1

Digital Coherent Receiver Simulation and Experiment

A

Project Report

on

the Collaborative Grants

from the Ministry of Education, Culture and Sports of Spain

Participante:

Bishal Neupane

(bishal.neupane@tsc.upc.edu)

Supervisores:

Prof. Jos A. Lzaro

(jose.lazaro@tsc.upc.edu)

Prof. Spadaro Salvatore

(spadaro@tsc.upc.edu)

Project Start Date: 15/11/2013

Project End Date: 30/06/2014

2

Contents

Abstract3

Introduction.4

Principle of Coherent Detection.5

Phase-Diversity Coherent Receivers7

Simulation of BPSK/QPSK Coherent Receivers.9

IQ Modulators Using two MZMs9

Phase Noise Estimation and Compensation Technique..14

Power-Law Phase Estimate.16

Experiment/Measurement of BPSK..19

Hilbert Transform CDR21

Conclusion..22

References..23

Appendix: Working Hours Report..24

3

Abstract In this report a brief summary of the tasks executed during the course of the project is presented.

The project has been carried out to facilitate the implementation of real-time coherently detected

optical receiver for high-speed optical communication systems. In this project, simulation of

optical coherent receiver system using phase modulation in a noisy channel with the presence of

laser and local oscillator phase noise has been studied using MATLAB script. The report concerns

the collaborative grants from ministry of education, culture and sports of Spain.

The project is centered around developing Matlab script files for simulation of optical

communication system comprising optical transmitter using Mach-Zehnder Modulator and

successful decoding of the information carried on the phase and amplitude of the optical signals

at the receiver using hybrid optical coherent mixer. The results of the simulation are to be verified

using measurements from a real-time scenario in the laboratory.

In this project we try to simulate coherently detected optical communication system and then

observe the compatibility of the algorithms developed with that of real-time scenario. The goal

of the project was also to facilitate collaboration among professors and students to further

research activities.

4

Introduction Recently there has been a renewed interest in coherent receivers in optical communications

society mainly because of the added advantages in terms of spectral efficiency, sensitivity to

various linear and non-linear dispersion and also the preservation of the state of polarization of

light signals in the electrical domain. Coherent receivers with phase and polarization diversity help

increase the spectral efficiency at higher bitrates by utilizing higher order modulation format like

n-PSK, QAM etc. Also, the implementation of equalization algorithms to alleviate various channel

impairments introduced in the optical link is becoming easier and robust as the complex signal

processing algorithms are becoming feasible due to increased processing power of modern DSPs.

Figure 1: Optical Coherent Receiver

As seen in figure 1, the coherent optical receiver mixes the incoming optical signal at the receiver

with a free running local laser called the local oscillator to extract all the properties of light signal

in the electrical domain. First, the two signals are mixed together and signal at intermediate

frequencies are produced at sum and difference of the incoming signal frequencies. Then, the in-

phase and in-quadrature signals are obtained using a balanced photo detectors which operate on

square-law principle. The setup in the figure corresponds to a phase diversity coherent receiver

where information about both the phase and amplitude of the received signal is preserved in the

digital domain for further signal processing to mitigate channel impairments unlike traditional

intensity based transmission systems where useful and rich properties of the light signal are lost

after detection by a photodetector.

Coherent receiver relies on the knowledge of the carrier phase since the local oscillator at the

receiver side acts as a total phase reference. Traditionally carrier synchronization was performed

either using an optical PLL or Electrical PLL using a hardware but the advancement in DSPs is

enabling polarization tracking and carrier synchronization to be done using a software [1].

5

Principle of Coherent Detection The basic working principles of coherent detection are described in this section. There are at the

core two basic types of coherent detection mechanisms called Homodyne and Heterodyne. Using

either of these techniques we can fully recover the information on the optical complex field,

namely, the amplitude, the phase and the state of polarization (SOP) [2].

At the heart of the coherent detection lies beating of LO signal with that of the incoming signal at

the receiver to produce signals at intermediate frequencies. The optical signal sent from the

transmitter can be written as,

(t) A (t)exp(j t)s s sE

where (t)sA is the complex amplitude and s is the angular frequency. In the same way, the

electric field of the local oscillator at the receiver side can be expressed by,

(t) A (t)exp(j t)LO LO LOE

where LOA is the complex amplitude with constant value since it is not carrying any useful

information like (t)sA coming from the transmitter and LO is the local oscillator (LO) angular

frequency. We can derive the powers of both information signal and LO signal using the complex

amplitudes as: 2| | /2s sP A and2| | /2LO LOP A , respectively.

In the setup above phase diversity technique is not used and is the simplest model. The

incorporation of the balanced photo detectors after the mixing of the signals helps to suppress

the DC component and increase the photocurrent. In the model shown above the mixing is

achieved by a 3-dB coupler that shifts either the signal field or the LO field by 180 degrees

between the output ports. Assuming the perfect matching between the states of polarizations

between signal and LO fields we can derive equations for electric fields incident on the

photodiodes and thus approximate the output photocurrent to decide which symbols were

transmitted [2].

Figure 3: Basic Configuration of a Coherent Receiver Figure 2: General Configuration of Coherent Receiver

6

Electric fields after 180 degree mixer are,

1

1(E E )

2s LOE

2

1(E E )

2s LOE

And respectively the output photocurrent can be derived as,

1

(t) exp(j t) A (t) exp(j t)(t) R Re

2

s s LO LOAI

[P P 2 cos{ t (t) (t)}]2

s LO s LO IF sig LO

RP P

2

(t) exp(j t) A (t)exp(j t)(t) R Re

2

s s LO LOAI

[P P 2 cos{ t (t) (t)}]2

s LO s LO IF sig LO

RP P

Where, Re represents the real part of the signal and IF is the intermediate frequency such that

IF s LO , while (t)sig and (t)LO are the phases of the incoming and LO signals

respectively. Moreover, R is the responsitivity of the photodiodes such that,

s

eR

Where, is Plancks constant and e is the electron charge while is the quantum efficiency of

the photodiode. In the equations above for the photocurrents 1(t)I and 2 (t)I , the intermediate

frequency term corresponding to the sum of frequencies is ignored as they are usually filtered

out in some way due to the limited bandwidth of the photodiodes.

And finally the photocurrent output from the balanced detectors are given by,

1 2(t) (t) (t) 2 (t) cos{ t (t) (t)}s LO IF sig LOI I I R P P

In the equation above, the local oscillator power is usually kept constant and the phase term

accounts only for the noise that varies with time due to the finite linewidth of such lasers.

7

Phase-Diversity Coherent Receivers The idea described above can be easily extended to include phase-diversity at the receiver, which

means use of higher order modulation that carries information both on the amplitude and phase

of the signal like QPSK, QAM etc. For this purpose a 90 degree optical hybrid mixer will be used

to extract the two in-phase and in-quadrature components of the information signal. Figure 3

shows the general configuration of a phase-diversity coherent receiver. Depending on the signal

frequency after the photodiodes, the configuration is categorized as being homodyne or

heterodyne. In homodyne setup, the intermediate frequency is 0 and thus the signal is baseband.

However, in heterodyne setup, the signal will be in some intermediate passband frequency and

then an electrical IQ-downconverter can be used to make the signal baseband. Homodyning

requires stringent requirements on the complexity of the receiver because the phase and

frequency of the LO laser has to be matched perfectly to that of the incoming signal but which is

often difficult to obtain in practice due to noise and instability present at the laser. The detailed

equations of the signals at various stages in the setup shown in figure 3 will be derived below [2].

If we assume the homodyne setup and think of 90 degree optical hybrid as capable of giving 4

outputs 1E , 2E , 3E , and 4E from two inputs sE and LOE , the outputs can be described as,

1

1(E E )

2s LOE

2

1(E E )

2s LOE

3

1(E E )

2s LOE j

Figure 3: Configuration of a Phase-Diversity Coherent Receiver

8

1

1(E E )

2s LOE j

Then the output photocurrents can be written as,

1 2(t) (t) (t) cos{ (t) (t)}I I I s LO sig LOI I I R P P

1 2(t) (t) (t) sin{ (t) (t)}Q Q Q s LO sig LOI I I R P P

In the above in-phase and in-quadrature signals if we write (t)sig as a combination of a phase-

modulated time-varying information part and a time-varying noise part such that:

(t) (t) (t)sig s sn . Here, (t)s refers to the information carrying phase term while (t)sn refers

to the additive phase noise term. If we substitute (t) (t) (t)sig s sn into the above equations

for I and Q terms, we get,

(t) cos{ (t) (t)}I s LO s nI R P P

(t) sin{ (t) (t)}Q s LO s nI R P P

where, (t) (t) (t)n sn LO is the total phase noise in the received signal. For an ideal reception

we have to be correctly able to estimate the noise term (t)n in order to make decisions on

symbols transmitted with sufficiently high certainty. We will explore some methods used during

the simulation in sections to follow.

In addition to the phase-diversity scheme mentioned above, a further degree of freedom can be

exploited to get higher spectral efficiency by using polarization multiplexing of light signals to

carry information on two polarizations orthogonal to each other so that the information on each

polarization can be transported safely without any interference. So, the coherent reception with

polarization-diversity will increase the spectral efficiency by a factor of 2. In order to incorporate

such a scheme in a coherent manner, a polarization beam splitter is used to split the incoming

light into two orthogonal polarizations and the 90 degree hybrids can be used to extract

information on two polarizations independently by mixing those signals with LO [3]. Polarization

can be tracked in the digital electrical domain and compensated for by using well-known adaptive

algorithms which are very efficient. Refer to the book on optical communications by Kazuro

Kikuchi [1] for detailed derivation of polarization and phase-diversity coherent receivers.

9

Simulation of BPSK/QPSK Coherent Receivers In this section some results obtained throughout the simulation of BPSK/QPSK coherent systems

is shown and the methods used behind those results are explained briefly. Figure 4 shows the

basic setup for simulation of BPSK/QPSK coherent system.

Figure 4: General Simulation setup

As shown in the figure 4, the transmitter side consists of a continuous wave (CW) laser with a

constant amplitude which will be used to carry information by the IQ modulator. The IQ

modulator in case of BPSK is just a Mach-Zehnder Modulator that modulates the pseudo-random

binary sequence (PRBS) on the phase of CW laser signal. BPSK is implemented by MZM such that

bit 1 corresponds to phase zero and bit 0 corresponds to phase change of pi.

IQ Modulators Using two MZMs In this section, the principle behind MZM and how it can be used to modulate the CW light to

carry information in both phase and amplitude will be explained briefly.

Mach-Zehnder modulators are external modulation techniques. A standard MZM can be created

by combining two phase modulators based on electro-optic waveguides principle. Figure 5 shows

how an MZM is formed. In the figure, the upper and lower arms delay the signal passing through

it because of the quantum properties associated to the electrodes. Effectively, the driving

voltages applied to each arms changes the refractive index of the waveguide which causes delay

CW laser

PRBS

IQ

modulator 90

degree

Hybrid

Noisy

Channel

DSP

10

of lightwave carrier, which in turn means a phase shift. This phenomenon is also known as the

Pockels effect. As seen, MZMs are based on the principle of interference. The light signals on

those two arms interfere either constructively or destructively at the output port to provide

intensity modulation as well as phase modulation.

Figure 5: Mach-Zehnder Modulator consisting of two Phase Modulator Arms

The phase change on one of the arms caused by the driving voltage can be written as,

2( (t) V )(t) biaslowerV

V

Similarly, the phase change in the upper arm can be deduced and using the properties of couplers

the input and output signal fields can be observed. Moreover, if we use two of the above shown

MZMs (figure 5) to modulate IQ data. First, one of the MZMs will modulate the in-phase part

while the other MZM will be used to modulate the in-quadrature part and in-phase modulated

part will be combined with 90 degree shifted version of the in-quadrature modulated part to

obtain total IQ modulation. This is the setup used in the simulation, two MZMs, one added with

90 degree phase shifted version of the other. Refer to one of several references for the detailed

workings and derivation of MZMs and IQ modulators formed by two MZMs [4] [5] [6].

Input field Output optical field

Waveguide

Electrodes

+

11

Here, we can see the result of BPSK phase modulation using two MZMs and the result of their

spectra. Initially, the random binary sequence is oversampled to be represented by many samples

corresponding to a given sampling frequency and the bandwidth of the system. While

oversampling the random bits, the resulting signal is also shaped to have a certain pulse pattern,

mainly non-return to zero or raised cosine. Now, the resulting sequence of data corresponds to

the electrical driving voltage as mentioned in figure 5. This driving voltage signal is used to

modulate a CW laser with constant amplitude to emulate phase changes of either zero degrees

for bit 1 or phase changes of pi for bit o. The BPSK modulation is achieved by biasing the DC

voltage at the minimum transmission point of the DC transfer function of MZM.

In the figure 6 below, we observe the signal characteristics in frequency domain. The picture on

the left shows the power distribution of a baseband signal concentrated around the center of the

frequency axis. However, in real communications scenario it is almost impossible to transmit the

data at such low frequencies, thus simulation of the signal at higher frequency also called carrier

frequency is performed. As seen, the carrier frequency was assumed to be 50 GHz in the

simulations while the symbol rate was fixed at 10 Gsymbols/seconds.

Figure 6: Spectrum of MZM modulated BPSK Signal Baseband and Pass band

One of the most reliable and fastest ways to observe the integrity of the signal at any point in the

transmission system is through eye-diagrams. The eye diagram shows the overlapping time

domain signals of fixed symbol duration in a single graph so the transition between different

symbols can be visualized and observed. It basically shows how well the different symbols can be

distinguished from each other. The best possible scenario would be the one shown on the left of

figure 7 as it represents the signal at the transmitter without any noise, thus has a very wide eye-

opening. However, since the signal in the context is BPSK, all the information is carried on the in-

phase part. As a result, we can only observe the in-phase component eye-diagram and analyze

the signal quality. The graph on the right of figure 7 shows how an added noise reduces the eye-

-8 -6 -4 -2 0 2 4 6 8

x 1010

0

0.005

0.01OUTPUT OF MZM, BASEBAND

Frequency [Hz]

Pow

er

[mW

]

-8 -6 -4 -2 0 2 4 6 8

x 1010

-400

-300

-200

-100

0OUTPUT OF MZM, BASEBAND

Frequency [Hz]

Pow

er

[dB

]

-8 -6 -4 -2 0 2 4 6 8

x 1010

0

0.005

0.01

0.015PASSBAND OPTICAL SPECTRUM

Frequency [Hz]

Pow

er

[mW

]

-8 -6 -4 -2 0 2 4 6 8

x 1010

-400

-300

-200

-100

0PASSBAND OPTICAL SPECTRUM

Frequency [Hz]

Pow

er

[dB

]

12

opening and causes higher probability of bit errors due to ambiguity in deciding the bits correctly

as representing 1 or 0.

Since the BPSK signal is completely defined by in-phase component we dont have any eye-

pattern on in-quadrature part. However, after an addition of complex noise we do see some effect

on eye-opening. Still, only the in-phase part is used for the decoding of a BPSK signal, so in

quadrature part acts like added noise.

Figure 8: IQ spectrum after Homodyne Detection (left) and Low-passed In-Phase Component (right)

The result of optical 90 degree hybrid mixer in case of frequency matched local oscillator is shown

in figure 8. It is seen that after mixing of the incoming signal with that of the local oscillator we

get signals at intermediate frequency components given at sum and difference between two

-8 -6 -4 -2 0 2 4 6 8

x 1010

0

0.05

0.1

0.15

0.2IQ Sepectrum after Homodyning

Frequency [Hz]

Pow

er

[mW

]

-8 -6 -4 -2 0 2 4 6 8

x 1010

-150

-100

-50

0IQ Sepectrum after Homodyning

Frequency [Hz]

Pow

er

[dB

]

-8 -6 -4 -2 0 2 4 6 8

x 1010

0

0.05

0.1

0.15

0.2In-Phase Low-Passed Sepectrum

Frequency [Hz]

Pow

er

[mW

]

-8 -6 -4 -2 0 2 4 6 8

x 1010

-200

-150

-100

-50

0In-Phase Low-Passed Sepectrum

Frequency [Hz]

Pow

er

[dB

]

0 5 10 15 20 25 30-2

-1

0

1

2Eye Diagram at the TX after MZM: REAL

0 5 10 15 20 25 30-2

-1

0

1

2Eye Diagram at the TX after MZM: IMAGINARY

0 5 10 15 20 25 30-2

-1

0

1

2Noisy EYE-DIAGRAM: InPhase

0 5 10 15 20 25 30-2

-1

0

1

2Noisy EYE-DIAGRAM: InQuad

Figure 7: Eye Diagrams at the transmitter and its noise added version

13

frequencies. But, we are only interested at the part of the signal that is concentrated at the zero

frequency. As a result, the unwanted frequency components are filtered out and only the

frequency components of interest are extracted for further processing and decoding of the data.

After the detection of phase components of the signal using squared-law photo detector device,

they are converted into a digital form using an ADC and processed further for phase/frequency

and other channel impairment compensations.

Due to finite linewidths of transmit and LO lasers the system introduces phase noise in addition

to the thermal and ASE noise. Both thermal and ASE noise can be approximated as Gaussian white

noise and can be considered together in simulations, as is done in [7].

0 10 20 30 40 50 60 70-25

-20

-15

-10

-5

0

5

10

15

20

25Signals at TX and RX

RX

TX

0 5 10 15 20 25 30 35-40

-20

0

20

40Eye Diagram at the RX after LO: REAL

0 5 10 15 20 25 30 35-20

-10

0

10

20Eye Diagram at the RX after LO: IMAGINARY

Figure 9: Received and sent time domain signals (left) and Eye-diagram after LO and low pass filter (right)

14

Phase Noise Estimation and Compensation Technique The increase in the processing capacity of DSPs means many phase estimation techniques can be

studied and applied in real time synchronous optical coherent communication systems as

opposed to traditional phase-locked loops (PLLs). A number of phase estimation techniques can

be modeled and studied for correctly mitigating the unwanted phase noise accumulated in a

signal mainly due to finite linewidth of lasers.

First well look at the basic method called Feedforward Phase Estimation method to understand

the principle behind such techniques and further improvements to minimize errors due to cyclic

slips.

1

2

3

4

30

210

60

240

90

270

120

300

150

330

180 0

Constellation without Phase Estimate

2

4

6

8

30

210

60

240

90

270

120

300

150

330

180 0

Phase Estimated Signal Constellation

Figure 10: Signal Constellation before (left) and after (right) phase estimation

15

Figure 11: Schematic of Feedforward Phase Estimation for QPSK [8]

The method shown above in figure 11 is the basic phase estimation technique that works very

well for QPSK systems and which is also favored by many for its simple DSP implementation.

Basically, the principle behind such an algorithm lies around removing the data phase modulation

by raising the signal to the power of modulation order, i.e. 2 for BPSK, 4 for QPSK and so on. After

the power raising operation the resulting signal will have contained only the phase corresponding

to the noise. Then we effectively average or use some filtering operation to smooth up the phase

noise and subtract it from the sum of phase noise and data phase.

If we write the received signal as the sum of actual data signal and some noise terms, we get,

[ t (t) (t)]r(t) (t)e (t)s

jd p

In the above equation, the received signal r(t) contains useful information phase (t)s and the

phase noise term (t) . Moreover, the whole signal is assumed to be affected by additional

complex Gaussian noise. This complex Gaussian noise can be thought of as the sum of all the

dominant noises like thermal noise and Amplifier Spontaneous Emission (ASE) noise which can be

affectively modeled as a Gaussian distribution.

If we write the previous equation in a digital form rather than time-domain form, we can proceed

with further study,

[ ( ) ( )]r( ) ( )e ( )s

j n n nn d n p n

Where, (n) (n) (n)s LO corresponds to the difference between phase noises introduced by

the transmitter laser and the receiver local oscillator. And, s LO is the difference between

angular frequencies of the data signal and LO signal. Above, (n)p is a complex Gaussian noise

function which has a variance 2p [7].

Arg (.)

Phase

Estimation

(.)/4 (.)^4

16

The phase noise is closely approximated by the Lorentzian linewidth formula assuming signal and

LO lasers have finite linewidth. As a result, the phase noise is a Wiener process (Gaussian random

walk function)

(n) (n 1) (n)w

Where, (n)w is a real Gaussian noise sequence having a variance 2w , and

2 2w sT v

v , is the combined linewidth typically in the range of 10e3 to 10e6 [9]. It is the full width at half

maximum of both lasers combined. And, sT is the duration of a single symbol.

In our equation of the received sequence, it can be assumed that the angular frequency term is

constant because with very few simple DSP calculations it can be estimated correctly and it varies

much slowly compared to the actual phase noise [7] [8].

Power-Law Phase Estimate Having formulated the distributions of noise terms in the previous section, lets take a close look

at the derivation of phase estimate step-by-step.

1) Remove data modulation from the received M-psk sequence by raising to the power of

modulation order M,

(n) r(n)Ms

2) Extract the phase from (n)s ,

(n) arg [s(n)]unwrapped

It is assumed that the phase noise is a wiener process which extends from negative infinity to

positive infinity, i.e. it is a random walk process as a result of cumulative nature of phase noise.

So, this steps extends the phase value returned by matlab from pi to +pi to

increments/decrements of 2*pi every time the phase crosses negative real axis.

3) Now, inherently, (n) M (n) q(n) , remember that q(n) corresponds to Gaussian noise

sequence with variance 2p and (n) is what we wish to estimate from the observable

quantity (n) .

4) The transfer function that smooths out the phase noise by modeling it as a wiener process

is given by,

1

1 1(z) (z)

1M z

Where,

17

2 2 2 2 2 2

2

2 4

2

w q w w q

q

M M M

And,

2 2 44 4q p p , for BPSK

2 2 4 6 816 144 384 192q p p p p , for QPSK.

5) After, successfully estimating the phase noise, the removal operation is performed by

multiplying the received sequence by the negative exponential of phase noise.

(n) (n)exp( j (n) offset)r r

Now, using (n)r

the decisions about the transmitted symbols can be made by evaluating

the phase boundaries. The phase offset term restores the signal constellation in its original

place in case it was rotated by some fixed amount.

There are variants of the method mentioned above depending on how to use the transfer

function and when. Also, further improvements can be made to the above mentioned algorithm

to make it more robust to the additive noise term. For detailed derivation of the transfer function

mentioned above and other variants of the algorithm the reader is referred to [7].

Below, OSNR vs BER characteristics is shown. The corresponding BER is evaluated on 10

Gsymbols/s BPSK data with 131072 number of symbols. BER is calculated in a simple fashion, i.e.

the number of bit errors divided by the total number of symbols transmitted through the system.

Figure 12: OSNR vs BER

After the simulation of BPSK optical coherent transmission, QPSK transmission was also studied.

Some of the main results are shown below. Previously the in-quadrature component did not have

much say in the symbol decision of BPSK signals but now the presence of information on both

18

Phase and Amplitude affects the eye-diagram of both in-phase and in-quadrature components as

seen in figure 9 below.

Moreover, the signal constellation becomes more sensitive noises as we move towards higher

order modulation format. This will require stringent constraints on powers of real and imaginary

components of the signal as well as other channel impairments and noises. The signal

constellation before and after the phase noise compensation are shown below in the figure 10.

0 5 10 15 20 25 30-2

-1

0

1

2Eye Diagram at the TX after MZM: REAL

0 5 10 15 20 25 30-2

-1

0

1

2Eye Diagram at the TX after MZM: IMAGINARY

0 5 10 15 20 25 30 35-10

-5

0

5

10Eye Diagram at the RX after LO: REAL

0 5 10 15 20 25 30 35-10

-5

0

5

10Eye Diagram at the RX after LO: IMAGINARY

Figure 13: QPSK signal Eye-Diagrams at TX (left) and RX (right)

0.5

1

1.5

30

210

60

240

90

270

120

300

150

330

180 0

Constellation without Phase Estimate

0.5

1

1.5

2

2.5

30

210

60

240

90

270

120

300

150

330

180 0

Phase Estimated Signal Constellation

Figure 14: QPSK signal constellation at RX before (left) and after (right) the phase error compensation

19

Experiment/Measurement of BPSK

Figure 15: General Measurement setup employed in the lab

The basic model of a real-time coherent optical communication system deployed in the lab is

depicted in Figure 2 above. The system comprises of an optical transmitter, an intermediate

channel, and finally a receiver. The transmitter is responsible for transmitting a continuous wave

light signal at 1550 nm which will be modulated by a Mach-Zehnder modulator before going

through the coherent mixer at the receiver.

The experiment was carried out on a signal with a frequency of 2 MHz having a NRZ/sinusoidal

pulse shape. The data sent from a signal generator to the MZM modulator was a known sequence

of 1s and 0s. The MZM is susceptible to the changes in polarization of the light signal, for this

reason a polarization controller was used just before the MZM to make sure the signal reaches

MZM in the best possible polarization state, with highest power. In the laboratory, the first

scenario was to experiment with homodyne setup. For emulating homodyne receiver, we used a

single laser diode source as both the transmitter and LO by splitting the signal 50-50 using a 3-dB

coupler. The BPSK modulated signal and the LO signal was fed to the COH24 single polarization

90 degree optical hybrid by Kylia. It is again very important to control the polarization of two

signals before feeding into the hybrid as the polarization miss-match will cause will degrade the

signal quality due to interference and low power.

The major concern during the measurements so far is the timing error and jitter caused by the

mixing of the signals in the 90 degree optical hybrid that causes the correct extraction of samples

Laser

Diode

Signal

Generator

MZM

Modulator

90

degree

Hybrid LO

Polarization

controller

3-dB

splitter

DSP

20

representing each symbols extremely difficult without clock-recovery circuit. It has been observed

that without a proper timing-recovery mechanism, the symbol decisions are likely to be

erroneous. Thus, as a start simple Hilbert transform based clock-data recovery algorithm was

tested and found to work well when the observed measurements are not too stable and not too

noisy, i.e. is to say that the signal transitions from the zero level are separated enough without

random fluctuations between bits 0s and 1s, like the one shown in.

The figure above shows the eye-diagrams of the input signal sequence and the in-phase signal at

the receiver after hybrid mixing. The figures shown above were smoothed out a little to reduce

unnecessary noise fluctuations. Moreover, it can be observed from the above diagram that the

system is not reliable because symbols do not have a perfect timing instance, they seem to be

moving side-ways making it difficult to observe exact symbol positions with a fixed amount of

duration. For an example the signal generated above corresponds to a frequency value, F =

2.2739176e6 Hz and oscillator sampling frequency, Fs = 500 Msamples/s, this setup of frequency

and sampling frequency means that we should have Fs/(2*F) = 109.94 number of samples per

symbol. Observe that the number of samples per symbols is already a floating point number which

introduces quantization errors when working with digital samples. Moreover, the biggest

problem is that this value is not constant during the period of whole sequence but rather

increasing or decreasing due to the shortcoming of proper clock-synchronization mechanism.

In addition, the image on the right of figure 16 corresponds to the in-phase component coming

out of the hybrid mixer, but if we look at the eye-diagram of the in-quadrature component in

figure 17, we observe that the signal is very noisy and unstable. One thing with BPSK is that in-

phase component sign is enough to decide the bits, however, in other applications of higher order

modulation format in-quadrature component also becomes critical in symbol decisions. And thus,

the system should be able to correctly sample the data at best possible instants of both the in-

phase and in-quadrature signals.

0 50 100 150 200 250 300 350-1

-0.5

0

0.5

1

1.5Eye-Diagram of the INPUT SIGNAL

0 50 100 150 200 250 300 350-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08Eye-Diagram of the INPHASE SIGNAL from Hybrid

Figure 16: The Eye-Diagrams of input signal (left) and in-phase signal after 90 degree hybrid (right)

21

Hilbert Transform CDR

Basically, the principle of Hilbert transform clock-data recovery (CDR) lies in the fact that Hilbert

transform produces peaks at the transition points of a signal. Thus, if we can track all the peaks

of the Hilbert transform we can find the duration in-between and effectively sample data at

0 50 100 150 200 250 300 350-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08Eye-Diagram of the IN-Quadrature SIGNAL from Hybrid

Figure 17: In-quadrature component eye-diagram after the hybrid mixer

0 200 400 600 800 1000 1200 1400 1600 1800 2000

-1.5

-1

-0.5

0

0.5

1

1.5

Input Signal Hilbert Transform

Hilbert

Input

Figure 18: The square input signal (Red) & its Hilbert transform (blue)

22

correct positions [10]. The Hilbert transform (blue curve) of the input signal (red curve) in figure

18 shows the usefulness of Hilbert transform to find peaks at the transition of a signal from one

level to the other. No matter whether the peak is a minimum or maximum, it is certain to contain

transition and we can use the gaps between these peaks to know how many symbols are likely to

be contained and where.

Conclusion To conclude, the project can give a momentum towards further development of the digital

coherent receiver from a ground point of view. The simulation of a coherent system has been

done in Matlab with script files and known to give intuition as well as better working environment

for system evaluations. Moreover, there are further improvements required to be able to develop

a fully-fledged coherent receivers in practical optical communications scenario. From the

foundations established during the course of this project, it should be fairly straightforward to

proceed with more reliable and robust algorithms to tackle real-time communications difficulties

like timing-recovery, carrier phase & frequency compensation, channel equalization and linear

and non-linear transmission impairments associated with practical optical communication

systems at very high bit rates. Nevertheless, useful momentum has been gained for further work

in the area during the whole project.

23

References

[1] E. Ip, A. P. T. Lau, D. J. F. Barros and J. M. Kahn, "Coherent detection in optical fiber systems," Optical Society of America, 2008.

[2] K. Kikuchi, High Spectral Density Optical Communication Technologies, 2010.

[3] S. Tsukamoto, Y. Ishikawa and K. Kikuchi, "Optical Homodyne Receiver Comprising Phase and

Polarization Diversities with Digital Signal Processing," Research Center for Advanced Science and

Technology, University of Tokyo.

[4] R.-J. E. Peter J. Winzer, "Advanced Optical Modulation Formats," in Proceedings of the IEEE, 2006.

[5] M. Seimetz, "Multi-format Transmitters for Coherent Optical M-PSK and M-QAM Transmission,"

Berlin, Germany, 2005.

[6] K.-P. Ho and H.-W. Cuei, "Generation of Arbitrary Quadrature Signals Using One Dual-Drive

Modulator," JOURNAL OF LIGHTWAVE TECHNOLOGY, vol. 23, no. 2, 2005.

[7] M. G. Taylor, "Phase Estimation Methods for Optical Coherent Detection Using Digital Signal

Processing," JOURNAL OF LIGHTWAVE TECHNOLOGY, vol. 27, no. 7, 2009.

[8] L. N. Binh, Optical Fiber Communications Systems : Theory and Practice with MATLAB and Simulink

Models, CRC Press, 2010.

[9] G. P. Agrawal, Fiber-Optic Communications Systems, John Wiley & Sons, 2002.

[10] Y. Malinge, "Improving Clock-data Recovery Using Digital Signal Processing," Northeastern

University, 2008.

24

Appendix Collaborative Grant Project Status

Student: Bishal Neupane () (Y3218219G) , Supervisor: Jose Antonio Lazaro

Technical University of Catalonia, UPC

Project Lead: Jose Antonio Lazaro

Project Title: Real-time Optical Coherent Receiver Simulations and Measurements

Today's Date: 15/11/2013 (vertical red line)

Start Date: 15/11/2013

End Date: 30/06/2014

WBS Tasks Start End Dura

tion (

Days)

Hours

Spent

1 Preliminary Reading 15/11/201

3 14/12/2013

1.1 Optical Transmitters 15/11/201

3 24/11/2013 9 20,25

1.2 Mach-Zehnder Modulators 18/11/201

3 24/11/2013 6 13,50

1.3 Optical Coherent Receivers 25/11/201

3 05/12/2013 10 22,50

1.4 Phase Noise in Optical Transmission Systems

30/11/2013 07/12/2013 7 15,75

1.5 Real-time Systems Challenges 09/12/201

3 14/12/2013 5 11,25

2 MATLAB Introduction 28/01/201

4 21/02/2014

2.1

MATLAB/Simulink Review for Optical communications

28/01/2014 12/02/2014 15 33,75

2.2 Implementation of Basic functions 15/02/201

4 21/02/2014 6 13,50

3 Start Simulation: BPSK 23/01/201

4 26/02/2014

3.1 Mach-Zehnder Modulators 23/01/201

4 02/02/2014 10 22,50

3.2 Noise and Filtering effects 03/02/201

4 07/02/2014 4 9,00

3.3 Optical Hybrid mixer 08/02/201

4 15/02/2014 7 15,75

3.4 Symbol Decisions/Phase noise 16/02/201

4 21/02/2014 5 11,25

25

3.4

Homodyne/Heterodyne Simulation Variants

17/02/2014 26/02/2014 9 20,25

4 Start Simulation: QPSK 27/02/201

4 12/04/2014

4.1

Bit Mapping and QPSK Modulation using Dual-MZMs

27/02/2014 04/03/2014 5 11,25

4.2

Passband Representation and representing complex signal by real signal

05/03/2014 08/03/2014 3 6,75

4.3

Homodyne/Heterodyne Simulation

09/03/2014 24/03/2014 15 33,75

4.4

Eye Diagrams/Simple BER Evaluations

23/03/2014 01/04/2014 9 20,25

4.5

Phase Noise Mitigation Techniques

02/04/2014 12/04/2014 10 22,50

5 Phase Estimation/BER Estimation 13/04/201

4 10/05/2014

5.1 Viterbi&Viterbi + KIKUCHI variant 13/04/201

4 25/04/2014 12 27,00

5.2 Feedforward NDA Average 27/04/201

4 10/05/2014 13 29,25

6 Measurements and Testing 11/05/201

4 30/06/2014

6.1

Laboratory Measurement Setup and tests

12/05/2014 28/05/2014 16 36,00

6.2

BPSK Measurement and Data Retrieval

01/06/2014 09/06/2014 8 18,00

6.2 Post Processing on MATLAB 10/06/201

4 27/06/2014 17 38,25

6.2 Writing Report and Evaluations 23/06/201

4 30/06/2014 7 15,75

Total Hours = 468,00

REFERENCES

Fiber based Mach-Zehnder interferometric structures: principles and required characteristics for efficient modulation format conversion, G. Ducournau*, O. Latry and M. Ktata

Fiber Optic Communication Systems, 3rd Edition, Govind. P. Agrawal

Optical Fiber Communications Systems: Theory and Practice with MATLAB and SIMULINK Models, Le Nguyen Binh

Digital Communications, McGraw-Hill, 4th ed., 2000, John G. Proak is

Algorithms for Coherent Detection, Michael G. Taylor

Digital coherent transceiver for optical communications from design to implementation, Master Thesis UPC, Esdras Anzuola Valencia, 2012

Frequency Estimation in Intradyne Reception, Andreas Leven, Senior Member, IEEE, Noriak i Kaneda, Member, IEEE, Ut-Va Koc, Member, IEEE,

Generation of Arbitrary Quadrature Signals Using One Dual-Drive Modulator, Keang-Po Ho, Senior Member, IEEE, and Han-Wei Cuei

Multi-format Transmitters for Coherent Optical M-PSK and M-QAM Transmission, Matthias Seimetz Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institut

Optical Phase-Shift-Keyed Transmission, A. H. Gnauck, Senior Member, IEEE, Fellow, OSA, and P. J. Winzer, Member, IEEE, Member, OSA

Spectrum of Externally Modulated Optical Signals, Keang-Po Ho, Senior Member, IEEE, and Joseph M. Kahn, Fellow, IEEE

Effect of MachZehnder Modulator DC Extinction Ratio on Residual Chirp-Induced Dispersion in 10-Gb/s Binary and AM-PSK Duobinary Lightw ave Systems, Paolo Zandano, Marco Pirola at el.

Optical Homodyne Receiver Comprising Phase and Polarization Diversities w ith Digital Signal Processing, Satoshi Tsukamoto, Yuta Ishikawa, and Kazuro Kikuchi

Advanced Optical Modulation Formats, By Peter J. Winzer, Senior Member IEEE, and Rene-Jean Essiambre, Member IEEE

Coherent detection in optical f iber systems, Ezra Ip*, Alan Pak Tao Lau, Daniel J. F. Barros, Joseph M. Kahn

Simple Measurement of Eye Diagram and BER Using High-Speed Asynchronous Sampling, Ippei Shake, Member, IEEE, Hidehiko Takara, Member, IEEE, and Satoki Kawanishi, Member, IEEE, Member, OSA

Estimation of Phase Noise for QPSK Modulation over AWGN Channels, Florent Munier, Eric Alpman,

A SIMULATION STUDY OF THE VITERBI AND VITERBI CARRIER PHASE ESTIMATION ALGORITHM, R.A. Harris and JI. Yarmood

Phase Estimation Methods for Optical Coherent Detection Using Digital Signal Processing, Michael G. Taylor, Member, IEEE

A BPSK/QPSK Timing-Error Detector for Sampled Receivers, Floyd M. Gardner, Fellow, IEEE

Improving clock-data recovery using digital signal processing, Yann Malinge, Northeastern University

Coherent optical communication systems, Kazuro Kikuchi