퐸_푘0 퐸_푙0 퐸_푚0 [훾푒

−

Factor K

−훼+푖∆훽

−푖훽퐿

푒

−1

Figure 2. FWM power as a function of factor K with the

channel spacing of 12.5 GHz and the SMF fiber length of

80km.

훾_퐻푁퐿퐹

]

(8)

−푖퐾∆훽

Deploying lossless for the SMF segment (훼 = 0), the

signal power symmetry for the link with OBP can be

satisfied. In this case, Eq. (8) shows that the fully

nonlinear compensation will be attained in the OBP-

assisted OFDM WDM LR-PON link with fully dispersion

management. Unfortunately, the attenuation coefficient of

the SMF fiber cannot be omitted that breaks the power

symmetric condition. This reduces the efficiency of the

OBP in nonlinear compensation in comparison with MSSI

technique. Thence, the total FWM power of the OBP-

assisted OFDM WDM LR-PON link is given as

w/o OBP

-20

-40

w OBP

-60

-80

-100

-120

−훼퐿

훾 훼 퐿

퐷

푃_퐹퐿 = 푃³[

( )

^푒푓푓(1 + ^{4푒 푠푖푛 (∆훽퐿/2)}) +

−훼퐿 2

훼 +∆훽

(1−푒

)

Channel spacing (GHz)

훾

훾훾

^퐻퐿푁퐹₂4푠푖푛²(^∆훽퐿) −

₎sin (^∆훽퐿) [훼 1 −

퐻퐿푁퐹

Figure 3. FWM power as a function of channel

(

퐾 ∆훽

퐾∆훽 훼 +∆훽

spacing with the factor K of 12 and the SMF fiber

length of 80km.

∆훽퐿

푒^−훼퐿푐표푠 ( ) + ∆훽 1 + 푒

sin (^∆훽퐿)]]

(9)

−훼퐿

)

(

)

Figure 3 shows that not only the FWM power depends

on the channel spacing but also the compensation

efficiency of the OBP does. The increase in channel

spacing causes the increase in the phase mismatch that

makes the average FWM power decrease. However, in

case of the OBP-assisted OFDM WDM LR-PON link, the

power of the FWM varies with the channel spacing as an

oscillation but it is always smaller than or equal to the

Kerr nonlinear power in case of not using OBP.

The first term of Eq. 9 describes the nonlinear FWM

power arisen in the SMF segment, which only depends on

the SMF coefficients. The second term in Eq. 9 is the

added nonlinear FWM power because of the presence of

the OBP, which only depends on the OBP coefficients.

The third one is the mixing nonlinear power that

compensates for nonlinearities of the both SFM and OBP

segments. Therefore, the compensation efficiency of the

OBP will increase when the third term is larger than the

second term. And this depends much on the factor K and

the coefficients of both segments.

Dependence of the mixing power on the dispersion at

different channel spacing is shown in Figure 4. The

dispersion dependence of the mixing power has a similar

tendency to the channel spacing dependence. The

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PROPAGATION

oscillation of the mixing power dependent on dispersion

can be observed and shows a reduction of the mixing

power in the OBP-assisted OFDM WDM LR-PON link

compared to that in the OFDM WDM LR-PON link

without OBP.

cannot be negligible. It can be seen that from Fig. 3, if

channel spacing is smaller than 5GHz, the Kerr nonlinear

power in the case of using OBP is always 10 dB smaller

than that in the case of not using OBP. Fortunately,

channel spacing of an OFDM signal is much smaller than

5 GHz. For example, if the OFDM signal in the OFDM

WDM LR-PON at the very high bitrate of 100 Gb/s using

64QAM and DCO-OFDM scheme has 190 data

subcarriers and 66 zero-padded subcarriers, the channel

spacing is about 0.18 GHz. Thus, the OBP can

compensate the Kerr nonlinearity caused by OFDM

subcarriers in the OFDM WDM LR-PON. When channel

spacing is larger than 5 GHz, which is the range of the

channel spacing of WDM systems, the Kerr nonlinear

power in case of using OBP fluctuates with large

amplitude. By choosing suitable value of K and channel

spacing, the OBP can compensate significantly the Kerr

nonlinearity caused by optical channels in the OFDM

WDM LR-PON. The performance improvement of the

OFDM WDM LR-PON thanks to OBP will be clarified

by Monte- Carlo simulation in the next section.

In the OFDM WDM system, the Kerr nonlinear noise

imposed on each subscriber of OFDM signals results from

two main sources:

(i)

FWM effect between subcarriers of each

OFDM channel. The Kerr nonlinear powers in

the link with and without OBP caused by

^OFDM( )

OFDM subcarriers, P

L , are derived from

Eq. 3 and Eq. 9, respectively in which P is the

power of each OFDM subcarrier and ∆β is

dependent on channel spacing between OFDM

subcarriers, and

(ii)

FWM effect between optical channels of WDM

system. The Kerr nonlinear powers in the link

with and without OBP caused by WDM optical

^WDM( )

carriers, P

L , are also derived from Eq. 3

and Eq. 9^F, respectively in which P is the power

of each optical channel and ∆β is dependent on

the channel spacing of WDM system.

III. SIMULATIONS AND RESULTS

A MATLAB based simulation model of IM-DD OBP

assisted OFDM WDM LR-PON is developed to

investigate the nonlinear compensation efficiency of

proposed OBP method. The simulation setup of the

system is similar to the block diagram described in Figure

1 that includes three main components: optical transmitter,

transmission link and optical receiver. The DCO-OFDM

signal is generated from the OFDM modulator in digital

domain that consists of 190 data subcarriers and 66 zero-

padded subcarriers. The MZM is used to optically

modulate the OFDM signal before launching into the

OBP. After pre-compensating at the OBP, the signal is

sent to the receiver via the transmission link of 80 km

standard single mode fiber (SSMF). Here, the data is

recovered with the reverse process of the transmitter. The

important system parameters and constants used in our

simulation are shown in Table 1.

-10

w/o OBP

w OBP

-20

-30

-40

-50

-60

-70

-80

Dispersion (ps/nm.km)

-10

-20

-30

-40

-50

-60

-70

-80

-90

-100

w/o OBP

w OBP

Table 1. Simulation parameters

Name

Symbol

Value

SMF parameters

Attenuation coefficient

Dispersion coefficient

Nonlinear coefficient

Fiber length

_SMF

D_SMF

_SMF

0.2 dB/km

17 ps/nm.km

1.4 W^-1.km^-1

80 km

Dispersion (ps/nm.km)

L_SMF

HNLF parameters

Figur 4. FWM power as a function of dispersion at

different channel spacing: (a) 12.5 GHz, (b) 25 GHz.

Attenuation coefficient

_HNLF

D_HNLF

_HNLF

L_HNLF

0.5 dB/km

1.7 ps/nm.km

6.9 W^-1.km^-1

150 m

Therefore, the total FWM power on each subcarrier in

case of using or not using OBP has the following form:

Dispersion coefficient

Nonlinear coefficient

Fiber length

^{푡표푡푎푙}( )

^푊퐷푀( ) ^푂퐹퐷푀( )

퐿 + 푃_퐹퐿

푃_퐹퐿 = 푃_퐹

(10)

Let’s consider the FWM effect caused by subcarriers

of an OFDM signal. Because the number of subcarriers of

an OFDM is quite large, the power of each subcarrier is

small but the channel spacing is very small too. Thus, the

FWM power caused by subcarriers of an OFDM signal

NW parameters

Attenuation coefficient

Dispersion coefficient

_NW

50 dB/m

D_NW

28 ps/nm.km

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channel spacing. At the optimum power range of SMF in

each optical WDM channel from -6 dBm to -2 dBm, the

OBP can improve the BER performance of the OFDM

WDM LR-PON up to 4 orders of magnitude at channel

spacing of 50 GHz.

Nonlinear coefficient

Waveguide length

_NW

10⁴W^-1.km^-1

7 cm

L_NW

System parameters

Optical signal frequency

f_s

193.1 THz

0.6 A/W

PD responsivity

Dark current

I_d

0.2 nA

Thermal noise PSD

M-ary

S_T

R_b

P_p

f_p

2x10^-23A/(Hz)^1/2

Data rate

100 Gbit/s

450 mW

Pump power

Optical pump frequency

193.3 THz

In the OBP, the OFDM signal after nonlinear and

dispersion pre-compensating is phase conjugated by an

OPC before transmitting via SSMF to the receiver. Thus,

the quality of the conjugated signal through FWM process

in the OPC plays an important role in the performance of

the OBP. In our simulation, the pump power and the input

power of the OPC are chosen carefully to ensure that the

conjugated signal does not add any more impairment to

the performance of the system [13]. The parameters of the

OFDM modulator need to be fixed to keep the data bitrate

of each optical channel of 100 Gbps. Hence, the channel

spacing between OFDM subcarriers is constant in all

simulations, only the channel spacing between optical

WDM channels is varied to examine the system’s

performance.

Figure 6. BER vs dispersion of SMF in each optical

WDM channel: a) with different channel spacing, b)

with and without OBP at channel spacing of 25GHz, c)

with and without OBP at channel spacing of 50GHz.

Figure 5. BER vs optical launched power of SMF in

each optical WDM channel with different channel

spacing.

The BER performance in each optical WDM channel

of OFDM WDM LR-PON versus dispersion of the SMF

is plotted in Fig. 6 in three cases: a) using OBP with

different channel spacing, b) with and without OBP at

channel spacing of 25 GHz, and c) with and without OBP

at channel spacing of 50 GHz. In these simulations, the

power of OBP and the power of the SMF are kept

unchanged at the value of 3.7 mW. It can be seen from the

Fig. 6a that the BER varies with the dispersion coefficient

of the SMF as an oscillation. This oscillation is attributed

by the dependence of the FWM efficiency on the phase

mismatch as indicated in the analytical evaluation.

Because the Kerr nonlinearity occurs strongly at the small

value of dispersion so that the BER curve fluctuates with

large magnitude. When the dispersion increases, the

Figure 5 demonstrates that the OBP can improve

significantly the performance of the OFDM WDM LR

PON. By adjusting the EDFA gain properly, the optical

power at the input of the SMF is always varied in the

range from -14 dBm to 2 dBm. At the given power of the

OBP, the best efficiency of the OBP is obtained at the

power range of the SMF that reaches to the system’s

power symmetry at any channel spacing. When the power

of the SMF is too small or too high, the residual FWM

power after two segments of the link is large that degrades

the efficiency of the OBP. In the case of the channel

spacing of 50 GHz, the BER is always lower about one

order of magnitude than that in the case of 25 GHz

because nonlinear Kerr power is inversely proportional to

SOÁ 04A (CS.01) 2020

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EFFICIENCY OF NONLINEAR COMPENSATION FOR WDM-PON BASED OFDM USING OPTICAL BACK

PROPAGATION

optical OFDM IM/DD system,” Optical Fiber Tech., vol.

magnitude of the oscillation reduces as results of large

phase mismatch. Thus, the average BER also decreases

gradually with dispersion of the fiber. In the case of not

using the OBP, the BER performance of the OFDM

WDM system in the range of small dispersion is better

than that in the higher dispersion value. At the small value

of dispersion, the BER performance suffers dominantly

from the nonlinear noise and can ignore the dispersive

noise. However, at the high value of dispersion, both

nonlinear and dispersive noises and their mutual

interactions that deteriorates sharply the system’s

performance. Fig. 6b and Fig. 6c show that by employing

the OBP for the OFDM WDM system, OBP exposes its

very good efficiency at the high value of dispersion.

When the dispersion coefficient of the fiber is small, the

fiber becomes a high nonlinear media. Under the power

asymmetry between two high nonlinear segments of the

link, the nonlinear power of each segment is exceeded the

nonlinear mixing power that downgrades the overall

performance of the system. However, when the dispersion

of the fiber increases, the nonlinear power of SMF

segment is small that can be compensated by the mixing

nonlinear power. At the channel spacing of 50 GHz, the

OBP can expose its efficiency for the fiber with dispersion

coefficient above 8 ps/nm.km. While this value reaches to

11 ps/nm.km in case of channel spacing of 25 GHz.

21, (2015), pp. 81-86.

[6] Y. Yang, Z. Zeng, S. Feng, C. Guo, “A simple OFDM

scheme for VLC systems based on μ-law mapping,” IEEE

Photonics Tech. Letters, vol. 28, (2015), pp. 641-644.

[7] Trang. T. Ngo, Hieu T. Bui, Nhan D. Nguyen,

“Performance improvement of IM-DD Optical OFDM

system using A-law companding transform,” in Proc. of

The Inter. Conf. on Advanced Tech. for Comm. (ATC), Ho

Chi Minh city, Vietnam, (2018), pp. 203-207.

[8] C. Lin, M. Holtmannspoetter, M. Asif, B. Schmauss,

“Compensation of transmission impairments by digital

backward propagation for different link designs,” 36th

European Conf. and Ex. on Optical Comm. (ECOC),

(2010).

[9] M. Morshed, L. Du, A. J. Lowery, “Mid-Span Spectral

Inversion for coherent optical systems: Fundamental

Limits to Performance,” J. Lightwave Tech., vol. 31, no. 1,

(2013), pp. 58-66.

[10] A. Ellis, M. McCarthy, M. Al-Khateeb, S. Sygletos,

“Capacity limits of systems employing multiple optical

phase conjugators,” Optics Express, vol. 23, no. 16,

(2015), pp. 20381-20393.

[11] M. Al-Khateeb, M. McCarthy, C. Sanchez, A. Ellis,

“Nonlinearity compensation using optical phase

conjugation deployed in discretely amplified transmission

systems,” Optics Express, vol. 26, no. 18, (2018), pp.

23954-23959.

[12] S. Kumar, D. Yang, “Optical backpropagation for fiber-

optic communications using highly nonlinear fibers,”

Optics Letters, vol. 36, (2011), pp. 1038-1040.

[13] Ngo T. T. Trang, Nguyen D. Nhan, Bui T. Hieu, “Optical

back propagation for nonlinear comensation in OFDM-

based long range-Passive Optical Networks”, VNU Journ.

of Sience: Mathematics-Physics, vol. 36, no. 1, (2020), pp.

54-63.

IV. CONCLUSIONS

We have investigated the distortion compensation

efficiency for the OFDM WDM LR-PON using an

advanced OBP, in which the OBP is positioned at the

transmitter site. This OBP consists of real optical devices

such as HNLFs, FBGs and the nonlinear waveguide. A

model of theoretical analysis is also used to evaluate the

efficiency of this technique and show that the OBP can

compensate significantly the Kerr nonlinearity in the

OFDM WDM system by choosing suitable parameters.

The simulation model of the OBP-assisted OFDM WDM

LR-PON at 100 Gbps is setup to validate the efficiency

of the proposed compensation method in real conditions.

The obtained results show that the BER performance of

the system can be improved many orders of magnitude

compared with that of the system without OBP.

Consequently, the implementation of the OBP-assisted

OFDM WDM LR-PON with very high bitrate of 100

Gbps is feasible in real conditions.

[14] G. Agrawal, Nonliner Fiber Optics, 4th ed., (2007).

[15] W. Shieh, X. Chen, “Information spectral efficiency and

launch power density limits due to fiber nonlinearity for

coherent optical OFDM systems,” IEEE Photonics J., vol.

3, no. 2, (2011), pp. 158-173.

[16] M. Al-Khateeb et. al, “Analysis of the nonlinear Kerr

effects in optical transmission systems that deploy optical

phase conjugation,” Optics Express, vol. 26, no. 3, (2018),

pp. 3145-3160.

GIẢI PHÁP BÙ PHI TUYẾN DỰA TRÊN KĨ

THUẬT TRUYỀN NGƯỢC TRONG MIỀN QUANG

ỨNG DỤNG CHO HỆ THỐNG OFDM-WDM

Abstract: Hiệu ứng phi tuyến Kerr là một trong các

yếu tố chính giới hạn hiệu năng của hệ thống OFDM-

WDM. Hơn nữa, có một giải pháp bù phi tuyến khả thi

mà không làm tăng thêm độ phức tạp cho phía thu là rất

cần thiết cho các ứng dụng của mạng quang thụ động

khoảng cách dài (LR-PON). Trong bài báo này, chúng tôi

đề xuất một mô hình bộ truyền ngược trong miền quang

(OBP) cải tiến, dựa trên phương pháp Fourier tách bước,

để bù lại ảnh hưởng phi tuyến và tán sắc trong hệ thống

OFDM-WDM. Bộ OBP đề xuất gồm các phần tử quang

có sẵn trong thực tế, trong đó sợi quang phi tuyến lớn

(HNLF) đóng vai trò toán tử phi tuyến, cách tử Bragg sợi

(FBG) đóng vài trò toán tử tuyến tính và ống dẫn sóng

phi tuyến đóng vai trò phần tử liên hợp pha và được đặt

tại phía phát nên rất phù hợp cho các ứng dụng LR-PON.

Hiệu quả của bộ OBP đề xuất trong hệ thống OFDM-

WDM được đánh giá dựa trên các tính toán lý thuyết và

kiểm chứng dựa trên mô phỏng Monte-Carlo. Các kết quả

thu được từ phân tích đánh giá và mô phỏng đều cho thấy

REFERENCES

[1] A. Emsia, M. Malekizandi, Q. T. Le, I. B. Djordjevic, F.

Kueppers, “1 Tb/s WDM-OFDM-PON power budget

extension techniques,” Photonics Conf. (IPC), (2013).

[2] H. He, J. Li, M. Bi, W. Hu, “20-Gbps low cost WDM-

OFDM-PON downstream transmission with tunable filter

and linear APD module,” Chinese Optics Leters, (2014).

[3] Trang. T. T. Ngo, Thu. A. Pham, Nhan. D. Nguyen, Ngoc.

T Dang, “Hybrid OFDM RoF-Based WDM-PON/MMW

Backhaul Architechture for Heterogeneous Wireless

Networks,” REV J. Elect. and Comm., vol.7, no. 3-4,

(2017), pp. 57-64.

[4] F. Offiong, S. Sinanovic, W. Popoola, “On PAPR

reduction in pilot-assisted optical OFDM communication

systems,” IEEE Access, vol. 5, (2017), pp. 8916-8929.

[5] Y. Xiao, M. Chen, F. Li, J. Tang, Y. Liu, L. Chen, “PAPR

reduction based on chaos combined with SLM technique in

SOÁ 04A (CS.01) 2020

TAÏP CHÍ KHOA HOÏC COÂNG NGHEÄ THOÂNG TIN VAØ TRUYEÀN THOÂNG

Ngo Thi Thu Trang, Tran Thuy Binh, Bui Trung Hieu, Nguyen Duc Nhan

bộ OBP đề xuất cải thiện đáng kể hiệu năng của hệ thống

khi mà các tham số như hệ số tán sắc và công suất bơm

được lựa chọn thích hợp.

Keywords: Ghép kênh phân chia theo tần số trực giao

(OFDM), Ghép kênh phân chia theo bước sóng (WDM),

Các giải pháp bù phi tuyến, Truyền ngược trong miền

quang (OBP), Mạng quang thụ động khoảng cách dài

(LR-PON).

Ngo Thi Thu Trang, M.E degree

of Computer and Communication

Engineering from Chungbuk National

University, Korea in 2005. Now, she

is a lecturer in Telecommunications

Faculty

Posts

and

Telecommunications

Institute

Technology (PTIT). Her research

interests

include

digital

optical

signal

communications,

processing, broadband networks.

Email: [email protected]u.vn

Tran Thi Thuy Binh, M.E degree

of Telecommunications from PTIT in

2003. At present, she is a lecturer in

PTIT, Telecommunicatons Faculty 1.

Her professional fields involve

nonlinearities

optical

communications, optical broadband

access networks.

Email: tran.binh95@gmail.com

Bui Trung Hieu received the

PhD degree in Czech and Slovakia

in 1992. He is currently an

Associate Professor of PTIT. His

research interests include optical

communication systems, optical

transport

devices.

network,

photonic

Email: [email protected].vn

Nguyen Duc Nhan, PhD degree

of Electrical Engineering and

Computer Systems from Monash

University, Australia in 2011. Now,

he is

lecturer in PTIT,

Telecommunications Faculty 1. His

research interests are numerical

modeling and analysis, signal

processing and its applications in

optical

communications

and

nonlinear fiber optics applications.

Email: [email protected].vn

SOÁ 04A (CS.01) 2020

TAÏP CHÍ KHOA HOÏC COÂNG NGHEÄ THOÂNG TIN VAØ TRUYEÀN THOÂNG

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