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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 24, NO. 7, APRIL 1, 2012617

Optimization of Optical Modulator for LTE RoF

in Nonlinear Fiber Propagation

Thavamaran Kanesan, Student Member, IEEE, Wai Pang Ng, Senior Member, IEEE,

Zabih Ghassemlooy, Senior Member, IEEE, and Joaquin Perez, Member, IEEE

Abstract—This letter proposes an optimized launch power

for the direct detection of optical orthogonal frequency-division

multiplexing (DD-OOFDM) for radio-over-fiber (RoF). The aim

is to optimize the physical layer connectivity for the third

generation partnership program—long-term evolution employing

RoF technologies. We also analytically derive an expression for

the distributed-feedback laser, laser-induced positive frequency

chirping, incorporating the phenomena that induce phase distor-

tion at the receiver, and explicitly explain the transient chirp of

DD-OOFDM. Results show that transmission at the optimized

launch power of −4 dBm improves the system power efficiency

of 16-quadrature amplitude modulation (QAM) DD-OOFDM by

∼20% and ∼37%, 64-QAM DD-OOFDM by ∼21% and ∼35%

compared to launch powers in the linear and nonlinear regions,

respectively.

Index Terms—External modulation, internal modulation, long

term evolution (LTE), radio-over-fiber (RoF).

I. INTRODUCTION

T

real time data from [1] shows that the user equipment only

receives data of < 20 Mbps with a 1 km cell size. In addition

a cell extension of only 3.2 km is achieved in [1] with

decode and forward relay nodes (RN) at the fixed condition

of LOS RN. It is essential to extend the cell coverage of a

single eNodeB (eNB) to the entire urban area, therefore this

letter will study the maximum potential transmission distance

that RoF can provide. In our earlier work, by adopting an

amplifying and forwarding RN with a non-LOS link from

eNB; for the RoF link of 10 km, an improvement of ∼31 dB

in terms of the signal-to-noise ratio (SNR) was observed

compared with the wireless radio frequency link [2].

In this letter, we are proposing and optimizing, by means

of a numerical simulation, the LTE signal with three differ-

ent optical modulators namely (i) the internally modulated

(IM) DFB, (ii) an externally modulated single-electrode-Mach-

Zehnder modulator (SE-MZM) and (iii) the dual electrode-

MZM (DE-MZM) with an external phase modulation (PM);

incorporating nonlinear fiber propagation and a direct detec-

tion (DD) based receiver. Previous work on the optimization of

the optical modulator for OOFDM has only been reported for

the Quadrature MZM and DE-MZM with no consideration of

HE 3GPP-LTE transmission in a dense urban area

provides a non line-of-sight (LOS) scenario where the

Manuscript received January 13, 2012; accepted January 17, 2012. Date of

publication January 27, 2012; date of current version March 16, 2012.

The authors are with the Optical Communications Research Group,

Northumbria Communications Research Laboratory, Northumbria University,

Newcastle-upon-Tyne NE1 8ST, U.K. (e-mail: wai.pang.ng@ieee.org).

Color versions of one or more of the figures in this letter are available

online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LPT.2012.2185927

the fiber nonlinearity [3]. It is important to optimize the DFB

modulator taking into consideration the PFC effect. This is

because the PFC induces signal spread similar to the chromatic

dispersion (CD) and thus jointly contributing to the signal dis-

tortion over a long propagation span. Therefore, it is desirable

to employ a chirp free external modulator in long haul fiber

communications, thus making it superior to the IM DFB.

Relative to the PFC effect, we introduce a new analytical

expression for the DFB laser induced PFC and further optimize

the optical launch power (OLP) for DD-OOFDM with the self

phase modulation (SPM) to mitigate PFC and CD induced

power penalties. SPM based CD compensation technique with

no dispersion compensating fiber has been reported in [4], but

only the frequency length product using a simple binary trans-

mission system with no OLP condition has been investigated.

Bao et al showed that the optimized OLP for each wavelength

division multiplexing channel for coherent-OFDM falls within

the range of −10 dBm to −8 dBm [5]. In [6] the effect of non-

linearity induced power penalty for DD-OOFDM have been

reported for OLP greater than 0 dBm. Additionally results

presented in [6] did not address the intermixing effect between

CD and SPM. In this letter we investigate CD induced power

penalty for the OLP level below 0 dBm, as well as proposing

the optimized launch power for the DD-OOFDM system.

II. ANALYSIS OF PFC BASED ON RATE EQUATION

The internal modulation of a laser with respect to an input

signal in a numerical simulation is viable by adopting rate

equations as given by (1) and (2), which depicts the rate of

change of carrier density dN/dt and the rate of change of

photon density dS/dt:

dN

dt

τc

dS

dt

1 + εS

where Id is the total current injected into the DFB, e is the

electronic charge, V is the volume; N is the carrier density, τc

is the carrier decay rate; G is the linear optical gain coefficient;

Nt is the transparency carrier density; ε is the nonlinear gain

coefficient, S is the photon density; Ã is the mode confinement

factor (MCF); τpis the photon decay rate and ζ is the fraction

of spontaneous emission.

The expression for a DFB induced PFC was derived from

the optical phase and frequency as given by:

?1

1041–1135/$31.00 © 2012 IEEE

=

=?G(N − Nt)

Id

eV−N

− G(N − Nt)

1 + εS

S −

S

(1)

S

τp

+?ζ N

τc

(2)

?v =

σ

4π

P

dP

dt

+ kP

?

(3)

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618IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 24, NO. 7, APRIL 1, 2012

where ?v is the instantaneous frequency deviation, σ is the

linewidth enhancement factor, P is the optical power and k is

the adiabatic chirp coefficient. The first term in (3) denotes the

transient frequency chirp and the second term is the adiabatic

frequency chirp. Theoretically, (3) would be sufficient to

describe PFC. However, there are two shortcomings regarding

(3); (i) the actual effect of PFC arises from the numerical

modeling of (1) and (2), therefore the expression should be

analyzed from (1) and (2) and not from the optical phase and

frequency to ensure an accurate outcome; and (ii) the adiabatic

chirp, which is not applicable to the OOFDM signal due its

time domain noise-like features. In a 16-QAM DD-OOFDM

system, an average phase shift of ∼8° can be observed by

numerically integrating (1) and (2) of DFB to investigate the

actual PFC effect. Therefore, a new analytical expression is

required for PFC, which is outlined in the following sections.

A. Analytical Derivation of PFC

Investigationof PFC requires a detailed derivation of (1) and

(2). This could be carried out by solving (1) and (2) through

the relativity of stimulated emission arises from the coupled

wave theory and will result in a relationship given as:

?dN

From the principal of laser emission, dZ/dt of (4) describes

the rate of change of the instantaneous process of electron

hole recombination in terms of dN/dt with respect to MCF

and with the addition of dS/dt.

The respective solution of (4) is:

dZ

dt

= ?

dt

?

+dS

dt.

(4)

Z = ?N + S

(5)

where Z is the instantaneous process that results from the

direct integral of (4). The expansion of (1) and (2) within (4)

while assuming that the instantaneous process to operate solely

based on the bimolecular recombination process and neglect-

ing the fraction of spontaneous emission ζ will result in:

dZ

dt

Equation (6) is the new closed form expression for the rate

of change of the instantaneous process and the solution of (7)

is obtained by applying the Integrating Factor method, which

yields:

= ?

Id

edwl−1

τcZ.

(6)

Z(t) = e−1

τc(tlim−t0)Z(t0) +

tlim

?

t0

e−1

τc(tlim−t)

?

edwlId(t)dt

(7)

where to is the beginning of a symbol period, tlim is the

symbol period and t is the continuously varying time of the

input signal. The 1stterm of (7) represents the initial condition

and the 2ndterm shows the actual integral of the input signal

that is bounded within the MCF. Transient chirping or general

frequency chirping is related to the changes in N which in turn

reflects changes in the refractive index. In (3), the expression

only describes chirping with respect to P; but chirping is

also induced by Id. The instantaneous process Z(t) explicitly

shows that Id actually alters N taking τc into consideration.

Generally, OFDM has an envelope with a Gaussian distribution

based on the central limit theorem. Mathematically, an integral

function of a sinusoidal signal is a cosinusoidal signal as a

result of phase variation. Therefore, integral of Id in (7) is

composed of the time varying OFDM signal with Gaussian

distribution, which results in the signal phase and envelope

variations. This phenomenon will directly affect the refractive

index of DFB and deduce the characteristics of transient chirp.

III. OPTIMUM LAUNCHING CONDITION

The most feasible approach of compensating CD would

be to take advantage of optical fiber nonlinear propagation

characteristics without introducing an additional complexity or

cost. It is known that light propagation through a dispersive

and a nonlinear fiber channel is governed by the generalized

nonlinear Schrödinger equation (NLSE) [4]. When combined

with the fiber CD, the SPM induced chirp give rise to the

nonlinear distortion. However at the 1550 nm transmission

window and using a single mode fiber (SMF) (adopted in

this work) the distortion term has an opposite phase to PFC

and CD induced distortions. Therefore, the nonlinear induced

phase distortion can be used to compensate for the dispersion

induced power penalty by controlling OLP applied to SMF.

However, there is a maximum limit to OLP, beyond which the

SPM induced chirp will become the dominant effect.

A. System Model

In this letter the physical layer connectivity from eNB

according to the LTE standard is modeled in MATLAB using

16 and 64-QAM at 400 Mb/s and 600 Mb/s with OFDM

as depicted in Fig. 1. These signals are then used to drive

three different optical modulators; (i) DFB, (ii) SE-MZM and

(iii) DE-MZM. The latter two are adopted from [3]. The

generalized NLSE is adopted to model the linear and nonlinear

propagation of SMF [4]. The optical receiver is based on DD

with the addition of a frequency domain based equalizer.

B. Results and Discussion

Figs. 2(a) and (b) depict the power penalty against OLP for

16-QAM and 64-QAM DD-OOFDM at the facet of optical

modulators at a bit error rate (BER) of 10−5. The maximum

link span achieved are ∼68 km (∼57 km), ∼79 km (∼62 km)

and ∼88 km (∼71 km) for 16-QAM (64-QAM) for DFB, SE-

MZM and DE-MZM, respectively. In both figures there are

three distinctive regions: A) CD or CD and PFC induced power

penalty (linear); B) the optimum OLP due to the intermixing

effect of SPM with CD and the PFC (DFB); and C) the

SPM induced power penalty (non-linear). Regions A and more

importantly B are not identified in literatures [4, 6]. In the

region B, see Figs. 2(a. ii) and 3(a. ii), the optimum OLP

is within a range of ∼−6 dBm to ∼−3 dBm, which offers

the lowest average power penalties of ∼18 dB and ∼14 dB

for 16-QAM and 64-QAM for all three optical modulators,

respectively. The observation within the region B shows that

DFB, SE-MZM and DE-MZM achieve the optimum operating

point nominally at −4 dBm, however the external modulators

are operating at the chirp free condition. The fundamental

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KANESAN et al.: OPTIMIZATION OF OPTICAL MODULATOR FOR LTE RoF619

SE-MZM

ADC

2.6 GHz

Ich

Qch

90

Data

Data

OFDM

Demodulator

EQ

EQ

Zeros

DE-MZM

Q

I

Tdt

0

Tdt

0

OFDM Modulator

DataData

Zeros

DAC

2.6 GHz

Ich

Qch

I

90

Q

DAC

PD

PD

LD

LD

PD

DFB

QAM

QAM

QAMQAM

∫∫

Fig. 1.Block diagram of LTE-RoF using direct and external modulations.

(a) (ii)

Launch power (dBm)

Ideal Modulator (57 km)

DFB (57 km)

SE-MZM (62 km)

DE-MZM (71 km)

Region A

Region B

Power Penalty @ 10-5BER (dB)

Launch power (dBm)

Ideal Modulator (68 km)

DFB (68 km)

SE-MZM (79 km)

DE-MZM (88 km)

Region A

Region B

Region C

(i)

(b) (ii) (i)

Region C

-10-8-6-4 -2024

0

-15

20

40

60

80

0

-15

20

40

60

80

-10

-5

05 1015

-10 -50510 15 -10 -8

-6-4 -2024

12

14

16

18

20

22

5

10

15

20

Fig. 2.

and (b) 64-QAM DD-OOFDM. (i) Analysis with three distinctive regions.

(ii) Analysis emphasizing more on Region B.

OLP against power penalty analysis of (a) 16-QAM DD-OOFDM

behind this occurrence is that SE-MZM and DE-MZM signals

have traversed further, thus resulting in CD accumulation along

the propagationpath. Thereforethis makes up to the element of

the PFC. This phenomenon is clearly observed in Figs. 2(a. ii)

and 2(b. ii) with the power penalty of the ideal case increasing

beyond −6 dBm. This is due to the shorter link span, therefore

lower accumulated CD.

A launch power of < −7 dBm (i.e. region A), results

in an increased average power penalty of ∼20 dB and

∼18 dB for 16-QAM and 64-QAM, respectively. The power

penalty increases significantly for OLP > 0 dBm (i.e. region

C). For DE-MZM higher power penalties are observed at

the region C. This is because the nonlinear phase noise

becomes the dominant term compared with the CD induced

distortion and therefore DE-MZM requires higher SNR as

a tradeoff for longer transmission spans. Focusing on the

optical modulators, SE-MZM outperforms both DFB and DE-

MZM by an average power efficiency of 3.5 dB and 6 dB for

16-QAM and 64-QAM, respectively.

From Fig. 2 we have used an OLP of −4 dBm to investigate

the BER performance for 16-QAM and 64-QAM as shown

in Figs. 3(a) and (b), respectively. At a BER of 10−5from

Fig 3(a), the highest achievable transmission distance, between

all RoF configurations, is ∼88 km for the DE-MZM modulator

at an SNR of ∼32 dB. DFB offers the lowest transmission

span of ∼68 km at an SNR of ∼29 dB; while for SE-

MZM the required SNR is ∼26 dB for ∼79 km transmission

span. The DFB scheme achieves the shortest transmission

span compared with both external modulators due to the

associated PFC that correlates with the CD effect on the

optical carrier. Likewise, Fig. 3(b) experiences the same signal

degradation pattern with a reduced link span to achieve the

1015 20 25

SNR(dB)

30354045

Log (BER)

theory

DFB (68 km)

SE-MZM (79 km)

DE-MZM (88 km)

-5

-4

-3

-2

10 15 2025

SNR(dB)

3035 4045

-5

-4

-3

-2

Log (BER)

theory

DFB (57 km)

SE-MZM (62 km)

DE-MZM (71 km)

(a)

(b)

Fig. 3.

DD-OOFDM.

BER analysis of (a) 16-QAM DD-OOFDM and (b) 64-QAM

required BER. The fundamental of this occurrence is related

to the indirect proportionality between the bit rate and the

transmission distance. It is important to optimize the optical

modulators at the maximum transmission span.

The powerpenaltyimprovement,

optimized OLP; from the average power penalty across three

optical modulators of Figs. 3(a) and (b) for 16-QAM DD-

OOFDM and 64-QAM DD-OOFDM, are ∼20% (∼37%) and

∼21% (∼35%) with respect to the lower launch point from

region A of −7 dBm (higher launch point from region C

of 0 dBm).

observedfor the

IV. CONCLUSION

In this letter, we have analytically derived the relationship

of the (1) and the (2) to explain the PFC effect; as a result

we presented a precise expression for the DFB laser induced

PFC that is appropriate to the DD-OOFDM induced transient

chirp and the phase distortion at the receiver. Optimization

was carried out for the LTE-RoF link with three optical mod-

ulators and results have revealed that DE-MZM achieves the

longest transmission span with a requirement of higher SNR.

The overall system power penalty improvement observed

across three optical modulators at 400 Mb/s (16-QAM) and

600 Mb/s (64-QAM) are ∼28.5% and ∼28%; showing a

marked improvement with respect to Regions A and B.

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