Abstract—In this research, the effect of laser phase noise fixing is investigated for different optical channel parameters such as dispersion, attenuation and link distance for Coherent Optical Orthogonal Frequency Division Multiplexing (CO-OFDM) systems. The effect of laser phase noise is examined at different data rates and link distances utilizing only one RF and optical carrier. In this research Phase Shift Keying (PSK) is used as a digital modulation format to maintain the maximum data rate with the acceptable BER value. By fixing the laser phase noise 1.7 Tb/s (111*16 Gb/s) can be obtained from 191.4 to 185.9 THz at 50 GHz spacing over 1000 km link distance using only one optical cable in C and L bands according to the Telecommunication Standardization Sector (ITU-T). In that case high level modulation formats (N-PSK) should be performed with DWDM technique. Keywords—Coherent communications, Fiber optical

communication, OFDM modulation, Optical link design.

I. INTRODUCTION Thanks to its many advantages already known in wireless

communications, OFDM is a convenient solution to struggle with RF microwave multipath fading. On the other hand, optical communications is also defined as a backbone of whole communication systems because of its high capacity with economical and good performance. Recently, fiber optical communication and OFDM method are combined to obtain both advantages in a communication link called CO-OFDM. OFDM has become a popular modulation format because of its powerful performance to RF microwave multipath fading. For that reason OFDM has been extensively implemented in various digital communication standards such as WIMAX, LTE, WIFI. The most important point should be focused on is OFDM splits a high-data rate data-stream into a number of low-rate data-streams that are transmitted simultaneously over a number of subcarriers [1]. On this basis, Coherent optical OFDM (CO-OFDM) has been proposed as an impressive technique for long haul

Manuscript received May 11, 2011. This work was supported partly by

Halmstad University and Karadeniz Technical University. A. Yazgan is with the Electrical Electronics Engineering Department,

Karadeniz Technical University, PK 61080 Turkey (corresponding author to provide phone: 00904622290453; fax: 00904623257405; e-mail: ayhanyazgan@ ktu.edu.tr).

I. Hakki Cavdar is with the Electrical Electronics Engineering Department, Karadeniz Technical University, PK 61080 Turkey (e-mail: cavdar@ ktu.edu.tr).

transmission to remove inter-symbol interference (ISI) caused by chromatic dispersion in fiber optical medium [2]. The main challenge of CO-OFDM is that the phase noise of the local oscillator must be compensated for. In conventional CO-OFDM systems, phase noise is compensated by estimating the local oscillator (LO) offset using the cyclic prefix or preambles [3]. In this paper we focused on the effect of fixing laser phase noise using OFDM pilot subcarriers with different optical channel parameters. We also show that how the phase compensation affects the SNR-BER performance of CO-OFDM system. Attenuation factor and dispersion effect of a SSMF (standard single mode fiber) in C band have also taken into consideration. Attenuation effect is eliminated using Erbium Doped Fiber Amplifiers (EDFA) by properly chosen pump power and cable length to get the minimum nonlinearity. The first transmission experiment has been reported for 1000 km SSMF transmission at 8 Gb/s, and more CO-OFDM transmission experiment have rapidly been reported by S. Jensen et. al. for 4160 km SSMF transmission at 20 Gb/s [4,5]. Direct detection systems have also been worked by J. M. Tang and K. Alan Shore with their work 30 Gb/s Signal Transmission over 40-km link distance [6]. Supporting electronic equalizers, data rates can reach up to 100 Gb/s as reported by Chris R. S. Fludger et. al. with their work Coherent Equalization and POLMUX-RZ-DQPSK for Robust 100-GE Transmission [7]. High spectral efficiency modulation formats can be used to improve the system capacities. But high spectral efficiency formats use multi-level modulation techniques which are usually susceptible to intersymbol interference in optical communication system [8]. Binary PSK (BPSK) and Quadarture PSK (QPSK) is used as a digital modulation format to reach 40 Gb/s data rate with minimum susceptibility. It is known that 50 GHz spacing is being used for very high density wavelength division multiplexing (VHDWDM) [9]. In order to improve the spectral efficiency, BPSK can be upgraded to Quadrature Phase Shift Keying (QPSK) with two suitable RF carriers instead of one. In this case, data rate is 2 times higher than before. On the other hand communication system will be more sensitive to noise.

The rest of this paper is organized as follows. Section II concisely presents the theory of Coherent Optical OFDM systems. The channel model is also given in Section II. Section III discusses other relevant aspects of the application and gives the result that we have after laser phase noise fixing process. Section IV concludes the paper.

Examination of the Effect of Fixing Laser Phase Noise in Coherent Optical OFDM Systems with

Different Channel Parameters Ayhan Yazgan and I. Hakki Cavdar

978-1-4577-1411-5/11/$26.00 ©2011 IEEE TSP 2011121

II. PRINCIPLE OF CO-OFDM CO-OFDM has almost same structure with OFDM.

Actually CO-OFDM uses the advantages of OFDM in optical medium. OFDM is a multi carrier modulation (MCM) system and has a lot of advantages over single carrier systems especially in terms of data rate. Implementing OFDM we must choose the subcarriers orthogonal to each other and the transmission channel affects each subcarrier as a flat channel. This is another advantage because the major disadvantage of classical MCM is that it requires excessive bandwidth. Assuming that f0=0, NSC is the number of subcarriers, Ts is the sampling period, φn is the phase of the nth subcarrier; an OFDM symbol is given by (1). As a convenience, the OFDM signal in (1) shows only one OFDM frame [10-12].

∑−

=

=1

0

)exp().2exp(1)(SCN

nn

SCn

SCss j

NknjC

NkTS ϕπ (1)

As shown in Fig. 1, basically, CO-OFDM system consists

of an electrical OFDM transmitter, an OFDM RF to optical up converter, an optical communication link, an OFDM optical to RF down converter and an electrical OFDM receiver. We model CO-OFDM transmission system as parallel linear channels satisfying minimum nonlinearity condition for the EDFA and Mach- Zehnder modulators (MZM) as shown in Figure 2. It has been proposed and analyzed that by biasing the MZM at null point, a linear conversion between the RF signal and optical field signal can be achieved [13-16]. It has also been shown that by using coherent detection, a linear transformation from optical field signal to RF signal can be achieved [1-8]. So as to obtain the minimum nonlinearity, we choose the EDFA as an amplifier assuming with selected properly pump power and suitable excited cable length. The received optical signal for one OFDM symbol after traversing through communication channel is given in (2-4).

))(().2exp(.)))(2(exp(1

111 njxpetfjctffjE D

Nsc

nnnLDLOLDs ϕπφπ ∑

=++= (2)

LnD

222

1)( ωβϕ = (3)

tDcπ

λβ2

2

2 = , LfDfvn nt

LDD

22

.)( πϕ = (4)

Fig. 1. CO-OFDM block diagram

Fig.2. Optical Channel model for single mode optical fiber

The optical channel model is given in Fig.2. Equations in

(5-6) explain this channel model mathematically. In this model the group velocity delay, includes a dc term φ0, a linear term proportional to the time delay of the first subcarrier τ0, and a quadrature term proportional to the fiber chromatic dispersion Dt in the unit of ps/(nm.km). fLD is the optical carrier frequency and φD(n) is the phase dispersion of each subcarrier owing to the fiber chromatic dispersion [17-20]. cmn and c’mn are transmitted and received signal respectively, hn is the transfer function for the nth subcarrier, φm is the phase drift of the mth OFDM symbol, and nmn is the optical noise for the related subcarrier. The transfer functions of the subcarriers in optical fibers are assumed as static within one OFDM frame. The phase drift within one OFDM symbol can be considered as constant and common to all the subcarriers [21-22]. But after one symbol duration, we recalculate the phase drift and compensate it. We chose 20 kHz linewidth for each laser diode which is close to the value achieved with commercially available. In order to struggle with ISI which causes disappearing of orthogonality between subcarriers in CO-OFDM system a cyclic prefix is added at the beginning of the data subcarriers. If a cyclic prefix whose extension is longer than the channel delay spread is added in front of the CO-OFDM symbol, the delay spread that is the effect of chromatic dispersion can not create ISI as given in (7) where v is the light velocity in fiber cable, fLD is the optical carrier frequency, Dt is the chromatic dispersion, ∆f is the subcarrier spacing and ∆G is the guard interval length.

mnmnmnmn njhcc += )exp(..' ϕ (5)

)))(2(exp( 00 nfjh Dnn ϕτϕ +Π+= (6)

GfsctLD

NDfv Δ≤Δ2

(7)

Receiving data with low BER, laser phase drift must be

estimated and fixed from the received signal. For this purpose pilot carriers of the OFDM signal can be used. This procedure is given (8) where φ-

m is the laser phase drift to be estimated, “pa” is the phase angle of the information symbol, pa(cmn) is known transmitted pilot subcarrier and pa(c’mn) is the received information symbol.

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∑=

−−=

SPN

nmnmn

PSm cpacpa

N 1

' )]()([1ϕ (8)

The average of the difference between transmitted and received subcarrier phases will be strongly related to the average laser phase shift. Laser phase noise fixing process is carried out just after the laser phase drift estimating process is completed, Equations given below in (9-11) explain the procedure mathematically [23, 24].

)exp('−

−= mmn

fs

mn jcc ϕ (9)

2

*

n

nfs

mnmnhhcc =

− (10)

III. RESULTS AND DISCUSSION The variables of fiber optical channel were determined

based on three parameters. The first one is a phase component whose variation depends on the subcarrier frequency and occurs because of chromatic dispersion, the second one is laser phase noise effect and the last component is the optical noise. 0.2 dB/km attenuation coefficient is chosen for a single mode fiber cable. The link distance is the main factor to determine the number of EDFA which is chosen 14 for 1000 km link distance. Due to its lack of sensitivity of amplitude changing, phase shift keying (PSK) has been chosen to constitute an OFDM symbol. Optical fiber parameters and basic OFDM parameters are given Table 1. Comparing pure silica, doping can change material dispersion parameter. For example germanium-doped silica has different material dispersion parameter depends on the percentage of the germanium used [25]. For that reason different dispersion parameters are assigned as an input although we use the same wavelength.

TABLE 1 BASIC PARAMETERS FOR COMPUTER SIMULATION

Parameter Value Wavelength 1550,92 nm Velocity of light in fiber cable 200000 km/s Fiber optical cable length 100 -1000 km Chromatic dispersion parameter of fiber (Dt)

6 ps/(nm.km), 17 ps/(nm.km)

Modulation BPSK,QPSK Data Rate (Gb/s) 5, 8, 16,40 Sampling frequency fS fs > 20 GHz Sampling Period TS TS < 50 ps Useful symbol duration TU 25.6 ns Cycling prefix duration TCP 3.2ns, 6.4 ns Symbol duration TSYM=TU+TCP 28.8 ns, 32ns Data subcarrier number NSD 448 Pilot subcarrier number NSP 64 Total subcarrier number NSC=NSD+NSP 512

In this work, firstly SNR-BER graphics are obtained for two different dispersion parameters to show the effect of chromatic dispersion parameter. Comparing with the laser phase noise effected results, running the laser phase noise reduction process, we have 5.5 dB SNR advantage for the dispersion parameter 17 ps/(nm.km), as shown in Fig. 3-a. On the other hand as it can be seen in Fig. 3-b, if we choose the dispersion parameter 6 ps/(nm.km), we have 3 dB SNR advantage for 10-4 BER value. If we choose dispersion parameter constant 6 ps/(nm.km), in Fig.4, we need better SNR values to achieve 10-4 BER value because of increasing data rate from 5 Gb/s to 16 Gb/s.

Data rates 5, 8 and 16 Gb/s show only how the CO-OFDM system is affected with the increasing the number of bits transmitted per second. Standard schemes at these data rates use 10 Gb/s or 40 Gb/s rates (such as STM-256). 40 Gb/s results can be seen in Fig.6-7. To reach up to 1.7 Tb/s for long haul transmission through one single fiber core, it is clear that DWDM should be applied to the CO-OFDM system.

(a)

(b)

Fig. 3. BPSK SNR-BER performance for 100 km link distance and 8 Gb/s data rate. (a) Dt: 6 ps/(nm.km), b) Dt: 17ps/(nm.km).

123

(a)

(b)

Fig. 4. BPSK SNR-BER performance for 100 km link distance and Dt: 6

ps/(nm.km). (a) 16 Gb/s. b) 5 Gb/s.

It is well known that BER threshold of 10-2 is a sufficient level for advanced Forward Error Correction (FEC) algorithm to get produce sufficient BER values [1].

Fig.5. shows constellation diagrams of BPSK modulated received data for one OFDM symbol. If we compare Fig.5 (a) and (b), switching SNR from 3 dB to 13 dB, under the condition of 8 Gb/s data rate and 1000 km link distance, constellation diagrams change dramatically because of noise effect. On the other hand if we compare Fig.5 (b) and (c), switching dispersion parameter from 17 ps/(nm.km) to 6 ps/(nm.km), under the condition of 10 dB signal to noise ratio, constellation diagrams change their shape from an ellipsoid to a circle. This result is directly related to the chromatic dispersion effect producing extra imaginary part which comes out as a phase shift in constellation diagrams. Switching from BPSK to QPSK, data rates reach up to 40 Gb/s seen in Fig.6-7. In that case data rate is increased but higher SNR is also needed to keep the same BER values obtained from BPSK results.

(a)

(b)

(c)

Fig. 5. BPSK Constellation diagrams L:1000 km, 8 Gb/s data rate. (a) Dt: 17 ps/(nm.km), SNR:3 dB. (b) Dt: 17 ps/(nm.km), SNR:13 dB. (c) Dt: 6 ps/(nm.km), SNR:13 dB.

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Fig. 6. 40 Gb/s QPSK SNR-BER performance, L:100-300 km , Dt: 17 ps/(nm.km)

Fig. 7. 40Gb/s QPSK Constellation diagrams L:100 km, Dt: 17ps/(nm.km) SNR:11 dB.

IV. CONCLUSION Transmission performance of CO-OFDM is examined and

simulated especially at long distances and high data rates. Since the laser phase noise is the main topic of this paper, it is previously observed. Simulations based investigations also show that CO-OFDM is able to efficiently eliminate the chromatic dispersion in electrical domain if the laser phase noise is properly compensated. According to the simulation results, it is clear that laser phase noise fixing process is more effective in high dispersive mediums for high data rates. In this study it is important to know that results are given for one optical channel (such as 1550,92 nm) instead of whole WDM in order to support different WDM configurations.

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