Performance Analysis of a Spectrally Efficient QAM Coherent OFDM Optical Link

1

𝑇𝑆

𝑇𝑆

∫ exp⁡(𝑗2𝜋(𝑓𝑘 − 𝑓𝑙 )𝑡)𝑑𝑡

0

= exp⁡(𝑗𝜋(𝑓𝑘 − 𝑓𝑙 )𝑇𝑆)

𝑠𝑖𝑛 (𝜋(𝑓𝑘−𝑓𝑙 )𝑇𝑆 )

π (fk−fl )TS

(3)

The two subcarriers become orthogonal to each other

if they satisfy the following condition

⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑓𝑘 − 𝑓𝑙 = 𝑚

1

𝑇𝑆

(4)

where m must be a positive integer. As OFDM uses

partially overlapped spectrum of the subcarriers it provides

higher Spectral efficiency as co mpared to the tradit ional

MCM techniques. Also if the subcarrier frequencies are

spaced at a multiple of inverse of the symbol period, the

signal can be recovered back without any ICI.

CO-OFDM is imp lemented by optical I-Q modulat ion

in conjunction with coherent detection. It shows higher

performance in terms of bandwidth efficiency and receiver

sensitivity. A generic CO-OFDM system is shown in Fig.

1, it has five basic functional blocks: OFDM transmitter,

in RF-to-optical (RTO) up-converter, optical link, optical

to RF (OTR) down converter, and OFDM receiver. The

coherent system provides OFDM linearity in RTO up -

conversion and OTR down -conversion. OFDM brings

coherent system co mputation efficiency and ease of

channel and phase estimation. Due

its superior

scalability with the b it rate of the transmission systems,

CO-OFDM is well-positioned to be an attractive choice of

modulation format for the next generation of 100 Gb it/s

transmissions [9].

to

RF OFDM

Transmitter

RF to Optical

Up-converter

Data

Fiber

Link

Optical

Amplifier

𝑠(𝑡) = ∑

∞

𝑖=−∞

∑

𝑁𝑆𝐶

𝑘=1

𝑐𝑘𝑖𝑠𝑘 (𝑡 − 𝑖𝑇𝑠 )

(1)

Data

RF

OFDM

Receiver

Optical to RF

Down-converter

𝑆𝑘(𝑡) = ᴨ(𝑡)exp⁡(𝑗2𝜋𝑓𝑘 𝑡) (2)

Fig. 1. A generic Coherent OFDM network

where

Sk(t) represents the kth subcarrier of the OFDM

fk represents the k th frequency of the subcarrier

Ts represents the symbol period

cki is the ith information symbol at the k th subcarrier

ᴨ = {1⁡, 𝑓𝑜𝑟⁡0 < 𝑡 ≤ 𝑇_𝑆⁡⁡}

The correlation between any two subcarriers in an

OFDM symbol can be represented as

𝛿𝑘𝑙 =

1

𝑇𝑠

𝑇𝑠

∫ 𝑆𝑘𝑆𝑙

0

∗𝑑𝑡

In CO-OFDM

in each symbol period 𝑇𝑆 , 𝑁𝑆𝐶

number of symbol carriers are transmitted thus giving

symbol period 𝑅 = 𝑁𝑆𝐶 𝑇𝑆⁄ . Bandwidth of the OFDM

signal is given by [8]

𝐵𝑂𝐹𝐷𝑀 =

2

𝑇𝑆

+

𝑁𝑆𝐶 −1

𝑡𝑆

(5)

where 𝑡𝑆 is the observation period of DFT window. The

spectral efficiency can be expressed as

⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝜂 = 2

(6)

𝑅

𝐵𝑂𝐹𝐷𝑀

where R

is the symbol rate, 𝐵𝑂𝐹𝐷𝑀 is the OFDM

Performance analysis of a spectrally efficient QAM coherent OFDM optical link 301

bandwidth and the factor of 2 represents the two

polarization states of the fiber.

impulse response filter desirable performance can be

achieved.

4. Digital signal processing in coherent

detection

signals,

In long haul transmission Reduced Guard Interval

frequency

frame

joint

CO-OFDM

synchronization has been

realized using Almouti

Algorith m [13] and d igital co mputation of Fract ional

Fourier Transform [14].

and

like

carrier

synchronization,

Earlier, Phase Locked Loop (PLL) was used for

synchronizing the carrier, but its performance is limited

when used with high speed optically modulated signals,

hence it is being rep laced by DSP un it. The DSP

component makes it possible to perform many offline

dispersion

functions

compensation and polarizat ion align ment. It performs the

compensation of fiber impairments in digital do main and

helps to recover the signal after coherent detection [10].

DSP is providing us with the suitable technology for

building h igh speed coherent optical networks beyond

100G [11]. Emp loying DSP at the transmitter or receiver

side makes the reception for advanced modulation formats

simp ler and also enables the impairments to be processed

and compensated for in the digital domain [12].

available

co mponent

The Universal DSP

in

OPTISYSTEM

includes 12 functions and algorithms

starting with a preprocessing stage (add noise to signal,

DC blocking and normalization) fo llowed by the signal

recovery stage (Bessel Filter, Resamp ling, Quadrature

Imbalance (QI) Co mpensation, CD Co mpensation, NL

compensation, Timing recovery, Adaptive Equalizer, down

sampling and carrier phase estimation). It uses the Gram-

Schmidt orthogonalization procedure to co rrect for non

orthogonalizat ion in received signal. An all pass digital

filter can be used to compensate for CD resulting fro m

propagation over fiber. The dispersion compensating filter

can be imp lemented in either the frequency domain or

time do main. The slope of this function depends on the

fiber characteristics and length. Dispersion compensation

is achieved by filtering the inco ming signal using a phase

the fiber. Dispersion

that of

response opposite

compensation filtering can be done two ways: Finite

Impulse Response (FIR) or Infinite Impu lse Response

(IIR). This component is mainly responsible in enhancing

the performance of the link and depending on the transfer

function in frequency domain or impulse response of finite

to

5. Measure of performance-error vector

magnitude

Error Vector Magnitude (EVM ) is a suitable standard

for measuring performance of optical links limited by

Additive White Gaussian Noise (AW GN)

In

literature, many researchers use the EVM values to

compare

links

employing higher order modulation formats.

the performance of d ifferent optical

[15].

EVM is a measure of the effective distance between

the received symbol and its expected ideal position in the

constellation diagram. The EVM of the received signal is

calculated as

𝐸𝑉𝑀 =

̅̅̅̅̅̅̅̅̅̅̅̅̅̅

√|𝑆−⌊𝑆𝐷⌋|2

̅̅̅̅̅̅̅̅̅̅ ∗ 100% (7)

|⌊𝑆𝐷⌋|2

where S represents the signal sequence and 𝑆𝐷 is the

decision of S. Thus EVM can be used in coherent optical

lin ks emp loying advanced modulation techniques like

QAM to measure the system performance and evaluate the

quality of received signal Also using the values of EVM

we can dependably estimate the BER [16]. For a system

emp loying M-ary modulation, EVM and BER for a 16-

QAM vector signal can be expressed as

⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝐵𝐸𝑅 =

3

4

𝑄 (√

1

5𝐸𝑉𝑀2)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡ (8)

where Q(.) is the Gaussian co-error function. In order to

get optimu m perfo rmance, the BER of the optical lin k

should be less than 10 -9 and EVM value should be less

than 10%.

Fig. 2. Simulation setup of Coherent M-ary QAM-OFDM optic link

302 P. Rishi, S. Tamil Selvi

6. Simulation setup and results

The simu lations for this work have been done using the

tool OPTISYSTEM by Optiwave, the designed link is

shown in Fig. 2. At the transmitter both modulation and

mu ltip lexing are achieved digitally using an Inverse Fast

Fourier Transform (IFFT). The symbol rate employed is

10 Bd and bits are generated at the rate of 40 Gbps for

QAM-16 and 50 Gbps for QAM-32. The QAM sequence

generator provides square shape constellation with 4

bits/symbol fo r QAM-16 and 5 b its/symbol for QAM-32.

This sequence is modulated by OFDM modulator having a

maximu m of 128 subcarriers out of which 80 subcarriers

are being used. It uses symbol extension as cyclic prefix to

mitigate inter symbol interference. A Continuous Wave

Distributed Feedback (CW DFB) Laser and two Mach-

Zehnder modulators are used to up-convert fro m the RF to

the optical domain. CW DFB is centered at frequency of

193.1 THz, emits power of 10 dBm and has 0.1 M Hz

linewidth.

The signal is then propagated through a Standard

the

fiber. Non

impairments

Single Mode Fiber (SSMF) having attenuation of 0.2

dB/Km and dispersion value of 16.75 ps/nm/km. As the

signal travels through the fiber it becomes degraded due to

linear and

linear

in

impairments become significant when the power in the

signal is increased in order to increase the system capacity.

A coherent QAM receiver based on homodyne detection is

used to down-convert the data to the RF do main. The

connection between

and

demodulator depicts the training sequences used for

synchronization and channel estimation. The BER test set

generates a sequence which is given as input to the QAM

sequence generator, after the sequence passes through the

entire link it is compared with the initial sequence to

calculate BER.

the OFDM modulator

The system parameters used for the simulat ion study

are given in Table 1. The sy mbol rate employed is 10 Bd

and the bit rates used are 40 Gbps and 50 Gbps for QAM-

16 and QAM-32 schemes respectively. The simu lations

have been carried out using the tool OPTISYSTEM.

Table 1. Simulation Parameters of Coherent M-ary QAM OOFDM link

Global Parameters

QAM -16 Sequence

Generator

OFDM M odulator

CW-DFB Laser

Single M ode Fiber

CO-OFDM Receiver

OFDM Demodulator

BER Test Set

Simulation Parameters

(a)

Bit rate

Symbol rate

Sequence length

Samples per bit

Number of samples

Bits per symbol

Constellation type

Gray code

Cyclic prefix

No of prefix points

Average OFDM power

No of subcarriers used per port

Subcarrier location

Frequency

Power

Linewidth

Attenuation Coefficient

Dispersion Coeff. (D)

Dispersion Enabled

Birefringence type

PM D Coeff. (Dp)

(b)

(c)

(d)

(e)

(a)

(b)

(c)

(a) M ax possible subcarriers

(b)

(c)

(d)

(e)

(f)

(a)

(b)

(c)

(a)

(b)

(c)

(d)

(e)

(f) M odel Type

(g)

(h)

(i)

(a)

(a)

(b)

(a)

(b)

NL effect Enabled

Aeff

n2

Power

No. of prefix points

No. of training Symbols

Bit Rate

No. of pilot symbols

40 Gbps

10 Baud

32768

1

32768

4

Square

True

128

Symbol Extension

10

15 dBm

80

25-104

193.1 THz

10 dBm

0.1 M Hz

0.2 dB/km

16.75 ps nm-1km-1

GVD,TOD

Stochastic

0.05 ps/km1/2

Scalar

SPM

80 µm2

26 x 10-21 m2/W

10 dB

10

10

Bit Rate*(80/120)

6

The performance o f these systems has been analyzed

in terms of BER, Error Vector Magnitude (EVM) and

constellation diagrams. A series of simulat ions were

performed, in the first one the BER performance of a

Performance analysis of a spectrally efficient QAM coherent OFDM optical link 303

single polarization QAM-16 OFDM link with DD was

studied. In the second simulat ion keeping other parameters

constant performance of coherent detector follo wed by

Universal DSP and decision component (no OFDM) was

analyzed by varying length of SSMF. The universal DSP

impairment

dig ital

component

compensation

inco ming

in

transmission signal after coherent detection. The Decision

component processes the I and Q electrical signal channels

and performs a decision on each received symbol based on

normalized threshold settings.

performs

to aid

recovering

do main

the

The Figs. 3-7 summarize the BER and EVM values

obtained for different link designs and variation in fiber

length. A DD QAM-16 lin k g ives errorless transmission up

to 20 km only. Whereas a QAM-16 modulated signal when

detected with coherent detector followed by a universal

DSP element increases the SSMF length to 150 km for

EVM=9.64%. In coherent detection the receiver can

extract any informat ion wh ich is embedded in either phase

and/or frequency; this makes the receiver much more

sensitive than Direct Detection (DD). Employ ing OFDM

at the coherent detector further increases the transmission

length to 250 km for EVM of 10.16%. Subsequently

QAM-16 OFDM coherent detection link performance was

compared

(DP)

configurations.

for single and Dual Po larization

With single polarizat ion in each QAM-16 signal

1baud is made up of 4 bits whereas after DP in each

QAM-16 signal each baud consists of 8 bits, thus DP

QAM doubles the data rate of the optical lin k and adds

additional degree of freedo m. This increased channel

capacity is at the cost of slightly increased BER and EVM

values. To further increase the system capacity a single

polarization QAM-32 OFDM link was simulated. Each DP

QAM-64 signal carries 16 b its in each baud as compared

with 8 bits in each baud for SP QAM-64 signal. But as we

move to higher o rder modulation formats like QAM-64 it

results in a large increase in the transmitter and receiver

complexity.

Fig. 4. EVM vs. Fiber Length for a QAM-16 link with

Coherent Detection and universal DSP (no OFDM)

Fig. 5. EVM vs. Fiber Length for QAM-16 Single

Polarization CO-OFDM

Fig. 6. EVM vs. Fiber Length for QAM-16 DP CO-OFDM

Fig. 3. EVM vs. Fiber Length for a QAM-16 Single

Polarization DD OFDM

Fig. 7. EVM vs. Fiber Length for QAM-32 Single

Polarization CO-OFDM

304 P. Rishi, S. Tamil Selvi

The performance of different M-ary optical lin ks is

also compared using constellation diagrams in Figs . 8-11.

Fig. 8 illustrates how placing a DSP component after the

coherent receiver aids in CD co mpensation in digital

domain using filtering. As exp lained in section 4, DSP

component

that

compensates for any residual CD, polarization mode

dispersion and reduces ISI. Due to frequency and phase

offset there is rotation of constellation to compensate it

frequency offset estimat ion is made by DSP co mponent,

equalizer

adaptive

includes

an

also carrier phase estimation is done to compensate for any

phase mis match between the LO and the signal. The

results obtained for a QAM-16 CO-OFDM lin k are shown

in Fig. 9, the constellation rotation in Fig. 9(c) has been

compensated in 9(d). Figs. 10 and 11 co mpare the coherent

QAM-32 link performance with and without employing

OFDM technique. It can be clearly seen that with OFDM

the spacing between constellation points increases and

hence the CD present in the optical fiber is compensated.

(a) (b) (c)

Fig. 8. QAM-16 coherent 20 km optical link (no OFDM) (a) Spectrum of input signal (b) Constellation at the output of

coherent optical receiver (c) Constellation at the output of DSP component

(a) (b) (c)

(d) (e) (f)

Fig. 9. QAM-16 CO-OFDM 20 km optical link (a) Spectrum of the input signal (b) Constellation at the output of coherent

optical Receiver (c) Constellation before channel estimation (d) Constellation after channel estimation (e) Constellation after

carrier phase estimation (f) EVM

Performance analysis of a spectrally efficient QAM coherent OFDM optical link 305

(a) (b) (c)

Fig. 10. QAM-32 coherent 20 km optical link (no OFDM) (a) Spectrum of input signal (b) Constellation after channel

estimation (c) Constellation after carrier phase estimation

(a) (b) (c)

(d) (e) (f)

Fig. 11. QAM-32 CO-OFDM 20 km optical link (a) Input spectrum (b) Constellation at coherent receiver (c) Constellation

before channel estimation (d) Constellation after channel estimation (e) Constellation after phase estimation (f) EVM

7. Conclusions

CO-OFDM is inherently spectrally efficient technique

as it has overlapped subcarriers. It has been found that

OFDM when used along with the higher order modulation

format QAM has effectively co mpensated CD and

polarization mode dispersion

in single mode fiber.

Co mbin ing CO-OFDM QAM with dual polarization

further pushes the Spectral efficiency but at the cost of

increased receiver complexity.

In this work, M-ary QAM OFDM system was

considered and its maximu m reach length was analyzed

for M = 16, 32, 64. It was found that for a QAM-16 link,

using direct detection the reach length obtained was only

306 P. Rishi, S. Tamil Selvi

20km but with coherent detection it was increased to 150

km. It was verified that for a QAM-16 OFDM link, by

emp loying dual polarization

is

increased but at the cost of reduced reach length. As we

move to higher order modulation namely QAM-32 based

OFDM, dual polarization outperforms single polarization.

Similar results were obtained for QAM-64 based OFDM

link.

the system capacity

In future this work can be further extended to study

the compensation of non linear effects present in fiber.

Also the effect of increasing the laser power on the system

performance can be analysed. Another aspect that can be

considered is that what type of changes need to be

incoprporated in DSP co mponent so that a particular BER

and EVM is maintained as we move fro m QAM-16 to

QAM-32 technique.

References

[1] J. He, R. A. Norwood, M. Brandt-Pearce, I. B.

Djordjevic, M. Cvijetic, S. Subramaniam, R.

Himmelhuber, C. Reynolds, P. Blanche, B. Lynn, N.

Peyghambarian, Comput. Electr. Eng. 40(1), 216

(2014).

[2] J. H. Lin, A. Ellis, D. Rafique, Adv. Photonics 1,

SPWC2 (2011).

[3] G. Li, “Terabit-per-Second Fiber Optical

Communication Becomes Practical,” OSA Century

of Optics, 1975-1990 (2016).

[4] E. M. Ip, J. M. Kahn, J. Light. Technol. 28 (4), 502

(2010).

[5] T. Pfau, S. Hoffmann, O. Adamczyk, R. Peveling, V.

Herath, M. Porrmann, R. Noé, Opt. Express 16(2),

866 (2008).

[6] P. J. Winzer, 2009 Conf. Lasers Electro-Optics 2009

Conf. Quantum Electron. Laser Sci. Conf., no.

February, pp. 3–4, 2009.

[7] E. Ip, A. Pak, T. Lau, D. J. F. Barros, J. M. Kahn,

Optics Express 16(2), 861 (2008).

[8] W. Shieh, H. Bao, Y. Tang, Opt. Express 16(2), 841-

859 (2008).

[9] W. Shieh, X. Yi, Y. Ma, Q. Yang, Journal of Optical

Networking 7(3), 234, (2008).

[10] G. Goldfarb, G. Li, SPIE Newsroom, (2007).

[11] M. Tomizawa, A. Kaneko, S. Kimura, NTT

Technical Review 14(9) (2016).

[12] J. Yu, J. Zhang, Digit. Commun. Networks 2(2), 65

(2016).

[13] O. Omomukuyo, D. Chang, O. Dobre, S. Member, R.

Venkatesan, S. Member, T. M. N. Ngatched, IEEE

Photonics Technology Letters 28(24), 2783 (2016).

[14] O. Omomukuyo, S. Zhang, O. Dobre, S. Member, R.

Venkatesan, S. Member, T. M. N. Ngatched, S.

Member, IEEE Photonics Technology Letters

29(23), 2016 (2017).

[15] R. Schmogrow, B. Nebendahl, M. Winter, A. Josten,

D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann,

M. Huebner, C. Koos, J. Becker, W. Freude, J.

Leuthold, IEEE Photonics Technol. Lett. 24(23),

2198 (2012).

[16] R. Zhang, J. Ma, Z. Wang, J. Zhang, Y. Li, G. Zheng,

W. Liu, J. Yu, Q. Zhang, Q. Wang, R. Liu, Opt. Fiber

Technol. 20(3), 261 (2014).

____________________

*Corresponding author: [email protected]