光学预放大接收机下直检测率OFDM信号的位误码率估算

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本文主要探讨了直接检测光正交频分复用(Direct-Detected OFDM, D-OFDM)信号在光学通信中的比特误码率(BER)估计问题，特别是在使用光学前置放大器接收器的情况下。作者Wei-Ren Peng、Kai-Ming Feng、Alan E. Willner（IEEE Fellow和OSA Fellow）和Sien Chi（OSA Fellow）针对这一技术进行了深入研究。在传统的D-OFDM系统中，每个子载波的信号会受到电平噪声和信号强度的影响，因此首先计算每个子载波的BER是关键步骤。他们考虑了每个子载波的电气信号信噪比(SNR)，并通过统计平均方法来估算整个系统的ensemble BER，即所有子载波误码率的平均值。这种方法被证实与传统的精确错误计数方法相吻合，即使在高阶调制如16-QAM和64-QAM下，仍然能保持较高的准确度，尽管存在光学滤波和极化模色散(PMD)效应的影响。研究结果显示，在10^(-9)的BER阈值下，对于16-QAM和64-QAM系统，相对于传统的4-QAM系统，所需的额外功率预算分别为3.8 dB和8.2 dB。这表明随着调制阶数的提升，为了保证相同的误码性能，需要更大的信号强度来对抗噪声和非线性效应。这对于系统设计者来说，意味着在选择适当的调制方式和功放策略时，必须考虑到这些额外的功率需求。此外，文章可能还讨论了如何通过优化系统架构或采用更先进的数字信号处理技术来减少这些额外的功率消耗，以及如何在实际应用中平衡误码率、带宽效率和功耗之间的关系。这项工作为理解和优化D-OFDM在光纤通信中的性能提供了重要的理论依据和技术指导，有助于提升系统的可靠性和效率。

1340 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 27, NO. 10, MAY 15, 2009

Estimation of the Bit Error Rate for Direct-Detected

OFDM Signals With Optically Preampliﬁed Receivers

Wei-Ren Peng, Kai-Ming Feng, Alan E. Willner, Fellow, IEEE, Fellow, OSA, and Sien Chi, Fellow, OSA

Abstract—In this paper, we provide a numerical bit error rate

(BER) estimation approach for direct-detected orthogonal fre-

quency division multiplexing (OFDM) signals in the presence of

optical preampliﬁed receivers. The individual BER of each subcar-

rier is ﬁrst computed by considering their electrical signal-to-noise

ratio (SNR), and then the ensemble BER is derived simply by

taking the average of all the subcarriers’ BERs. The calculated

BER is veriﬁed by the conventional error-counting approach with

high precision and is still accurate with higher quadratic-ampli-

tude modulation (QAM) formats, even under the inﬂuences of

the optical ﬁltering and polarization mode dispersion (PMD) ef-

fects. Based on our simulation approach, the required extra power

budget for 16- and 64-QAM relative to 4-QAM format are found to

3.8 and 8.2 dB, respectively, at a BER of 10

. Furthermore,

we use this approach to compare the receiving sensitivities and

PMD tolerances for the previous proposed gapped and interleaved

radio-frequency (RF)-tone-assisted OFDM systems. The results

show that the gapped OFDM has a better sensitivity while the

interleaved OFDM has a more PMD-tolerable capability.

Index Terms—Bit error rate (BER), direct detection, optical

ﬁber communication, orthogonal frequency division multiplexing

(OFDM), optical modulation.

I. INTRODUCTION

PTICAL orthogonal frequency division multiplexing

(OFDM) has recently been proposed as a promising

format for optical long-haul transmission since the ﬁber chro-

matic dispersion (CD) could be electrically compensated for by

digital signal process (DSP) procedures at the receiver [1]–[3].

The direct-detected OFDM, which uses only one photodiode

and thus is very simple to be implemented, with eight-channel

wavelength division multiplexing (WDM) system has been

successfully transmitted through 1000 km of uncompensated

standard single-mode ﬁber (SSMF) [4], and with single channel

using virtual single sideband OFDM (VSSB-OFDM) format

also has reached 1600 km of SSMF with only

3 dB power

penalty [5]. Moreover, by utilizing the polarization division

Manuscript received July 29, 2008; revised November 23, 2008. First pub-

lished April 24, 2009; current version published May 08, 2009.

W.-R. Peng is with the Department of Photonics and Institute of Electro-

Optical Engineering, National Chiao Tung University, HsinChu 300, Taiwan

(e-mail: pwr.eo92g@nctu.edu.tw).

K.-M. Feng is with the Institute of Communications Engineering, National

Tsing Hua University, HsinChu 300, Taiwan (e-mail: kmfeng@ee.nthu.edu.tw).

A. E. Willner is with the Department of Electrical Engineering, University of

Southern California, Los Angeles, CA 90089 USA.

S. Chi is with the Yuan-Ze University, Chung Li 320, Taiwan.

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

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/JLT.2008.2012173

multiplexing (PDM) and the self-polarization diversity re-

ceiving, the capacity of a direct-detected OFDM system can be

further doubled with a moderate receiver complexity [6].

To explore in detail how the signal performance would change

with various system parameters, one direct and simple approach

is to evaluate system performances in terms of the bit error

rate (BER). Conventional BER calculation is evaluated by the

error-counting approach, which typically is time and memory

consuming, because to get a certain degree of statistic conﬁ-

dence at low BER, numerous OFDM symbols have to be gen-

erated for counting the errors bit by bit. Thus, an accurate and

highly efﬁcient BER estimation is crucially desired for under-

standing, designing, and optimizing an OFDM system.

A Q-factor approach, which assumes a Gaussian distribution

for the electrical beat noise and estimates the average electrical

signal-to-noise ratio (ESNR) from the received constellations,

is suggested approximating the BER of a 4-quadratic-ampli-

tude modulation (QAM), direct-detected OFDM system [7], [8].

However, there is no evidence in [7] and [8] to justify how well

this Q-factor approach can match the practical error-counting

method in an OFDM system. Thus, both the appropriateness of

the Q-factor approach, which is simply extracted from the re-

ceived constellations without considering the individual ESNR

of each subcarrier, and the suitability of the Gaussian assump-

tion to the electrical beat noise are still unsolved issues.

In this paper, we show that the exact BER of an optically

preampliﬁed direct-detected OFDM signal can be accurately es-

timated by ﬁrst evaluating the individual ESNR of each sub-

carrier and then averaging the BERs of all subcarriers [9]. The

ESNR of each subcarrier can be easily obtained by numeri-

cally computing the power spectral density (PSD) of both the

signal and the beat noises. We found that both the PSD of the

received data subcarrier and the beat noises are colored due

to the ﬁltering effect, which also has been described in [10],

thus yielding a nonuniform ESNR distribution over the sub-

carriers. The numerical results, supported by the error-counting

method, show our scheme can well predict the exact BER even

under tight optical ﬁltering or severe polarization mode disper-

sion (PMD) conditions. Moreover, although a larger QAM size

is more spectrally efﬁcient, the required extra power at a BER

of 10

for the 16- and 64-QAM are found to be 3.8 and

8.2 dB, respectively, relative to the 4-QAM format based on

our BER evaluation technique. In addition, by using our ap-

proach, we compare the sensitivities and PMD tolerances at

BER

10 for the previous gapped and interleaved radio-fre-

quency (RF)-tone-assisted OFDM systems. The results show

that the gapped OFDM exhibits a

2.3 dB better sensitivity

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