OTDR based Estimation of Optical Fiber Link Residual OFDM CFO

Adriana Lipovac

, Vlatko Lipovac

, Mirza Hamza

and Vedran Batos

Dept. of Electrical Engineering and Computing, Univ. of Dubrovnik, Dubrovnik, Croatia

Dept. of Telecommunications, Faculty of Electrical Engineering, Univ. of Sarajevo, Sarajevo, Bosnia and Herzegovina

Keywords: OTDR, BER, Dynamic Range, OFDM CFO.

Abstract: Optical time-domain reflectometer (OTDR) has long been and is still considered the main test tool for

characterizing fiber optic links, i.e. identify and localize refractive and reflective events such as breaks, splices

and connectors, and measure their insertion/return loss. Specifically, sufficient dynamic range and thus alike

signal-to-noise-ratio (SNR) enable clear far-end visibility even of long fiber links. Moreover, under such

conditions, the highest achievable optical bit-error-rate (BER) floor is to the large extent determined by major

reflective events such as the specific trace distortion caused by connectors and splices, each with significant

return loss. Realizing this has provided the opportunity window to extend the standard OTDR capabilities list

by the appropriate trace postprocessing to predict the BER floor. Accordingly, considering the SNR high, and

thereby the inter-symbol interference dominant error generating mechanism, we applied the time-dispersion

channel model that determines the BER floor by the rms delay spread of the (fiber) channel power-delay

profile. We verified the BER floor prediction in the exemplar practical test situation, by measuring the actual

BER on the same fiber link, and found the obtained values well matching the OTDR - based predicted ones.

Furthermore, when no dominant reflective events are identified on the OTDR trace, it implies very small time

dispersion allowing the OFDM symbol cyclic prefix to always prevent inter-symbol interference. This retains

the CFO to solely determine the residual BER floor and vice versa, enabling indirect estimation of CFO-

induced phase distortion by simple BER testing. With this regard, we abstracted CFO with the AWGN being

justified by the Central Limiting Theorem to enable efficient and quite accurate short-term BER (and so CFO

phase error) predictions.

1 INTRODUCTION

Optical time-domain reflectometer (OTDR) has long

been used as a test tool of choice during installation and

maintenance of fiber optic communication systems. It

has been useful for fault locating and troubleshooting -

basically identifying various refractive and reflexive

events such as e.g. breaks, as well as measuring

attenuation, splice and connector insertion/return

losses, and fiber length (Lipovac, 2020; Wenzer, 2018;

Hui, 2009; Hui, 2020), Figure 1.

In short, OTDR transmits a pulse of laser light

through the fiber, while detecting the reverse-

direction travelling incoming signal, commonly

referred to as Rayleigh backscatter that is being

reflected back by irregularities in the optical fiber

structure, with the reflections’ delays expressed as in

distance units, by appropriately scaling the time axis

multiplying it with the speed of light in the fiber (Lu,

2017; Alekseev, 2016; Hartog, 2008; Lu, 2016).

Figure 1: OTDR architecture.

Basically, an OTDR is made of a microprocessor,

pulse trigger and generator, laser diode, optical

coupler, detector, analog-to-digital converter and

display, Figure 1.

So, initiated by the microprocessor accordingly

commanding the trigger and generator, these make

the laser transmitting a series of pulses unaffectedly

passing through the optical directional coupler (ODC)

to the near end of the actual fiber. However, in the

Lipovac, A., Lipovac, V., Hamza, M. and Batos, V.

OTDR based Estimation of Optical Fiber Link Residual OFDM CFO.

DOI: 10.5220/0010762900003121

In Proceedings of the 10th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2022), pages 91-96

ISBN: 978-989-758-554-8; ISSN: 2184-4364

reverse direction, the ODC re-routes the reflected

backscatter signal to not come back (and potentially

harm) the transmitting laser, but to the avalanche

photodiode (APD) or positive-intrinsic-negative

(PIN) diode detector. Then, following the detector,

the signal passes through the analog-to-digital

converter (ADC) to the microprocessor for analysis

and forming the OTDR trace on the display, where

the analysis includes signal averaging to increase

SNR.

Furthermore, in any phase of network lifetime

cycle – no matter be it development, production,

installation or maintenance of fiber transmission

systems, the end-to-end bit-level transmission

performance is most adequately described by the bit-

error-rate (BER), which is measured out-of-service,

using the pseudo-random binary sequence (PRBS)

generator and receiver. (Most often, single BER test

(BERT) unit comprises both the generator and the

receiver, which presumes a loop-back at the far end

of the fiber.)

Specifically, we focus here the residual

(irreducible) BER, also commonly referred to as BER

floor, which is achievable under high-SNR

conditions, when practically it is just time dispersion

that remains out of the bit error generating

mechanisms.

Moreover, considering Orthogonal Frequency-

Division Multiplexing (OFDM) signal transmission

over optical fiber link, the BER floor is generally also

determined by the two main OFDM shortcomings -

the carrier frequency offset (CFO) and (large) peak-

to-average power ratio (PAPR).

However, coming closer to our final test scenario

of OFDM transmission over homogeneous optical

fiber links, we consider no dominant discrete events

(neither reflective, nor refractive ones detected by

OTDR), as well as enough large optical receiver

dynamic range (DR) or used any PAPR reduction

method) to prevent the non-linear high-power

transmitting amplifier from generating errors.

Finally, we consider time dispersion small enough

to allow the OFDM symbol cyclic prefix (CP) prevent

any inter-symbol interference (Lipovac, 2021).

This all imply that, under such conditions

common in practice, the CFO remains the sole

determining factor of the residual BER, which

enables indirect estimation of CFO-induced phase

distortion by much simpler BER testing (Lipovac,

2021).

This motivates our investigation of how accurate

and reliable is to estimate the fiber BER floor and

OFDM CFO from the related OTDR trace?

So, in Section 2, after reviewing the relevant

OTDR basic concepts, we firstly present the BER

floor model as a function of the crucial time

dispersion parameter – rms delay spread of the

reflective events dominant optical channel PDP that

is considered determined by the OTDR trace.

Then, in case of uniform OTDR trace decay with

a number of smaller discrete refractive events –

attenuations, we modelled the residual BER and CFO

by applying the link abstraction principle.

In Section 3, we present and discuss the obtained

preliminary test results for the exemplar test situation,

providing the according analysis to qualify matching

between the OTDR - based and directly measured

BER floor and CFO values. Conclusions are

summarized in Section 4.

2 ANALYSIS

The backscatter signal returning to the OTDR

consists of both Rayleigh scattering and Fresnel

reflections, where the former enables calculating fiber

attenuation as a function of distance, which is

represented by the constantly falling part of an OTDR

trace. However, Fresnel reflection occurs when the

light pulse light hits an abrupt change in refraction

index, which causes a strong reflection back, and so

enables detection of physical events identifiable by

spikes in OTDR trace due to connectors, mechanical

splices, bulkheads, fiber breaks or opened connectors

(the higher the spike with respect to the backscatter

levels, the greater the reflectance), Figure 2.

Figure 2: Typical OTDR trace for a longer fiber with

various reflective and refractive events (5 dB/Div;

4 km/Div).

2.1 Basic OTDR Analytical OFDM

BER Floor Model

More precisely, when the OTDR transmits the light

pulse of power P

into the fiber, then the power P

(z)

of the pulse propagating downstream the fiber, is the

PHOTOPTICS 2022 - 10th International Conference on Photonics, Optics and Laser Technology

exponential function of distance z of the observation

point from the fiber near-end (OTDR):

(z) =P

⸱10

−α⸱z/10

(1)

where α=α

+α

is the sum of the scattering and

absorption losses expressed in dB/km.

The total scattered power at distance z is:

(z) = α'

⸱Δz⸱P

(z) (2)

where α'

= 0.23⸱α

and Δz denote the fiber loss and

the light pulse length, respectively.

The latter can be expressed as:

Δz = w⸱v

= w⸱c/n

≈ w⸱c/n (3)

where: w, v

, n

, and c denote the pulse duration, the

group velocity in the fiber, the group refractive index

(justifiably approximated by the ordinary index n),

and the speed of light in vacuum, respectively.

Determined by the fiber numerical aperture, i.e.

by limited efficiency of an optical fiber to confine the

incident light, only a certain part S<1 of the scattered

light travels back to the OTDR (and is being subjected

to equal loss as during forward propagation), and

reaches the arbitrary point that is z apart from the

OTDR, with the total backscattered power:

(z) = S⸱α'

⸱Δz⸱P

⸱10

−2α⸱z/10

(4)

implying that the backscattering power reflected from

the end of the fiber (z = L) is:

(L) = S⸱α'

⸱Δz⸱P

⸱10

−2α⸱L/10

(5)

So, for example, in order to estimate the

backscattered power at 1550 and 1300 nm, we need

to adopt some typical parameters’ values in (5), such

as the ones in Table 1.

Table 1: Typical parameters’ values.

2.2

OFDM BER Floor Model for OTDR

Trace with Significant Reflective

Events

On the other hand, the orthogonal frequency-division

multiplexing (OFDM) has become widely spread in

optical communications as attractive modulation

format for long-haul transmission (Hui, 2020).

As it is challenging to uniquely relate the OTDR

trace events (primarily the reflective ones) to the

parameter(s) determining the OFDM BER error floor

under high-SNR conditions and therefore dominant

time dispersion, which implies that we can apply the

OFDM BER floor model (Lipovac, 2021),

specifically when sampling time is just upon the

arrival of the first impulse of the channel impulse

response.

So, we consider the power-delay profile (PDP)

as the sum of N impulses with powers

, and delays

Ni ,...2,1=

(Lipovac, 2021).

Then, with no loss in (OFDM) generality, for

simple NRZ transmission, the BER floor for the trace

with significant reflections is:

[]

BER

28.0

⋅≈

(6)

where:

[]



⋅=

π2

(7)

is the standard rms delay spread (normalized to the

symbol time T

) of the channel PDP P

(z), which we

consider to conform to the OTDR backscatter trace

(as describing time dispersion alike).

The BER floor condition of high SNR is fulfilled

with large enough OTDR dynamic range, which is

basically achieved with long enough transmitted

pulse.

However, on the contrary, an OTDR trace being

effectively an attenuated two-way squared response

of the fiber channel to the transmitted laser pulse, can

only be considered the PDP for short enough laser

pulse considered an impulse.

Thus, with this regard, the crucial OTDR attribute

is dynamic range, which is the difference between the

backscatter level at the front end and the noise floor

at the far end of the fiber, where the latter is mostly

considered as where SNR equals unity, Figure 3.

Figure 3: Dynamic range definitions with two definitions of

the noise floor.

OTDR based Estimation of Optical Fiber Link Residual OFDM CFO

Measured in decibels, DR is the difference

between the backscatter level at the front end of the

fiber and the noise floor at the far end of the fiber,

where most often the latter corresponds to the signal

level (i.e. where SNR=1).

Thus, small dynamic range disables proper

OTDR measurements at the fiber end, Figure 4.

)

Figure 4: OTDR trace; a) small dynamic range, b) large

dynamic range.

Longer pulses provide larger dynamic range, as

well as worse event resolution and longer attenuation

dead zone, Figure 5.

)

Figure 5: OTDR trace; a) small dynamic range, b) large

dynamic range.

Furthermore, in addition to pulse width, receiver

bandwidth is another crucial performance criterion,

which determines the actual OTDR resolution

(Charlamov, 2013).

So, for each OTDR laser pulse width and desirable

attenuation dead zone, we can calculate the impulse

response and bandwidth of an optical receiver.

With this regard, in Table 2 some exemplar

OTDR receiver bandwidth (BW) values for given

pulse width (PW) values, are presented.

Table 2: OTDR pulse width and bandwidth.

Considering that:

(z) = P

(c/2·n⸱τ) = C

⸱10

−α·c·n⸱τ/10

;

= S⸱α'

⸱Δz⸱P

(9)

the response of the fiber-made link onto the OTDR-

transmitted pulse P

1/2

(z), is the convolution of the

latter with the fiber impulse response h(τ).

1/2

(τ) = P

1/2

(τ)

h(τ) ; τ = (2z·n)/c (10)

So, to obtain h(τ), we need to de-convolve it from

1/2

(τ), which means to solve (9) per h(τ), leading to:

h(τ) = c/2n⸱E

⸱S⸱η

⸱exp(-2αz) (11)

where c, n, E

and η

stand for speed of light, laser

energy, average refractive index of the actual fiber,

and APD quantum efficiency, respectively.

However, pragmatically looking, large OTDR

dynamic range still makes its transmitted pulse (of

about 1 µs duration) short enough (with respect to the

reciprocal of the OTDR receiver bandwidth) – almost

as of an impulse described by delta-function:

(z) = δ(-2αz) (12)

so that (10) modifies to:

1/2

(z) = δ(-2αz)

h(z) = h(z) ; z = c⸱ τ /2 (13)

Consequently, the normalized power – delay

profile of the fiber can be approximated by the

normalized (to unity area) relative OTDR trace as:

׀h(τ)׀

= P

(z = c⸱ τ /2) (14)

Thereby, we can consider the OTDR trace to be

the first approximation of the average fiber PDP.

2.3 AWGN Abstraction of CFO from

Uniform-Decay OTDR Trace

Regardless of whether any kind of CFO

compensation used or not, the task here is to quantify

the residual CFO-caused phase error for given

conditions (Lipovac, 2016).

Furthermore, back to basics, the well-known BER

expression for the M-QAM signal transmission over

the additive white Gaussian noise (AWGN) channel,

as a function of the ratio of the energy E

of a bit to

noise spectral density N

, is (Lipovac, 2021):

3log

log

BER



⋅



⋅



−





(15)

where Q denotes the Gaussian tail function.

PHOTOPTICS 2022 - 10th International Conference on Photonics, Optics and Laser Technology

Now, as it is already elaborated in Introduction,

the scenario of interest here is OFDM transmission

over homogeneous fiber link, where we consider no

dominant discrete events of any kind detected in the

OTDR trace, and qualified as either reflective or

refractive. This practically implies that we can then

justifiably consider CFO as the main error generating

mechanism, and thus determining BER.

Moreover, from the OTDR trace, we can read out

the SNR (i.e. E

) value at the far end, and

substitute it into (12), considering that it abstracts the

actual BER with the AWGN one (as if a number of

mutually independent small distortions in summary

enable the application of Central Limit Theorem) of

the according mean and variance (Lipovac, 2021).

Then, having calculated this AWGN-modelled

BER due to CFO, we can calculate the maximal

squared CFO-caused phase deviation as (Lipovac,

2016):

()

CFO s

max

log

fMT

Φ BER

BER M

−

Δ≈⋅ ⋅

⋅

−

 ⋅ 











⋅≤≤

(16)

where

CFO

fΔ

denotes the CFO.

3 TEST RESULTS

3.1 Test System

The HP 8147A optical time domain reflectometer was

used for preliminary BER floor prediction model. It

was designed long ago and aimed for lightwave

network operators during installation and field

maintenance of their networks.

The OTDR with the plug-in optical interface

module supporting both 1310 nm and 1550 nm

windows, was connected in the test configuration

alternately with the BER tester (BERT) according to

Figure 6.

Figure 6: OTDR and two-way BERT configuration.

OTDR aided fiber testing is naturally out-of-

service, which is certainly not what network operators

favour with neither OTDR, nor BER testing (BERT).

That is why, to make our tests, we connected both the

OTDR and then the BERT to unused Gbit/s “dark”

fiber, and so not interrupt active fibers carrying live

traffic by neither OTDR nor BER tests.

The high-SNR condition that was earlier

considered by the proposed BER floor model as

equivalent to the requirement for large dynamic

range, which is mostly achieved by using long enough

transmitted pulses.

However, as on the contrary, longer pulses are

less credibly considerable as impulses, thus our

choice of about 1 µs long pulse seems to be a good

compromise for the fibers under test.

3.2 Preliminary Test Results

The exemplar OTDR setup, discovered and qualified

events, and screen shots of detailed test traces are

presented in Figures 7 a) – c):

Figure 7: OTDR screen shots: a) setup; b) discovered and

qualified events; c) detailed trace printout.

As it is summarized in Table 3, good matching is

evident between the estimated and the actually

measured residual BER values, both in case of

considering the same test traces as having or not

OTDR based Estimation of Optical Fiber Link Residual OFDM CFO

having dominant reflective events. In the latter case,

abstracting the CFO by the AWGN model provided

the CFO phase error prediction.

Table 3: OTDR trace based estimate vs. measured BER

floor; 50 and 80 km fiber link, 1 Gbit/s.

Link length 50 km 80 km

BER_OTDR

SNR>>

4.13·10

-12

6.31·10

-12

BER_OTDR

CFO

4.24·10

-12

6.41·10

-12

BER_BERT 4.49·10

-12

6.89·10

-12

maxk

ΦΔ

[rad]

4.7·10

-8

6.1·10

-8

This validates the proposed model.

4 CONCLUSIONS

A simple prediction of fiber optic link residual BER

coming out directly from the OTDR trace, is proposed

to extend the standard OTDR functionalities beyond

bare identifying and characterizing various bit-error

generating events, and so enable troubleshooting of

fiber optic links, but also predict the residual BER, as

the ultimate end-to-end transmission performance.

This came out of the idea to consider the reflective

events in the OTDR trace as determining the time

dispersion standard describing parameter – mean

delay spread, so modelling the residual BER of the

fiber link.

The obtained preliminary test results that we

conducted on a dark fiber (to avoid the network

operator dissatisfaction with out-of-service testing),

validated the analytical model, showing good

matching between the OTDR-predicted and actually

measured residual BER, for short transmitted pulses

and large enough OTDR receiver (photodetector)

bandwidth, at least 40 % wider than the reciprocal

pulse width.

Furthermore, when no dominant reflective events

are identified on the OTDR trace, it implies very

small time dispersion allowing the OFDM symbol

cyclic prefix to always prevent inter-symbol

interference, retaining the CFO to solely determine

the residual BER floor. Thus, we abstracted CFO with

the AWGN to enable efficient and quite accurate

short-term BER (and so CFO phase error) predictions.

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PHOTOPTICS 2022 - 10th International Conference on Photonics, Optics and Laser Technology