ON THE BER ESTIMATION OF EXPERIMENTAL DIRECT

DETECTION OFDM SYSTEMS

Tiago Alves and Adolfo Cartaxo

Group of Research on Optical Fibre Telecommunication Systems, Instituto de Telecomunicac¸˜oes, DEEC

Instituto Superior T´ecnico, Avenida Rovisco Pais 1, 1049-001, Lisboa, Portugal

Keywords:

Optical ﬁber communications, Orthogonal frequency division multiplexing, Performance evaluation.

Abstract:

We propose to extend the exhaustive Gaussian approach (EGA) to assess the bit error ratio (BER) of ex-

perimental direct detection optical orthogonal frequency division multiplexing setups. Excellent agreement

between the actual probability density function (PDF) of each subcarrier and the Gaussian PDF estimated

from a set of experimental runs is shown. The proposed EGA allows evaluate quickly the BER as only a few

hundreds of runs are required to reach stabilized BER estimates. The BER estimated by EGA has shown an

excellent agreement with the BER estimates provided by direct error counting.

1 INTRODUCTION

Orthogonal frequency division multiplexing (OFDM)

has been proposed in the past few years as a promis-

ing technology to be used in different range opti-

cal networks (Llorente et al., 2008; Lin et al., 2008;

Schmidt et al., 2009). The main impairments of

OFDM-based networks have been extensively ana-

lyzed experimentally and through numerical simu-

lation (Schmidt et al., 2009; Schuster et al., 2008;

Alves and Cartaxo, 2009; Lowery, 2008; Jansen et al.,

2009; Peng et al., 2008). The performanceassessment

has been accomplished by using three main ﬁgures

of merit: direct error counting (DEC), error vector

magnitude (EVM) and Q factor. DEC provides rig-

orous bit error ratio (BER) estimates but the amount

of transmitted data required to achieve low BER lev-

els may lead to unacceptable measurement time. The

assessment of the system performance from EVM and

Q factor approaches allows overcome this limitation.

However, these approaches may lead to unreliable

estimates of the system performance as the statisti-

cal distribution of the subcarriers distortion may not

be rigorously taken into account due to the assump-

tions of the analytical formulation each approach re-

lies on. Furthermore, the different signal-to-noise

ratio (SNR) of each subcarrier is not considered by

these approaches. Further information regarding the

validity range of these ﬁgure of merits to evaluate the

performance of DD OFDM systems can be found in

(Alves and Cartaxo, 2010), where the BER was as-

sessed for two types of DD-OFDM systems through

numerical simulation.

In a previous work, a novel approach to evaluate

the BER of each subcarrier of a direct detection (DD)

optical OFDM system through numerical simulation

has been proposed (Alves and Cartaxo, 2009). In

that case, the mean and the standard deviation (STD)

of each subcarrier of each OFDM symbol are ob-

tained through numerical simulation and analytically,

respectively, and an exhaustive Gaussian approach

(EGA) is used to evaluate the BER of each subcar-

rier. The main advantage of the EGA is the possibil-

ity to take into account separately the noise and inter-

ference effects. In this work, we propose to extend

that approach to experimental DD-OFDM systems by

evaluating the statistical properties of each subcarrier

required by the EGA from a set of experimental runs.

2 EXHAUSTIVE GAUSSIAN

APPROACH DESCRIPTION

The EGA considers that the received components (I

and Q) of each OFDM subcarrier are well described

by a Gaussian distribution (conﬁrmed numerically in

(Alves and Cartaxo, 2009)). The extension of the

EGA to experimental setups is based on the estima-

tion of the mean and STD of each subcarrier over a

set of experimental runs. In this case, the BER of the

I or Q component of the k-th subcarrier is given by:

154

Alves T. and Cartaxo A. (2010).

ON THE BER ESTIMATION OF EXPERIMENTAL DIRECT DETECTION OFDM SYSTEMS.

In Proceedings of the International Conference on Data Communication Networking and Optical Communication Systems, pages 154-158

DOI: 10.5220/0002988701540158

 SciTePress

BER

(I,Q)

[k] =

∑

i=1

(i)

(I,Q)

[k]=0





(I,Q)

[k] −m

(i)

(I,Q)

[k]

(i)

(I,Q)

[k]





∑

i=1

(i)

(I,Q)

[k]=1





(i)

(I,Q)

[k] −F

(I,Q)

[k]

(i)

(I,Q)

[k]





. (1)

where m

(i)

(I,Q)

[k] is the mean and σ

(i)

(I,Q)

[k] is the STD

of the k-th subcarrier of the i-th OFDM symbol at the

output of the system setup, given by:

(i)

(I,Q)

[k] =

∑

n=1

(i)

(I,Q),n

[k]

(i)

(I,Q)

[k] =

∑

n=1



(i)

(I,Q),n

[k] −m

(i)

(I,Q)

[k]



(2)

where y

(i)

(I,Q),n

[k] is the received I or Q component of

the subcarrier transmitted in the n-th run and N

is the

number of runs. In eq. (1), a

(i)

(I,Q)

[k] identiﬁes the bit

transmitted in the (I,Q) component of the k-th sub-

carrier of the i-th OFDM symbol and F

(I,Q)

[k] is the

decision threshold level of the k-th subcarrier. N

the number of transmitted OFDM symbols per run

and Q(x) = 0.5erfc



√



. Eq. (1) considers that bi-

nary phase shift keying (BPSK) or quadrature phase

shift keying (QPSK) symbol mapping is used. Nev-

ertheless, the estimation of the BER using the EGA

for other more efﬁcient mappings can still be accom-

plished by developing a generalized version of eq. (1)

and using the same procedure to evaluate the means

and the standard deviations of each subcarrier as the

one described in this work. If BPSK symbol map-

ping is used (with symbols j and −j), the means and

the standard deviations of eq. (1) are relative to the Q

component only. Instead, if QPSK is used and assum-

ing that the I and Q signal components at the equal-

izer output are uncorrelated and that Gray mapping is

used, the BER of each OFDM subcarrier is given by

BER[k] =

[1−(1−BER

[k]) (1−BER

[k])], where

BER

[k] and BER

[k] are the BER of the I and Q

components of each subcarrier at the equalizer out-

put given by eq. (1). The overall BER is evaluated

averaging the BER over all information subcarriers.

It should be stressed that the EGA described by

eq. (1) to evaluate the BER of each subcarrier con-

siders a Gaussian distribution for noise and allows

characterizing correctly the statistical distribution of

the distortion rather than using a Gaussian distribution

to characterize the distortion induced on all subcarri-

ers, as assumed when the BER is calculated from the

EVM or the Q factor. This indicates that distortion-

induced degradation due to, for instance, electro-optic

modulator nonlinearity, non-ideal frequency response

of the different devices, I/Q imbalance or phase offset,

should be correctly accounted by eq. (1). The distor-

tions effects that are not addressed in this work will

be investigated in future work.

3 EXPERIMENTAL SETUP

OFDM ultra-wideband(UWB) signals are used in this

work to demonstrate the accuracy of the extended

EGA to estimate the BER in experimental setups. The

results presented in (Alves and Cartaxo, 2009) sug-

gest that the proposed method can also be used to es-

timate experimentally the BER of other DD-OFDM

signals, as the ones proposed for long-haul systems.

The OFDM-UWB radio signal is composed by 128

subcarriers from which 100 are used as information

subcarriers, the spectrum occupies 528 MHz of band-

width and the time interval of each OFDM symbol is

312.5 ns. Further details on the OFDM-UWB signal

generation can be found in (Alves and Cartaxo, 2009),

(ECMA-368, 2007).

Figure 1 shows the experimental setup used to as-

sess the accuracy of the proposed EGA. The measured

spectra of the OFDM-UWB signal along the setup are

also shown as insets in Figure 1. The OFDM-UWB

baseband signal is generated off-line and converted to

the electrical domain by a Tektronix AWG7052 oper-

ating in continuous mode. The OFDM-UWB signal

is composed by 32 symbols and BPSK mapping is

employed. The baseband OFDM-UWB signal is up-

converted to the ﬁrst UWB subband with carrier fre-

quency of 3.4 GHz and is then applied to a Sumitomo

single-electrode 10 Gbit/s intensity modulator biased

at the quadrature point. Due to the lack of electrical

ampliﬁers with adequate bandwidth, only a 4% mod-

ulation index (deﬁned as the ratio between the root

mean square voltage of the OFDM signal applied to

the modulator arms and the modulator bias point) is

reached and, as a consequence, a high optical signal-

to-noise ratio (OSNR) has to be used to achieve ac-

ceptable BER levels. A variable optical attenuator

(VOA) and an optical ampliﬁer (noise ﬁgure of 4.5

dB) are used to adjust the OSNR (deﬁned in a ref-

erence optical bandwidth of 0.1 nm). At the optical

receiver, the signal is optically ﬁltered by a Kylia de-

multiplexer with 50 GHz of channel spacing and 32

GHz of bandwidth, and photodetected by a Discov-

ery Semiconductors PIN with 0.7 A/W and 9 GHz

of bandwidth. The detected OFDM-UWB signal is

down converted and low-pass ﬁltered to reduce the

ON THE BER ESTIMATION OF EXPERIMENTAL DIRECT DETECTION OFDM SYSTEMS

155

2.4 2.9 3.4 3.9 4.4

frequency [GHz]

193.095 193.1 193.105

frequency [THz]

2.8 3.1 3.4 3.7 4

5 dB/div.

0 250 500

frequency [GHz]

frequency [MHz]

20 dB/div.

5 dB/div.

AWG

LPF

Laser

VOA

EDFA

OSA

10%

90%

VOA

EDL

LPF

5 Gs/s

DSO

5 Gs/s

DSP

synchronization marker

BER

Estimation

AWG: arbitrary waveform generator

DSO: digital signal oscilloscope

DSP: digital signal processing

LO: local oscillator

EDL: electrical delay line

EDFA: erbium doped fiber amplifier

LPF: low-pass filter

PC: polarization controller

VOA: variable optical attenuator

OSA: optical spectrum analyzer

PIN: positive-intrinsic-negative

OF: optical filter

TF: transmission fiber

BER: bit error ratio

Figure 1: DD optical OFDM system used to assess the accuracy of the EGA in experimental setups. Measured spectra of the

signals at different points of the system setup (insets).

noise and the out-of-band distortion. Two different

Mini-Circuits low pass ﬁlters (LPF) are used in the

experiments in order to analyze different distortion

situations: the VLFX-225 (-3 dB bandwidth of 345

MHz) and the VLFX-300 (-3 dB bandwidth of 450

MHz). Finally, the OFDM signal is acquired by a real

time oscilloscope Agilent DSO81204A that is con-

nected to a PC to perform the OFDM demodulation

and equalization by digital signal processing (DSP),

and BER measurement.

4 EXPERIMENTAL RESULTS

In this study, the accuracy of the proposed approach

is assessed considering only noise and distortion in-

duced by the frequency response of the devices. The

number of experimental runs required to get stabilized

BER estimates is also analyzed while ﬁbre transmis-

sion and nonlinear system effects will be addressed in

future work.

The validity of the Gaussian distribution consid-

ered for each OFDM subcarrier in the EGA is ana-

lyzed by comparison with the actual probability den-

sity functions (PDF) obtained experimentally. 4×10

runs have been used to evaluate the PDFs.

Figure 2 shows the actual PDFs of the Q compo-

nent of four OFDM subcarriers at the equalizer output

and the PDFs obtained when the Gaussian distribu-

tion is considered. Figure 2 shows that the Gaussian

distribution ﬁts very well the actual PDF of the sub-

carriers and that the subcarriers located at the edges

of the spectrum present high variance leading to dif-

−3 −2 −1 0 1 2 3

−3.5

−2.5

−1.5

−0.5

0.5

signal amplitude

log

PDF

−3 −2 −1 0 1 2 3

−3.5

−2.5

−1.5

−0.5

0.5

signal amplitude

log

PDF

Figure 2: PDF of the subcarriers at the system output for

OSNR=27.3 dB and considering the subcarriers located in

a) the edges and b) the middle of the OFDM-UWB spec-

trum. Gaussian PDF (lines) and actual PDF (marks). LPF:

VLFX-225.

ferent SNRs between the subcarriers, as mentioned

before. As the tail region is also adequately described

by a Gaussian distribution, Figure 2(a) indicates that

a very good accuracy of the BER estimates obtained

from the EGA is expected. The main advantages of

DCNET 2010 - International Conference on Data Communication Networking

156

0 200 400 600 800 1000

−7

−6

−5

−4

−3

−2

−1

runs

log

BER

OSNR=25.4dB

OSNR=26.4dB

OSNR=27.3dB

OSNR=28.4dB

OSNR=29.3dB

lines: DEC; marks: EGA

LPF: VLFX−225

0 20 40 60 80 100

−9

−7

−5

−3

−1

subcarrier index

log

BER

lines: DEC; marks: EGA

OSNR=26.4dB

OSNR=27.3dB

LPF: VLFX−225

Figure 3: a) BER as a function of the noise runs. b) BER as

a function of the subcarriers index.

the proposed EGA are the fast and good estimates

of the system performance independently of the BER

levels. Hence, one of the key parameters of the EGA

is the number of runs needed to achieve good BER

estimates.

Figure 3(a) depicts the BER of the OFDM sys-

tem as a function of the number of runs used in the

EGA to estimate the properties of the Gaussian dis-

tribution. The BER obtained from the DEC is also

shown as a reference. In order to obtain a good con-

ﬁdence on the BER estimates, the BER provided by

DEC is evaluated when at least 100 errors occur in the

subcarrier with worst performance. Figure 3(a) shows

that a few hundreds of noise runs are enough to obtain

conﬁdent overall BER estimates using the EGA, inde-

pendently of the OSNR level. Nevertheless, in the fol-

lowing, 1000 noise runs are considered in order to get

a reasonable conﬁdence on the estimation of the BER

of the subcarriers showing lower BER. Figure 3(b)

shows the BER as a function of the subcarrier index

(subcarriers with lower indexes correspond to subcar-

riers transmitted at lower frequencies) for two OSNR

levels. The BER obtained with DEC is evaluated over

3.3 ×10

and 4.3 ×10

runs for the case with lower

and higher OSNR, respectively. Figure 3(b) shows

that the BER of each subcarrier provided by EGA ﬁts

well the BER measured by DEC. The discrepancy ob-

served in the estimated BER of the center subcarriers

is attributed to rare error events. Figure 3(b) shows

also that some subcarriers present high BER peaks.

25 27 29 31 33

−10

−8

−6

−4

−2

OSNR [dB]

log

BER

DEC: filled marks

EGA: empty marks

LPF: VLFX−300

LPF: VLFX−225

Figure 4: BER as a function of the OSNR.

This is due to the non-ideal frequency response of the

devices.

Figure 4 presents the BER of the optical OFDM-

UWB system as a function of the OSNR for the two

LPFs considered along this work. The BER obtained

with DEC is evaluated when at least 100 errors occur

on the subcarrier with worst performance. The com-

parison between the BER estimated by both methods

shows that the BER can be estimated using the EGA

with a very good agreement with DEC, independently

of the OSNR levels, avoiding the high amount of data

necessary to estimate the BER from DEC. For in-

stance, for the VLFX-225 LPF and OSNR=29.3 dB

case, the BER estimated by DEC requires (to get 100

errors in the subcarrier showing worst performance)

the transmission of 3.84×10

OFDM-UWB symbols

whereas the EGA only requires 3.2 ×10

symbols.

This difference is still higher when the estimation of

lower BER levels is desired as more symbols are re-

quired to estimate the BER using DEC.

5 CONCLUSIONS

An extension of the exhaustive Gaussian approach

(EGA) to estimate the BER of each subcarrier in ex-

perimental direct-detection OFDM setups has been

proposed. It has been experimentally shown that

the actual statistical distribution of each OFDM sub-

carrier is well described by a Gaussian distribution

whose statistical properties are estimated over a set

of few hundreds of noise runs. Additionally, the ex-

perimental results have shown that the BER of each

OFDM subcarrier estimated by the EGA agrees very

well with the actual BER obtained from direct error

counting with the advantage of providing fast esti-

mates, independently of the estimated BER levels.

The comparison between the BER estimates pro-

vided by the EGA with ones obtained using the EVM

or the Q factor approaches in DD OFDM experimen-

tal setups will be reported elsewhere.

ON THE BER ESTIMATION OF EXPERIMENTAL DIRECT DETECTION OFDM SYSTEMS

157

ACKNOWLEDGEMENTS

The work of Tiago Alves was supported by Fundac¸˜ao

para a Ciˆencia e a Tecnologia (FCT) from Por-

tugal under contract SFRH/BD/29871/2006. This

work was also supported in part by the EU FIVER-

FP7-ICT-2009-4-249142 project and FCT-funded

TURBO-PTDC/EEA-TEL/104358/2008 project.

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