high-order modulation for optical fiber transmission ... modulation for optical fiber transmission...

Springer Series in Optical Sciences 143

High-Order Modulation for Optical Fiber Transmission

Phase and Quadrature Amplitude Modulation

Bearbeitet vonMatthias Seimetz

1. Auflage 2009. Buch. xxii, 252 S. HardcoverISBN 978 3 540 93770 8

Format (B x L): 15,5 x 23,5 cmGewicht: 629 g

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Chapter 2Transmitter Design

Abstract This chapter gives a detailed overview of how optical high-order mod-ulation signals are generated. It describes transmitters for the generation of opti-cal ASK-signals, DPSK-signals and QAM-signals and considers star-shaped andsquare-shaped QAM constellations (Star QAM and Square QAM). Since all thetransmitters are composed of fundamental key components (laser, modulators, pulsecarver), the functionality of these components is discussed at the beginning of thischapter. The subsequent description of the different transmitters includes opticaltransmitter parts as well as electrical parts. It contains much detailed informationsuch as the concrete assembly of the coders and level-generators. The quality of thetransmitter output signals has a critical influence on the overall system performance.Therefore the electrical field for the optical output signals is analytically derived forall transmitters shown, and differences in signal characteristics, symbol transitionsand chirp behavior are emphasized. This helps us understand the system behaviorof the transmitters discussed later on in Chap. 7.

2.1 Transmitter Components

The following subsections briefly describe some fundamental key components ofoptical transmitters for high-order modulation.

2.1.1 Lasers

The ideal carrier for optical transmission is a lightwave with constant amplitude,frequency and phase. In practice, however, this perfect carrier can unfortunatelynot be generated. In the last decades, optical light sources have been increasinglyimproved. Light emitting diodes (LED) with very high spectral widths of severaltens of nanometers and low output powers and multi-mode Fabry-Perot lasers with

M. Seimetz, High-Order Modulation for Optical Fiber Transmission, 15Springer Series in Optical Sciences 143, DOI 10.1007/978-3-540-93771-5 2,c Springer-Verlag Berlin Heidelberg 2009

16 2 Transmitter Design

some discrete spectral lines and a total spectral width of several nanometers can nowbe replaced with single-mode distributed feedback (DFB) lasers or external cavitylasers (ECL) with linewidths in the sub-MHz region. When performing direct mod-ulation (which means that the data is modulated onto the laser drive current), thewidth of the emitted optical spectrum is determined by the incidental frequencymodulation of the laser under amplitude modulation, often referred to as chirping ofthe laser, when the laser linewidth is small compared with the chirp-induced spec-tral broadening. To avoid this effect, external modulation can be employed. Thenthe laser acts as a continuous wave (CW) light source. Throughout this book, whichdeals with advanced modulation and detection schemes, only single-mode lasersand external modulation are considered.

The normalized electrical field of an ideal optical carrier as emitted from a CWlaser can be expressed in complex notation as

Ecw(t) =

Ps e j (s t+s ) es (2.1)

In (2.1),

Ps represents the field amplitude, s /(2) the frequency, s the initialphase and es the polarization of the optical carrier. The character s indicates thesignal laser.

In practice, laser phase and amplitude noise, often called intensity noise, haveto be taken into account. They have their origin in spontaneous emission photonswhich induce intensity fluctuations P(t) and phase fluctuations, which are repre-sented by the signal laser phase noise ns (t).

Ecw(t) =

Ps + P(t) e j (s t+s+ns (t)) es . (2.2)

The laser phase noise is caused by spontaneous emission photons, not generatedin phase with the stimulated emission photons but with random phase [7]. In thetime domain, the evolution of the actual phase can be understood as a random walk.Within a time interval , the phase exhibits a random phase change of

1ns (t) = ns (t) ns (t ). (2.3)

Since the phase changes1ns (t) are caused by a high number of independent noiseeventsmore precisely the generation of spontaneous emission photonsthey canbe modeled as Gaussian distributed according to the Central Limit Theorem. Fur-thermore, when assuming a white power spectral density of frequency noise ns (t),which represents a realistic practical assumption [8, 13], the variance of the phasechange 1ns (t) can be expressed as

12ns ( ) = Wns | | =2| |tc, (2.4)

2.1 Lasers 17

where Wns is the constant power spectral density of the frequency noise and tc rep-resents the coherence time which physically denotes the maximum delay differenceup to which two components of the emitted optical field can stably interfere. Whenfurther neglecting intensity noise, the power spectral density of the optical field canbe shown to exhibit the Lorentzian-shaped spectrum

WEcw () =2tc Ps

1 + [( s)tc]2. (2.5)

The laser linewidth of the signal laser is defined as the full-width half-maximumbandwidth of this power spectral density and is specified by

1s =Wns2

=1 tc

. (2.6)

When the laser linewidth given by (2.6) is introduced into (2.4), the variance of thephase change 1ns (t) can be calculated by

12ns ( ) = 21s | |, (2.7)

showing that the phase uncertainty increases with the laser linewidth and the ob-served time interval. A more detailed analysis of the mechanisms and statistics ofphase and frequency noise can be found in [13]. As will become clear later on in thisbook, laser phase noise can have a limiting effect on system performance, especiallyfor high-order modulation formats with many phase states and when employing co-herent synchronous detection.

Intensity noise can also lead to significant degradation in system performance,in particular for coherent detection with high local oscillator (LO) laser powersand when not implementing balanced detection [12, 18]. In the data sheets of laserdiodes, the relative intensity noise (RIN) is usually specified. The RIN, integratedover a reference bandwidth 1 f , relates the variance of the intensity fluctuations tothe squared mean power: 1 f

0RI N ( f ) d f =

P2(t)P(t)2

. (2.8)

The mean optical power P(t) is equivalent to the signal laser output power Ps orthe output power of the LO laser Plo, respectively, because P(t) = 0. In a sim-ple approach, the intensity fluctuations can be modeled with Gaussian statistics anda white noise spectrum [2]. In reality, the RIN has more complex spectral charac-teristics, as can be observed for instance from [13, 20]. RIN values of laser diodestypically range from -160 dB/Hz to -130 dB/Hz.


2.1.2 External Optical Modulators

The optical part of high-order modulation transmitters is composed of one or morefundamental external optical modulator structures, which are briefly described inthis subsection: the phase modulator (PM), the Mach-Zehnder modulator (MZM)and the optical IQ modulator (IQM). The speed attainable as well as the character-istics of the transmitter output signals depends on the properties of the technologyand materials used for the modulators.

An optical phase modulator can be fabricated as an integrated optical device byembedding an optical waveguide in an electro-optical substrate, mostly Li NbO3,see Fig. 2.1a. By utilizing the fact that the refractive index of a material, and thusthe effective refractive index ne f f of the waveguide, can be changed by applying anexternal voltage via a coated electrode, the electrical field of the incoming opticalcarrier can be modulated in phase [20].

( )inE t

electro-optic substrate

electrode waveguide

( )outE t

( )u t

( )inE t ( )outE t

1( )u t

2( )u t

b a

Fig. 2.1 a Integrated optical phase modulator. b Integrated optical Mach-Zehnder modulator.

Phase modulation P M (t) is a function of the wavelength , the length of theelectrode lel (interaction length) and the change of the effective refractive index1ne f f (t). When solely considering the Pockels effect [20], the change of the re-fractive index can be assumed to be linear to the applied external voltage u(t).

P M (t) =2

1ne f f (t) lel u(t) (2.9)

In the specifications, the necessary driving voltage for achieving a phase shift of ,denoted as V , is typically given. Thus, the relation of the incoming optical carrierEin(t) and the outgoing phase modulated optical field Eout (t), when neglecting theconstant optical phase shift of the modulator, can be expressed as

Eout (t) = Ein(t) e jP M (t) = Ein(t) ej u(t)V . (2.10)

2.1 Modulators 19

By utilizing the principle of interference, the process of phase modulation canalso be used to cause an intensity modulation of the optical lightwave, when the in-terferometric structure shown in Fig. 2.1b is employed. This represents a dual-driveMach-Zehnder modulator. In the case of dual-drive MZMs, the phase modulatorsin both arms can be driven independently, in contrast to single-drive MZMs. Theincoming light is split into two paths, both equipped with phase modulators. Afteracquiring some phase differences relative to each other, the two optical fields arerecombined. The interference varies from constructive to destructive, depending onthe relative phase shift. Without considering the insertion loss, the transfer functionof a MZM is given by

Eout (t)Ein(t)

=12

(e j1(t) + e j2(t)

). (2.11)

In (2.11), 1(t) and 2(t) represent phase shifts in the upper and lower arms of theMZM. For a specified driving voltage to obtain a phase shift of in the upper andlower arms, V1 and V2 , respectively, and with the driving voltages u1(t) and u2(t)as defined in Fig. 2.1b, phase shifts are related to the driving signals with

1(t) =u1(t)V1

, 2(t) =u2(t)V2

. (2.12)

When operating the MZM in the push-push mode, which means that an identicalphase shift (t) = 1(t) = 2(t) is induced in both arms (for instance with u1(t) =u2(t) = u(t) and V1 = V2 = V ), a pure phase modulation is achieved, sothat the relation between the electrical input and output field is given by (2.10)as for the simple PM. On the other hand, when one arm gets the negative phaseshift of the other arm (1(t) = 2(t), e.g. with u1(t) = u2(t) = u(t)/2 andV1 = V2 = V ), the MZM is operated in the push-pull mode and a chirp-freeamplitude modulation is obtained. The input and output fields are then related with

Eout (t) = Ein(t) cos(1M Z M (t)

2

)= Ein(t) cos

(u(t)2V

), (2.13)

where 1M Z M (t) = 1(t) 2(t) = 21(t) is the induced phase difference be-tween the fields of the upper and lower arm. By squaring (2.13), the power transferfunction of the MZM is obtained:

Pout (t)Pin(t)

=12

+12

cos (1M Z M (t)) =12

+12

cos(

u(t)V

). (2.14)

It should be noted that u(t) was defined in a way that u(t) = V induces a phaseshift of for the PM as well as a phase shift of in the power transfer function ofthe MZM when it is operated in the push-pull mode.

In Fig. 2.2, two different MZM operation principles are illustrated. For achievingmodulation in intensity, the MZM can be operated at the quadrature point, with aDC bias of V/2 and a peak-to-peak modulation of V (see Fig. 2.2a). When the


MZM is operated at the minimum transmission point (see Fig. 2.2b), with a DCbias of V and a peak-to-peak modulation of 2V , a phase skip of occurs whencrossing the minimum transmission point. This becomes apparent from the fieldtransfer function. This way, the MZM can be used for binary phase modulation andfor modulation of the field amplitude in each branch of an optical IQ modulator.

Fig. 2.2 Operating the MZM in the quadrature point (a) and the minimum transmission point (b)

Mach-Zehnder modulators can be implemented in Lithium Niobate (Li NbO3),Gallium Arsenide (Ga As) and Indium Phosphide (I n P) [23]. Typical V drivingvoltages range from approximately 3 V to about 6 V.

A third fundamental modulator structure is the optical IQ modulator. It can becomposed of a PM and two MZMs, and is commercially available in an integratedform [1]. As illustrated in Fig. 2.3a, the incoming light is equally split into two arms,the in-phase (I ) and the quadrature (Q) arm. In both paths, a field amplitude modu-lation is performed by operating the MZMs in the push-pull mode at the minimumtransmission point. Moreover, a relative phase shift of /2 is adjusted in one arm,for instance by an additional PM. This way, any constellation point can be reachedin the complex IQ-plane after recombining the light of both branches (see Fig. 2.3b).Within the IQ modulator pictured in Fig. 2.3a, the induced phase differences of theMZMs in the upper and lower paths are

1I (t) =u I (t)V

, 1Q(t) =uQ(t)

V. (2.15)

When neglecting any insertion loss and setting the driving voltage of the PM tou P M = V/2, the field transfer function of the IQM can be expressed as

Eout (t)Ein(t)

=12

cos(1I (t)

2

)+ j

12

cos(1Q(t)

2

). (2.16)

V

OP

-V 0 -2V V 2V

1

-1

0

Field transfer function Power transfer function

u(t)

Operating the MZM at the quadrature point

OP

1

0

Field transfer function Power transfer function

u(t)

Operating the MZM at the minimum transmission point

-V 0 -2V V 2V -1

2V

b a

2.1 Pulse Carving 21

Fig. 2.3 a Optical IQ modulator. b Principle of IQ modulation.

By using (2.15) and (2.16), the amplitude modulation aI QM (t) and the phase mod-ulation I QM (t), performed by the IQM, can be calculated by

aI QM (t) = Eout (t)Ein(t)

= 12

cos2(

u I (t)2V

)+ cos2

(uQ(t)2V

), (2.17)

I QM (t) = arg[

cos(

u I (t)2V

), cos

(uQ(t)2V

)]. (2.18)

In (2.18), the arg [I, Q] operation denotes the calculation of the angle of a complexvalue from the real and imaginary parts in the range between and .

2.1.3 Pulse Carvers and Impulse Shapers

The shape of the transmitted optical pulses significantly affects the overall perfor-mance of optical fiber transmission systems. The pulse shape used in most commer-cial systems is NRZ, where a pulse filling the entire bit slot is transmitted for allsymbols with non-zero power. The power does not always go to zero when pass-ing from one symbol to another. In the case of RZ pulses, the optical power goesto zero within each symbol period. Therefore, power is smaller during the symboltransitions and the undesired frequency modulation (chirp) arising during the phasetransitions can not take effect or is at least reduced, depending on the optical pulsewidth and the rise time of the electrical driving signals.

Optical IQ modulator

I

Q

Amplitude Modulation

in the I-arm

Amplitude Modulation

in the Q-arm

IQMj (t)Q (t) e

Reachable Signal Space

( )inE t ( )outE t

( )Iu t

( )Qu t= / 2PMu V

b a Principle of IQ modulation


Optical signals with RZ pulse shape can be created either by electronically gen-erating RZ waveforms or by carving RZ pulses in the optical domain, using an extraoptical pulse carver. When employing the latter method, RZ pulses with a duty cy-cle of 50% can be generated with a MZM, which is operated at the quadrature pointand driven with a sinusoidal electrical signal with a peak-to-peak amplitude of V , afrequency corresponding to the symbol rate rS = 1/TS and a phase offset of /2.The electrical driving signal is given by u(t) = V/2 sin(2 t/TS /2) V/2,where TS denotes the duration of one symbol.

The field transfer function of the optical RZ pulse carver for generating RZpulses with a duty cycle of 50% is defined as

Eout (t)Ein(t)

= cos[

4 sin

(2

tTS

2

)

4

]. (2.19)

Even when employing optical pulse carving, the final optical pulse form at thetransmitter output depends also on the shape of the electrical driving signals. Thesecan be formed by electrical impulse shapers (IS) before feeding into the modulatordriving electrodes. In system simulations, electrical pulses without overshoots andwith specified rise times can be generated by filtering a rectangular input time func-tion with a non-causal linear time invariant filter with the Gaussian shaped impulseresponse

h(t) =2

Te

e(2t/Te)2. (2.20)

The resulting output pulse of the electrical impulse shaper is given by the convolu-tion of the rectangular signal with the impulse response h(t) and is specified by

p(t) =12

[er f c

(2 (t TS)

Te

) er f c

(2tTe

)]. (2.21)

In (2.20) and (2.21), Te represents the filter time constant, which can be approxi-mately related to the electrical rise time 1t as

1t 34

Te, (2.22)

as long it is assumed that the symbol time TS is much longer than the filter timeconstant Te [2].

Having now discussed some fundamental components used in the various trans-mitters for high-order modulation, some basics for multi-level signaling are brieflypresented in Sect. 2.2. Afterwards, the transmitters for particular modulation for-mats are described in detail.

2.3 ASK Transmitters 23

2.2 Multi-Level Signaling

In digital optical transmission with high-order modulation, m data bits, denoted hereas{b1k , b2k , .., bmk

}, are collected and mapped to a complex symbol bk chosen from

an alphabet A of elements An (n = 1..M,M = 2m). Each symbol bk can be inter-preted as a complex phasor with the in-phase and quadrature coordinates bik and b

qk ,

respectively,

bk = bik + jbqk , (2.23)

and with amplitude and phase states given by

abk =

bik2+ bqk

2, bk = arg

[bik, b

qk

]. (2.24)

One of the M = 2m symbols is assigned to each symbol interval (denoted by theinteger k, which has a range of 1 to ) of length TS = m TB , where rB = 1/TBis the data rate. The assignment of respective combinations of m bits to symbolswith particular amplitude and phase states (bit mapping) is defined in a so calledconstellation diagram. For the best optical signal to noise ratio (OSNR) perfor-mance, bit mapping should be arranged so that only one bit per symbol differs froma neighboring symbol (Gray coding). The symbols are transmitted on the reducedsymbol rate rS = 1/TS = rB/m.

For the theoretical description of the electrical driving signals in Sect. 2.6, thein-phase and quadrature symbol coordinates are scaled to unity, limiting the max-imum coordinates of the I-axis and Q-axis to one. These normalized in-phase andquadrature coordinates are denoted as ik and qk throughout this book. By scalingthe symbol coordinates bik and b

qk to unity, the normalized in-phase and quadrature

coordinates ik and qk can be expressed as

ik =bik

bimax, qk =

bqkbqmax

, (2.25)

where bimax and bqmax are given by

bimax = maxn{|Re {An}|} , b

qmax = maxn

{|I m {An}|} . (2.26)

The relation between ik and qk and the data bits is specified by the bit mapping usedrespectively and illustrated more precisely later on.

2.3 ASK Transmitters

The most simple optical multi-level signaling scheme is the M-ary ASK, where in-formation is encoded into several intensity levels. The binary ASK (2ASK), usually


denoted as OOK, is the standard modulation format in commercially deployed opti-cal transmission systems. The 2ASK constellation diagram defines only two symbolpoints. Just one bit b1k is assigned to each symbol, as it is depicted in Fig. 2.4b. Fig-ure 2.4a shows a 2ASK transmitter when performing external modulation.

b a

CW MZM MZM RZ

Data

2ASK signal

IS

Pulse carving

1 0

{ }1b

i

q

Fig. 2.4 a 2ASK transmitter with external modulation. b 2ASK constellation diagram.

The optical part consists of a CW laser, an optional MZM for RZ pulse carvingand a MZM for intensity modulation, which is operated at the quadrature point. Anice side effect of using a MZM for intensity modulation, is the nonlinear compres-sion of the MZM transfer function at high and low transmission, which can suppressripples on electrical driving signals.

The electrical data signal can be formed by an impulse shaper as explained inSect. 2.1.3. The optical transmitter output signal for RZ-ASK, when neglecting lasernoises and polarization, can be described by

Es(t) =

Ps e j (s t+s ) cos(

u(t)2V

) cos

(

4sin(

2t

TS

2

)

4

), (2.27)

whereas the second cosine-term disappears in the case of NRZ. The electrical driv-ing signal for 2ASK is defined as

u(t) = V + V

k

(b1k p (t kTS)

), b1k {0, 1} . (2.28)

High-order ASK formats have been investigated in [21] and [24] where it wasshown that they require high signal to noise ratios for direct detection, especially inoptically amplified links due to the intensity dependence of the signal-ASE noise. Inprinciple, they can be generated with the same optical transmitter. However, multi-level electrical signals would have to be produced by an adequate electrical drivingcircuit to drive the MZM.

The generation of multi-level electrical driving signals is quite challenging forhigh data rates because the eye spreading increases when overlapping different bi-nary electrical signals to create a multi-level signal, which leads to a degradation ofthe system performance. The eye-spreading can be defined as 1e = (1 + 2)/de,

2.4 DPSK Transmitters 25

where 1 and 2 describe the ripples (or the spreadings) in the upper and lower levelsand de is the height of the eye diagram, as shown in Fig. 2.5. For instance, if twobinary signals are summed to a quaternary signal, the eye spreading is increased bya factor of three [6].

ed

1

2

( )1 2 / = +e ed

Eye spreading

Fig. 2.5 Definition of eye spreading for a binary signal, based on [6]

2.4 DPSK Transmitters

Figure 2.6 shows constellation diagrams of different DPSK formats. All the con-stellation points lie in one circle. Bit mapping can theoretically be chosen arbitrar-ily. Here it is arranged in Gray code, so that only one bit per symbol differs from aneighboring symbol, leading to the best noise performance.

Fig. 2.6 DPSK constellationdiagrams with Gray coded bitmappings

1000

1100 0000

0110

1010

0011 0101

1111 1001

0010

0001

1011

0111

1110

1101

0100

{ }1 4,..,b b

i

q

DBPSK DQPSK

8DPSK 16DPSK

1 0

{ }1b

i

q

10 01

11

00

{ }1 2,b b

i

q

110 000

011

101

001 010

111 100

{ }1 2 3, ,b b b

i

q


Basically, optical DPSK signals can be constituted by many different transmittertypes. Optical complexity can be reduced through increased electrical complexityand vice versa. A single PM or MZM in the optical part would be sufficient togenerate arbitrary DPSK signals. However, multi-level electrical driving signals arerequired for high-order DPSK formats in that case. Their generation increases theelectrical effort and is problematic due to the eye spreading problem. Another op-tion is to use an optical IQ modulator alone. In this situation, the necessary numberof states of electrical driving signals corresponds to the number of projections ofthe symbols to the I-axis and the Q-axis. From a practical point of view, the IQmodulator is not the best choice for generating high-order DPSK signals because allconstellation points lie in one circle, and the distances between the signal states ofthe in-phase and quadrature driving signals are short.

The discussion of DPSK transmitters within this book is restricted to config-urations which require solely binary electrical driving signals. In Sect. 2.4.1 andSect. 2.4.2, respectively, two different configurations are presented which are de-noted here as serial DPSK transmitter and parallel DPSK transmitter.

2.4.1 Serial DPSK Transmitter

One way of generating optical DPSK signals with binary electrical driving signalsis to use m consecutive PMs, where m is the number of bits per symbol. This trans-mitter is shown in Fig. 2.7, and is called serial transmitter throughout this book.After the first PM (phase shift ), a DBPSK signal is obtained. After the second PM(phase shift /2) a DQPSK signal is obtained, and so on.

IS

IS

DBPSK DQPSK 8DPSK MDPSK

CW PM MZM RZ

Data

Dif

fere

nti

al

En

cod

er

1:m

D

EM

UX

PM PM

IS

IS

PM

/2(m-1) /2 /4

kmb

1kb

kmd

1kd

1( )PMu t 2 ( )PMu t 3 ( )PMu t ( )mPMu t

Fig. 2.7 DPSK transmitter with binary electrical driving signals, serial configuration

2.4 Parallel DPSK Transmitter 27

In the electrical part of the transmitter, the data signal is first parallelized with a1:m demultiplexer. Parallelized data bits

{b1k , b2k , .., bmk

}are then fed into a dif-

ferential DPSK encoder, whose complexity and configuration generally depends onthe order of the DPSK modulation, the structure of the optical transmitter part, aswell as the used bit mapping of the data to the constellation points. The differentialencoding is performed to enable differential detection, or to resolve phase ambiguityarising from carrier synchronization at the receiver (as described in Sect. 3.5). Whenemploying synchronous detection techniques without differential decoding, the dif-ferential encoder can be omitted and only PSK signals generated. The functionalityof the differential encoders is discussed in more detail in Sect. 2.4.3.

At the differential encoders outputs, the encoded output data{d1k , d2k , .., dmk

}is obtained and passed to electrical impulse shapers and subsequently to the opticalmodulators as illustrated in Fig. 2.7. The NRZ output signal of the serial DPSKtransmitter for a DPSK format with m bits per symbol is given by

Es(t) =

Ps e j (s t+s ) ej

u P M1(t)

V

e ju P M2

(t)V

... e j

u P Mm (t)V

, (2.29)

with the binary electrical driving voltages

u P Mn (t) =V

2n1

k

(dnk p (t kTS)

), (2.30)

where n = {1, 2, ..,m}, and dnk {0, 1} represents the n-th differentially encodedbit of a symbol consisting of m bits in the k-th symbol interval.

2.4.2 Parallel DPSK Transmitter

A second DPSK transmitter configuration, which also uses binary electrical drivingsignals, is composed of a combination of an optical IQ modulator and consecu-tive phase modulators, in the following called parallel transmitter and depicted inFig. 2.8. The optical IQ modulator accomplishes a DQPSK modulation, and higher-order DPSK signals are generated by the consecutive PMs.

The electrical transmitter part is identical to the one for the serial transmitter,with the exception of the internal setup of the differential encoder. To accomplishDQPSK modulation, the Mach-Zehnder modulators in the I-arm and the Q-arm ofthe IQM are operated at the minimum transmission point and driven by binary elec-trical driving signals

u I (t) = 2V + 2V

k

(d1k p (t kTS)

), (2.31)

uQ(t) = 2V + 2V

k

(d2k p (t kTS)

). (2.32)


CW

MZM

MZM RZ

MZM

3dB

-90

3dB PM

/4

PM

Data

Dif

fere

nti

al

En

cod

er

1:m

D

EM

UX

IS

IS

IS

IS

DQPSK 8DPSK MDPSK

/2(m-1)

kmb

1kb

kmd

1kd

( )Iu t

( )Qu t

3( )PMu t ( )mPMu t

Fig. 2.8 Parallel DPSK transmitter with binary electrical driving signals

The driving signals of the consecutive phase modulators are defined by (2.30) forn = {3..m}. The optical output signal of the parallel DPSK transmitter for NRZ linecoding is specified by

Es(t) =

Ps e j (s t+s ) aI QM (t) e jI QM (t) ej

u P M3(t)

V

... e ju P Mm (t)

V, (2.33)

where aI QM (t) and I QM (t) describe the amplitude and phase modulation of theIQM, given by (2.17) and (2.18), respectively, and the parameter V is assumed tobe the same for all the modulators used, for simplicity.

2.4.3 Differential Encoding

In the differential encoder, the data bits{b1k , b2k , .., bmk

}, which are mapped to

symbols as defined by the original bit mapping, for instance the Gray coded bitmapping in Fig. 2.6, are encoded in a way to represent phase differences. To achievethis, appropriate absolute phase states k must be adjusted at the encoder outputfor given phase differences bk and previously given absolute phase states k1 ac-cording to k = k1 + bk . The symbol assignment at the encoder output, whichdescribes the mapping of the differentially encoded bits

{d1k , d2k , .., dmk

}into sym-

bols with absolute phase states k , must be defined according to a particular opticaltransmitter configuration in order to drive the optical modulators adequately to ob-tain the desired absolute phase states.

Different symbol assignments are appropriate at the encoder output for the serialand the parallel DPSK transmitter, as shown in Fig. 2.9. Therefore different encodersare needed for each of the two configurations. For the serial transmitter, the symbolassignment must be arranged in chronologically increasing order, as illustrated in

2.4 Differential Encoding 29

DQPSK 8DPSK 16DPSK

Serial transmitter

Parallel transmitter

10 00

01

11

{ }1 2,d d

i

q

100 000

010

110

001 011

101 111

{ }1 2 3, ,d d d

i

q

1111

1000 0000

0100

1100

0010 0110

1010 1110

0011

0001

1101

0101

1011

1001

0111

{ }1 4,..,d d

i

q

10 00

01 11

{ }1 2,d d

i

q

011 101

111

001

110 010

000 100

{ }1 2 3, ,d d d

i

q

1001

0110 1010

1110

0010

1100 0100

0000 1000

1101

1011

0011

1111

0001

0111

0101

{ }1 4,..,d d

i

q

Fig. 2.9 Symbol assignment to absolute phase states at the differential encoder output for the serialDPSK transmitter (top) and the parallel DPSK transmitter (bottom)

the upper part of Fig. 2.9 for DQPSK, 8DPSK and 16DPSK, respectively. As regardsthe parallel transmitter, the symbols must be assigned differently. For instance, whendriving the MZM in the I-arm and the Q-arm of the IQM, each with a logical one,an optical phase of /4 is obtained, in contrast to the serial configuration, wherean optical phase of 3/2 results for driving both PMs with a logical one. Thesymbol assignment for the parallel transmitter used here is shown in the bottom partof Fig. 2.9 for DQPSK, 8DPSK and 16DPSK, respectively. Because the absolutephase is not relevant for differential detection, the symbol assignments can also bearbitrarily rotated for both transmitters.

In any differential encoder, the data bits of the current symbol{b1k , b2k , .., bmk

},

representing the current phase difference, are combined with the previous encoderoutput bits

{d1k1 , d2k1 , .., dmk1

}, representing the absolute optical phase of the

previous symbol, in a logical circuit, in order to specify the next encoder output bits{d1k , d2k , .., dmk

}which define the current optical phase. The general structure of a

differential encoder is depicted in Fig. 2.10.The following paragraphs derive logical relations which characterize the logical

circuit of the differential encoders for different DPSK transmitters. They are onlyvalid for employing the Gray coded bit mapping to phase differences and the symbolassignment to absolute phases as defined in Fig. 2.6 and Fig. 2.9, respectively. Othermappings are possible, but would yield other relations.


Fig. 2.10 General structure ofa differential encoder

Logical circuit

TS

kmb

2kb

1kb

kmd

1kd

2kd

TS TS

Differential Encoders for DBPSK and DQPSK

In the case of DBPSK, differential encoding can be achieved easily. A logical onein the current data indicates a phase change of . By combining the current data bitwith the previous encoder output bit in a simple XOR gate, the next encoder outputbit is obtained.

The encoders required within DQPSK transmitters are yet more complex. Theyhave to provide two output bits d1k and d2k , which depend on the input data bits b1kand b2k , as well as on the previous encoder output bits d1k1 and d2k1 . Within theserial transmitter, the encoder output signals are taken to drive the two PMs. Thefirst PM changes the phase between 0 and , and the second one changes the phasebetween 0 and /2. In this way, the four absolute phase states 0, /2, , and 3/2 can be adjusted with a symbol assignment in chronologically increasing order. Thetruth table for the DQPSK encoder of the serial transmitter is given by Table 2.1.

Table 2.1 Truth table for the differential encoder appropriate for the serial DQPSK transmitter

d1k d2k k d1k1 d2k1 k1 b1k b2k bk

0 0 0 0 0 0 0 1 00 0 0 0 1 /2 0 0 3/2 0 0 0 1 0 1 0 0 0 0 1 1 3/2 1 1 /20 1 /2 0 0 0 1 1 /20 1 /2 0 1 /2 0 1 00 1 /2 1 0 0 0 3/2 0 1 /2 1 1 3/2 1 0 1 0 0 0 0 1 0 1 0 0 1 /2 1 1 /21 0 1 0 0 1 01 0 1 1 3/2 0 0 3/2 1 1 3/2 0 0 0 0 0 3/2 1 1 3/2 0 1 /2 1 0 1 1 3/2 1 0 1 1 /21 1 3/2 1 1 3/2 0 1 0

2.4 Differential Encoding 31

By using Karnaugh maps, for instance, the logical relations for the encoder out-put bits d1k and d2k can easily be derived from Table 2.1 for the serial transmitter:

d1k = b2k d1k1 d2k1 + b1k d1k1d2k1 + b1k d1k1d2k1 + b2k d1k1d2k1 , (2.34)

d2k = b1k b2k d2k1 + b1k b2k d2k1 + b1k b2k d2k1 + b1k b2k d2k1 . (2.35)

In (2.34) and (2.35), + denotes logical OR, the particular terms are associated bylogical AND, and the overlines indicate logical negation. In practice, the encodercan be implemented using the adequate AND and OR gates.

Due to the different symbol assignment at the encoder output, the differentialencoder of the parallel transmitter differs from the one of the serial transmitter. Itstruth table is shown in Table 2.2. The corresponding logical relations for the twoencoder output bits d1k and d2k for the parallel DQPSK transmitter are

d1k = b1k d1k1 d2k1 + b2k d1k1d2k1 + b1k d1k1d2k1 + b2k d1k1d2k1 , (2.36)

d2k = b2k d1k1 d2k1 + b1k d1k1d2k1 + b2k d1k1d2k1 + b1k d1k1d2k1 . (2.37)

Table 2.2 Truth table for the differential encoder appropriate for the parallel DQPSK transmitter

d1k d2k k d1k1 d2k1 k1 b1k b2k bk

0 0 5/4 0 0 5/4 0 1 00 0 5/4 0 1 3/4 1 1 /20 0 5/4 1 0 7/4 0 0 3/2 0 0 5/4 1 1 /4 1 0 0 1 3/4 0 0 5/4 0 0 3/2 0 1 3/4 0 1 3/4 0 1 00 1 3/4 1 0 7/4 1 0 0 1 3/4 1 1 /4 1 1 /21 0 7/4 0 0 5/4 1 1 /21 0 7/4 0 1 3/4 1 0 1 0 7/4 1 0 7/4 0 1 01 0 7/4 1 1 /4 0 0 3/2 1 1 /4 0 0 5/4 1 0 1 1 /4 0 1 3/4 0 0 3/2 1 1 /4 1 0 7/4 1 1 /21 1 /4 1 1 /4 0 1 0


Differential Encoders for Higher-Order DPSK Formats

In the same manner, one can specify differential encoders for the higher-order DPSKtransmitters. Starting from the constellation diagrams with bit mappings and symbolassignments defined in Fig. 2.6 and Fig. 2.9, respectively, truth tables can be estab-lished. Subsequently, the corresponding Karnaugh maps can be evaluated in orderto determine the logical relations of the encoders.

Since the equations resulting for 8DPSK and 16DPSK are quite bulky, they aregiven in Appendix A. It becomes apparent here that the complexity of the differen-tial encoder grows significantly with the increasing order of the phase modulation.For 16DPSK, the differential encoder is very complex. For instance, the relation forthe encoder output bit d1k has 30 OR combined terms, each consisting of 4-7 ANDcombined inputs.

Now having provided all the relevant functional information about the setup ofthe serial and parallel DPSK transmitters, the following subsection discusses theproperties of their output signals.

2.4.4 Signal Properties

The structure of the transmitter affects the signal characteristics and the transmis-sion properties of the generated optical DPSK signals, due to the fact that the symboltransitions (amplitude and phase transitions) of the transmitters are different, espe-cially in the case of NRZ. An optical high-order modulation signal at the transmitteroutput can be generally described by

Es(t) =

Ps e j (s t+s ) a(t) e j(t), (2.38)

where A(t) = a(t) e j(t) represents the normalized complex modulation enve-lope of the optical signal with time dependent amplitude a(t) and phase (t). Thesquared amplitude a2(t) times the CW laser power Ps represents the instantaneoussignal power (which is proportional to the signal intensity). Another important pa-rameter, which has a significant influence on the transmission performance, is thederivative of the optical phase (t) = d(t)/dt . It is a measure for the undesiredfrequency modulation occurring during the symbol transitions, usually denoted aschirp.

The complex envelope of the DPSK transmitter output signals can be extractedfrom (2.29) and (2.33). The normalized intensity eyes, the IQ diagrams (I m {A(t)}versus Re {A(t)}, where a(t) is scaled here to unity for illustration purposes) and thechirp characteristics are plotted for both transmitter types discussed above and bothpulse shapes for 8DPSK modulation in Fig. 2.11, assuming a data rate of 40 Gbit/sand an electrical rise time of 1/4 of the symbol duration.

2.4 DPSK Transmitters - Signal Properties 33

0.372 1.1220

0.2

0.4

0.6

0.8

1

-1 0 1

-1

0

1

0.372 1.122-5

-2.5

0

2.5

5x 10

11

0.372 1.122-5

-2.5

0

2.5

5x 10

11

0.372 1.1220

0.2

0.4

0.6

0.8

1

-1 0 1

-1

0

1

0.372 1.122-5

-2.5

0

2.5

5x 10

11

0.372 1.122-5

-2.5

0

2.5

5x 10

11

0.372 1.1220

0.2

0.4

0.6

0.8

1

-1 0 1

-1

0

1

0.372 1.122-5

-2.5

0

2.5

5x 10

11

0.372 1.122-5

-2.5

0

2.5

5x 10

11

0.372 1.1220

0.2

0.4

0.6

0.8

1

-1 0 1

-1

0

1

0.372 1.122-5

-2.5

0

2.5

5x 10

11

0.372 1.122-5

-2.5

0

2.5

5x 10

11

Time Time Time Time

Time Time Time Time

Time Time Time Time

Re [A(t)] Re [A(t)] Re [A(t)] Re [A(t)]

Im [A

(t)]

Im [A

(t)]

Im [A

(t)]

Im [A

(t)]

Nor

m. I

nten

sity

In

tens

ity

Nor

m. I

nten

sity

In

tens

ity

Nor

m. I

nten

sity

In

tens

ity

Nor

m. I

nten

sity

In

tens

ity

Chi

rp (

1/s)

Chi

rp (

1/s)

Chi

rp (

1/s)

Chi

rp (

1/s)

Chi

rp

Nor

m. I

nt. (

1/s)

Chi

rp

Nor

m. I

nt. (

1/s)

Chi

rp

Nor

m. I

nt. (

1/s)

Chi

rp

Nor

m. I

nt. (

1/s)

Serial transmitter, NRZ Serial transmitter, RZ Parallel transmitter, NRZ Parallel transmitter, RZ

Fig. 2.11 Optical signal properties of different 8DPSK transmitters

When the serial transmitter and NRZ pulse shape are employed, symbol transi-tions are conducted on circles, and there is constant power during phase changes.Chirp appears during the symbol transitions, and its magnitude depends on thesteepness of the phase jumps. An intuitive measure for the disturbing effect of thechirp during transmission is the product of the chirp and the intensity as is shown inthe bottom eye diagrams of Fig. 2.11. It becomes apparent that the chirp has a strongeffect for the serial transmitter and NRZ pulse shape, due to permanent full power.In the case of RZ, there is almost no optical power during phase changes, and onlya very small residual impact of the chirp can be determined. For the parallel trans-mitter, the impact of the chirp is reduced even for the NRZ pulse shape. The symboltransitions are different due to the usage of an IQ modulator, and power is reducedfor some transitions (intensity dips). The chirp shows high peaks when the pointof origin is crossed in the IQ diagram (the phase jumps abruptly by ). Howeverthis is not problematic because no optical power exists at this moment. The prod-uct of the chirp and the intensity is clearly reduced compared with the serial NRZtransmitter, so a better transmission performance can be expected.


2.5 Star QAM Transmitters

When compared with pure phase modulation, combined phase and amplitude modu-lation (quadrature amplitude modulation, QAM) exhibits a reduced number of phasestates for the same number of symbols. The constellation points can be arranged ina square (Square QAM formats) or they can lie on multiple circles (Star QAM for-mats). The phases are arranged with equal spacing for Star QAM formats, as shownfor Star 16QAM in Fig. 2.13, so the phase difference of any two symbols corre-sponds to a phase state defined in the constellation diagram and phase informationcan be differentially encoded as for DPSK formats. Thus, Star QAM signals withdifferentially encoded phases are suitable to be detected by receivers with differen-tial detection. By contrast, Square QAM signals are conveniently detected by coher-ent synchronous receivers, but can also be detected by differential detection whenphase pre-integration is employed at the transmitter [9].

To accomplish the generation of Star QAM signals with differentially encodedphases, the same equipment can be used as for DPSK transmitters just described.The DPSK transmittersin serial or parallel configurationonly have to be ex-tended by an additional MZM for intensity modulation, to be able to place symbolson different intensity rings.

In principle, arbitrary Star QAM constellations are possible. The Star 8QAMformat (2ASK-DQPSK) was investigated in [11]. A Star 8QAM transmitter can becomposed of a DQPSK transmitter followed by an additional MZM and can usethe same differential encoders as a DQPSK transmitter. The transmitter for Star16QAM (2ASK-8DPSK) consists of an 8DPSK transmitter, extended by a MZMfor intensity modulation, as shown in Fig. 2.12 for the serial configuration.

IS

IS

Star 16QAM

CW PM MZM RZ

Data

8DP

SK

D

iffe

ren

tial

E

nco

der

1:4

DE

MU

X

PM MZM

IS

IS

PM

/2 /4

4kb

1kb

2kd

1kd

3kd

1( )PMu t 2 ( )PMu t 3 ( )PMu t ( )IMu t

Fig. 2.12 Optical Star 16QAM transmitter with differential phase encoding, serial configuration

Figure 2.13 illustrates the Star 16QAM constellation diagrams with Gray codedbit mapping (Fig. 2.13a) and symbol assignments at the encoder output for the serialand parallel transmitters (Fig. 2.13b and Fig. 2.13c).

2.5 Star QAM Transmitters 35

a

1101 0001

0111

1011

0011 0101

1111 1001

0110 0100

1100

1110 1010

1000

0000

0010

{ }1 2 3 4, , ,b b b b

i

q b

1001 0001

0101

1101

0011 0111

1011 1111

0100 0110

1000

1010 1100

1110

0000

0010

{ }1 2 3 4, , ,d d d b

i

q

0111 1011

1111

0011

1101 0101

0001 1001

1110 0100

0110

0000 0010

1000

1010

1100

{ }1 2 3 4, , ,d d d b

i

qc

1r

2r1r

2r1r

2r

Fig. 2.13 Star 16QAM Gray coded original bit mapping (a) and symbol assignments at the encoderoutput for the serial transmitter (b) as well as the parallel transmitter (c)

As for 16DPSK, four bits are mapped to one symbol. However, high spectralefficiency can be obtained here without using the very complex differential 16DPSKencoder. Instead, 8DPSK encoders can be employed. When compared with 8DPSK,the constellation diagram consists of a second circle with eight more symbols. Thefourth bit b4k indicates if a symbol belongs to the inner or the outer circle and isused to drive the additional MZM.

One degree of freedom which can optimize the OSNR performance for StarQAM formats with only two amplitude states, is the ring ratio R R = r2/r1, wherer1 and r2 are the amplitudes of the inner and outer circle, respectively, as illustratedin Fig. 2.13. The influence of the ring ratio on the OSNR performance is discussedlater on in the second part of this book.

Another Star QAM constellation with 16 symbols, composed of four amplitudeand four phase states (4ASK-DQPSK), has been investigated in [19]. The definitionof only four phase states has the advantage that data recovery is easier to accomplishfor differential detection. On the other hand, the use of more than two amplitudestates leads to high OSNR requirements for intensity detection and therefore to apoor overall OSNR performance.

Generally, when using the serial NRZ-Star QAM transmitter, an optical StarQAM signal with only two amplitude states can be mathematically described by

Es(t) =

Ps e j (s t+s ) ej

u P M1(t)

V

... e ju P Mm1

(t)

V

cos(

u I M (t)2V

). (2.39)

In (2.39), the phase modulator driving signals u P M1(t)...u P Mm1(t) are again de-fined by (2.30) with n = {1..(m 1)}. The electrical driving signal for intensitymodulation depends on the desired ring ratio, and is specified by

u I M (t) = 2 arccos

(1

R R

)

V +2 arccos

(1

R R

)

V

k

(bmk p (t kTS)

), (2.40)

where bmk {0, 1} corresponds to the last data bit of a symbol with m bits in thek-th symbol interval.


Similarly, the last phase modulator of the parallel DPSK transmitter, whose out-put signal is given by (2.33), can be replaced with an intensity modulator to obtainthe parallel Star QAM transmitter. Its output signal is then given by

Es(t) =

Ps e j (s t+s ) aI QM (t) e jI QM (t)

e ju P M3

(t)V

... e j

u P Mm1(t)

V

cos(

u I M (t)2V

). (2.41)

In Fig. 2.14, the eye diagrams of the normalized intensity, the IQ diagrams, andthe chirp characteristics are depicted for the serial and the parallel Star 16QAMtransmitter, considering NRZ and RZ pulse shapes and assuming a ring ratio of 1.8,a data rate of 40 Gbit/s and an electrical rise time of 1/4 of the symbol period.

0.5 1.50

0.2

0.4

0.6

0.8

1

-1 0 1

-1

0

1

0.5 1.5-5

-2.5

0

2.5

5x 10

11

0.5 1.5-5

-2.5

0

2.5

5x 10

11

0.5 1.50

0.2

0.4

0.6

0.8

1

-1 0 1

-1

0

1

0.5 1.5-5

-2.5

0

2.5

5x 10

11

0.5 1.5-5

-2.5

0

2.5

5x 10

11

0.5 1.50

0.2

0.4

0.6

0.8

1

-1 0 1

-1

0

1

0.5 1.5-5

-2.5

0

2.5

5x 10

11

0.5 1.5-5

-2.5

0

2.5

5x 10

11

0.5 1.50

0.2

0.4

0.6

0.8

1

-1 0 1

-1

0

1

0.5 1.5-5

-2.5

0

2.5

5x 10

11

0.5 1.5-5

-2.5

0

2.5

5x 10

11

Time Time Time Time

Time Time Time Time

Time Time Time Time

Re [A(t)] Re [A(t)] Re [A(t)] Re [A(t)]

Im [A

(t)]

Im [A

(t)]

Im [A

(t)]

Im [A

(t)]

Nor

m. I

nten

sity

In

tens

ity

Nor

m. I

nten

sity

In

tens

ity

Nor

m. I

nten

sity

In

tens

ity

Nor

m. I

nten

sity

In

tens

ity

Chi

rp (

1/s)

Chi

rp (

1/s)

Chi

rp (

1/s)

Chi

rp (

1/s)

Chi

rp

Nor

m. I

nt. (

1/s)

Chi

rp

Nor

m. I

nt. (

1/s)

Chi

rp

Nor

m. I

nt. (

1/s)

Chi

rp

Nor

m. I

nt. (

1/s)

Serial transmitter, NRZ Serial transmitter, RZ Parallel transmitter, NRZ Parallel transmitter, RZ

Fig. 2.14 Optical signal properties of different Star 16QAM transmitters

The same conclusions can be drawn as for 8DPSK. The impact of the chirp,which appears at the phase transitions, is reduced when the parallel configurationis employed, and is almost eliminated when RZ pulses are transmitted. This be-comes apparent from the product of the chirp and the intensity (bottom diagrams inFig. 2.14), introduced as an intuitive performance measure in Sect. 2.4.4.

2.6 Differential Quadrant Encoding 37

2.6 Square QAM Transmitters

In Star QAM constellations described in the last section, first suggested by Cahn in1960 [3], the same number of symbols is placed on different concentric circles. StarQAM signals can easily be generated by enhancing a phase modulation transmit-ter for an additional intensity modulation and can be differentially detected. On theother hand, these constellations are not optimal as regards noise performance, be-cause symbols on the inner ring are closer together than symbols on the outer ring.In order to improve noise performance, Hancock and Lucky suggested placing moresymbols on the outer ring than on the inner ring [5], leading to constellations withmore balanced Euclidean distances. But they came to the conclusion that such sys-tems are more complicated to implement. In 1962, the Square QAM constellation,shown in Fig. 2.15 for Square 16QAM, was introduced for the first time by Cam-popiano and Glazer [4]. Indeed, Square QAM signals are conveniently detected bycoherent synchronous receivers and offer only a small improvement in noise perfor-mance, butthinking in terms of two quadrature carriersrelatively simple mod-ulation and demodulation schemes are possible, due to the regular structure of theconstellation projected on the in-phase and quadrature axis. Today, the Square QAMis widely used in electrical systems. In optical transmission systems, however, it isstill very distant from a commercial practical implementation.

The next sections illustrate different transmitter options for generating opticalSquare QAM signals, which are denoted here as serial Square QAM transmitter,conventional IQ transmitter, enhanced IQ transmitter, Tandem-QPSK trans-mitter and multi-parallel MZM transmitter. Each of these transmitters featuresdifferent properties of its output signals and different complexities of its optical andelectrical parts, which can be traded off. Detailed information about the electricalparts is provided, especially for two particular modulation formats: Square 16QAM,to which a special focus is brought in this book, and Square 64QAM, which is in-cluded here as a very ambitious format. Before going into the details of the transmit-ters, Sect. 2.6.1 outlines the differential quadrant encoding which must be employedfor all transmitter configurations when the quadrant ambiguity arising at the carriersynchronization at the receiver shall be resolved through differential coding.

2.6.1 Differential Quadrant Encoding

A n times /2 (n = 0, 1, 2, 3) phase ambiguity (quadrant ambiguity) arises at thecarrier synchronization for synchronous detection of Square QAM signals, whichcan be resolved by so-called differential quadrant encoding. This encoding schemecombines a DQPSK encoding with a specific bit mapping, and was proposed by We-ber in [22]. Two of the m bits of a Square QAM symbol determine the quadrant andare differentially encoded using a DQPSK differential encoder. This way, these twobits can be unambiguously recovered even if the absolute position of the received


constellation diagram is ambiguous with n times /2. The remaining (m 2) bitscan also be determined correctly for any n times /2 rotation when the bit mappingis arranged as rotation symmetric with respect to these bits. As an undesired con-sequence, the bit mapping is then not further Gray coded, leading to an OSNR per-formance degradation compared with Gray coded bit mappings. Gray coded SquareQAM signals can be received for instance when sending training sequences.

1000

1001

1010

0110

1110

0010

0111

0011

1111

1011

0001

0101

1101 0100

0000

1100

{ }1 2 3 4, , ,b b b b

i

q

0000

0001

0010

1110

0110

1010

1111

1011

0111

0011

1001

1101

0101 1100 0100

1000

{ }1 2 3 4, , ,d d b b

i

q

a b

Fig. 2.15 a Bit mapping used for Square 16QAM, appropriate for differential quadrant encoding.b Symbol assignment after the DQPSK differential encoder.

Figure 2.15a shows a non Gray coded Square 16QAM bit mapping which isappropriate for differential quadrant encoding. It can be observed that any rotationof n times /2 (n = 0, 1, 2, 3) causes no difference to the last two bits b3k andb4k . The first two bits, b1k and b2k , determine the quadrant and are encoded witha DQPSK differential encoder. When using the differential encoder of the parallelDQPSK transmitter described in Sect. 2.4.3, the differentially encoded bits d1k andd2k at the encoder output are assigned to the quadrants as illustrated in Fig. 2.15b.

2.6.2 Serial Square QAM Transmitter

In contrast to Star QAM constellations, the phases are arranged unequally spaced inSquare QAM constellations, so that it is not possible to adjust all the phase states ofthe symbols by simply driving consecutive phase modulators with binary electricaldriving signals. In [6], it was shown that any optical QAM signal can be generated byusing a single dual-drive MZM (see Fig. 2.1b). In this case, however, the necessarynumber of states of electrical driving signals is quite high (e.g. 16-ary driving signalsare needed for Square 16QAM), and a big electrical effort has to be engaged in toenable the simplicity of the optical part.

2.6 Serial Square QAM Transmitter 39

Another transmitter with a simple optical part capable of creating any QAM con-stellation is constituted by only two consecutive optical modulators: a MZM foradjustment of the amplitude state and a consecutive PM to set the phase. This trans-mitter is denoted as serial Square QAM transmitter throughout this book and isshown in Fig. 2.16. One more MZM can be employed for RZ pulse carving. Thesimplicity of the optical receiver part necessitates the use of a complex electricallevel generator, since electrical driving signals with a high number of states must begenerated (12-ary electrical driving signals are required for phase modulation in thecase of Square 16QAM, for instance).

CW MZM MZM RZ

IS Data

Square QAM

DQ

PS

K

Dif

fere

nti

al

En

cod

er

IS

PM

Lev

el

Gen

erat

or

1:m

D

EM

UX

kmb

1kb

2kd

1kd

2kb

3kb

( )IMu t ( )PMu t

Fig. 2.16 Square QAM transmitter, serial configuration

The optical output signal of the serial Square QAM transmitter for NRZ pulseshape is given by

Es(t) =

Ps e j (s t+s ) cos(

u I M (t)2V

) e j

u P M (t)V

. (2.42)

In order to adjust the desired amplitude and phase levels, the multi-level electricaldriving signals for the MZM and the PM must be chosen as

u I M (t) = V +2V

k

arcsin

i2k + q2k

2

p (t kTS), (2.43)

u P M (t) =V

k

(arg

[ik, qk

] p (t kTS)

). (2.44)

Equations (2.43) and (2.44) are generally applicable to any QAM constellation, andik and qk represent the normalized symbol coordinates. For Square 16QAM, for in-stance, it holds ik {1,1/3, 1/3, 1} and qk {1,1/3, 1/3, 1}, and the nor-


malized symbol coordinates ik and qk are related to the data bits{d1k , d2k , b3k , b4k

}as defined by the bit mapping shown in Fig. 2.15b and as specified in Table 2.3.

Table 2.3 Relation between the data bits{d1k , d2k , b3k , b4k

}, the normalized symbol coordinates

ik and qk , the normalized symbol amplitudes and the symbol phases for Square 16QAM afterdifferential quadrant encoding for the bit mapping defined in Fig. 2.15b

d1k d2k b3k b4k ik qk Normalized amplitude Phase ()

0 0 0 0 -1/3 -1/3 1/3 2250 0 0 1 -1/3 -1 0.74 251.570 0 1 0 -1 -1/3 0.74 198.430 0 1 1 -1 -1 1 2250 1 0 0 -1/3 1/3 1/3 1350 1 0 1 -1 1/3 0.74 161.570 1 1 0 -1/3 1 0.74 108.430 1 1 1 -1 1 1 1351 0 0 0 1/3 -1/3 1/3 3151 0 0 1 1 -1/3 0.74 341.571 0 1 0 1/3 -1 0.74 288.431 0 1 1 1 -1 1 3151 1 0 0 1/3 1/3 1/3 451 1 0 1 1/3 1 0.74 71.571 1 1 0 1 1/3 0.74 18.431 1 1 1 1 1 1 45

The arcsin-function in (2.43) makes sure to approach the appropriate intensitylevels while taking the cosine field transfer function of the MZM into account.In [16], the electrical driving signals were classified as ideal and non-ideal. Theso-called ideal driving signals, which are not very practical to generate, can beregarded as a theoretical approach to completely compensate for the MZM charac-teristic, so that the electrical pulse shape is directly transposed to the optical fieldamplitude. The non-ideal driving signals presented here yield correct intensity andphase states, but lead to small differences during the symbol transitions because theydo not fully compensate for the cosine MZM characteristic. When observing (2.43),for instance, the corresponding ideal driving signal would be obtained by apply-ing the arcsin-function to the whole sum. More details about this classification ofthe driving signals can be found in [16].

One of the main challenges for the practical implementation of the serial SquareQAM transmitter is the generation of the multi-level electrical driving signals withan electrical level generator. The level-generator is located behind the differentialencoder, as depicted in Fig. 2.16, and acts as a digital-to-analog converter. Fig-ure 2.17 shows a possible setup of the level-generator for Square 16QAM, composedof AND-, NOR-, XOR- and XNOR-gates, an inverter, and attenuators. It illustratesthe complexity of the electrical part in the serial Square QAM transmitter.

2.6 Serial Square QAM Transmitter 41

XNOR

XOR

XOR

XOR

XOR

-1

AND

AND

AND

NOR

0.5

0.22

0.25

0.1

0.4

0.53

+

+

+

12-ary signal to PM

3-ary signal to MZM

PS

PS

PS

3kb

4kb

1kd

2kd

IS

IS ( )IMu t

( )PMu t

Inverter

Attenuators

Level generator

Fig. 2.17 Electrical level generator for the serial Square 16QAM transmitter, PS: power splitter

An optical Square 16QAM signal has 3 amplitude levels and 12 different phase

states. The normalized amplitudes (given by

i2k + q2k /

2) and phases (arg

[ik, qk

],

in degrees) assigned to particular symbols after the differential encoder are listed inTable 2.3. When considering the generation of the 3-ary electrical driving signal forthe MZM, the normalized amplitude is 1 if b3k and b4k are both logical one (ap-plication of an AND-gate), 1/3 if b3k and b4k are both logical zero (NOR-gate),and 0.74 if b3k and b4k are different (XOR-gate), respectively (see Table 2.3). Thisyields the configuration of the lower part of the level generator depicted in Fig. 2.17.The amplitude states of the MZM driving signal have to be further adjusted to com-pensate for the nonlinear MZM characteristic, resulting in the attenuation valuesshown in Fig. 2.17. For the generation of the 12-ary driving signal for the phasemodulator, it can be observed from Table 2.3 that the phase is equal to 18.43 plusn times 90 if b3k is logical one and b4k is logical zero (realization by an XOR-gateand an AND-gate), equal to 45 plus n times 90 if b3k and b4k are both logical zeroor both logical one (XNOR), equal to 71.57 plus n times 90 if b3k is logical zeroand b4k is logical one (XOR, AND), and that d1k and d2k determine the quadrant,


and thus the value of n (n = 0, 1, 2, 3). To obtain a PM driving signal normalizedto one, the appropriate values of the attenuators are also given in Fig. 2.17.

With the level generator described, the driving signals for the MZM and the PMare generated with the adequate relative values. It should be noted that the givenattenuation values are only valid if the logical gates are operated with DC couplingat the outputs to obtain unipolar digital output signals. In practice, both signals mustbe amplified by modulator drivers to obtain the appropriate driving voltages for themodulators.

2.6.3 Conventional IQ Transmitter

It can be concluded from Sect. 2.6.2 that the serial Square QAM transmitter fea-tures a simple optical part, but requires a complex electrical level-generator whichcan not easily be implemented for high data rates. Due to the beneficial projectionof the constellation points on the in-phase and quadrature axis, it is an advantage togenerate square shaped constellations with IQ transmitters. This way, the numberof states of the driving signals and thus the electrical complexity can effectively bereduced in comparison with the serial Square QAM transmitter. In Fig. 2.18, thesetup of the conventional IQ transmitter for Square QAM is illustrated.

CW

MZM

MZM RZ

MZM

3dB

-90

3dB

Sq

uar

e Q

AM

C

od

er

Data

DQ

PS

K

Dif

fere

nti

al

En

cod

er

1:m

D

EM

UX

IS

IS

Lev

el

Gen

.

Square QAM Signal

Lev

el

Gen

.

kmb

1kb

2kd

1kd

2kb

3kb

( )Iu t

( )Qu t

1kc

kmc

Fig. 2.18 Conventional IQ transmitter for Square QAM

The optical IQ modulator is also used within the parallel DPSK and Star QAMtransmitter (see Sect. 2.4.2 and Sect. 2.5) to perform a DQPSK modulation. Whereasthe in-phase and quadrature driving signals are binary for DQPSK, multi-level elec-trical driving signals are required to generate higher-order optical Square QAM con-stellations. The number of levels of the electrical driving signals is equal to the num-ber of projections of the symbol points to the I-axis and the Q-axis (e.g. quaternarydriving signals are required for Square 16QAM).

2.6 Conventional IQ Transmitter 43

The optical output signal of the conventional IQ transmitter for Square QAM forNRZ pulse shape can be simply described by

Es(t) =

Ps e j (s t+s ) aI QM (t) e jI QM (t). (2.45)

In (2.45), aI QM (t) and I QM (t) are the amplitude and phase modulation of theIQM, which are defined in (2.17) and (2.18), respectively. The in-phase and quadra-ture driving signals are now multi-level and specified as

u I (t) = V +2V

k

[arcsin (ik) p (t kTS)

], (2.46)

uQ(t) = V +2V

k

[arcsin (qk) p (t kTS)

]. (2.47)

For the ideal driving case, the arcsin-function would have to be applied to the wholesum in both equations [16]. In order to generate the appropriate driving signalswith simple level generators, the symbol assignment after the differential DQPSKencoder (see differential quadrant encoding, Sect. 2.6.1) must be rearranged by an-other coder, which is denoted as Square QAM coder in the following. In practice,it is possible to implement this coder together with the DQPSK differential encoderas one single component, possibly through the use of digital signal processing.

0000

0001

0010

1110

0110

1010

1111

1011

0111

0011

1001

1101

0101 1100

1000

0100

{ }1 2 3 4, , ,d d b b

i

q

0011

0010

0001

0111

1000

1111

1010

0101

0000

1011

1101

0100

1001

0110 1110 1100

{ }1 2 3 4, , ,c c c c

i

q

Fig. 2.19 Rearranging of the symbols by the Square 16QAM coder within the conventional IQtransmitter

Figure 2.19 illustrates how the bits have to be rearranged for Square 16QAM. Byrotating the symbols in the n-th quadrant by n times /2, the differentially encodedfirst bit d1k and the third bit b3k as well as the differentially encoded second bitd2k and the fourth bit b4k are arranged in chronologically increasing order withincreasing signal levels in the in-phase and quadrature arms, respectively. Table 2.4shows the truth table for the rearrangement of the symbols. It also illustrates the


relation between the normalized symbol coordinates ik and qk , used in (2.46) and(2.47), the data bits

{d1k , d2k , b3k , b4k

}and the output bits of the Square 16QAM

coder, denoted as{c1k , c2k , c3k , c4k

}, for the conventional IQ transmitter.

Table 2.4 Truth table of the Square QAM coder and relation of the data bits and the normalizedsymbol coordinates ik and qk when using the conventional IQ transmitter for Square 16QAM

d1k d2k b3k b4k c1k c2k c3k c4k ik qk

0 0 0 0 0 0 1 1 -1/3 -1/30 0 0 1 0 0 1 0 -1/3 -10 0 1 0 0 0 0 1 -1 -1/30 0 1 1 0 0 0 0 -1 -10 1 0 0 0 1 1 0 -1/3 1/30 1 0 1 0 1 0 0 -1 1/30 1 1 0 0 1 1 1 -1/3 10 1 1 1 0 1 0 1 -1 11 0 0 0 1 0 0 1 1/3 -1/31 0 0 1 1 0 1 1 1 -1/31 0 1 0 1 0 0 0 1/3 -11 0 1 1 1 0 1 0 1 -11 1 0 0 1 1 0 0 1/3 1/31 1 0 1 1 1 0 1 1/3 11 1 1 0 1 1 1 0 1 1/31 1 1 1 1 1 1 1 1 1

Because the symbol rearrangement is confined to the particular quadrants, thefirst two bits are not changed by the Square QAM coder, so that c1k = d1k andc2k = d2k . By analyzing the truth table given in Table 2.4, the following logicalrelations can easily be derived for the third and the fourth output bit of the Square16QAM coder:

c3k = d1k d2k b3k + d1k d2k b4k + d2k b3k b4k + d1k d2k b4k + d1k b3k b4k , (2.48)

c4k = d1k b3k b4k + d1k d2k b3k + d1k d2k b4k + d1k d2k b3k + d2k b3k b4k . (2.49)

The new symbol assignment allows for the use of a simple level generator to gen-erate the quaternary electrical driving signals in the in-phase and quadrature arms.This level generator is shown in Fig. 2.20, and is far less complex than for the serialSquare 16QAM transmitter. The bits c1k and c3k are used as inputs for the level-generator in the in-phase arm, and the bits c2k and c4k are used as inputs for the onein the quadrature arm. As can be seen from (2.46) and (2.47), the driving amplitudehas to take the value V if both input bits are logical zero, arcsin (1/3) 2V/if the first input bit is logical zero and the second logical one, arcsin (1/3) 2V/ ifthe first input bit is logical one and the second logical zero, and V if both input bitsare logical one. The DC coupled unipolar input signals simply have to be added withthe appropriate weights, and the resulting signal must be passed via a DC blocker

2.6 Conventional IQ Transmitter 45

to the consecutive impulse shaper, and then to a modulator driver to provide for therequired MZM driving voltages.

0.64

+ DC blocker

1 2/k kc c

IS ( ) / ( )I Qu t u t

3 4/k kc c

Level generator

Fig. 2.20 Level generator for the conventional Square 16QAM IQ transmitter

The Square 64QAM constellation is composed of 64 symbols in a square array.In Fig. 2.21, a Square 64QAM constellation diagram with rotation symmetric sym-bol assignments after differential quadrant encoding is shown.

0000

0001

0010

0010

0010

0011

0011

0011

0011

0001

0001

0001 0000 0000 1010

1011 1001

1000

0111 0101

0100 1110

1111 1101

1100

0110 0111

0101 0100

1010 1011

1001

1110 1111

1101 1100

0110 0111

0101 0100

1010 1011

1001 1000

1110 1111

1101 1100

1000

1001

1010

0100

0101

0110

0111

1100

1101

1110

1111

01 11

00 10

1011

90

270

180

0110

0010

0000

1000

{ }3 4 5 6, , ,b b b b

i

q{ }1 2,d d

Fig. 2.21 Rotation symmetric Square 64QAM constellation diagram after differential quadrantencoding; the bits in the corners are the first two bits of a symbol, being differentially encoded; thearrows indicate the rearrangement of the symbols by the Square 64QAM coder.


One symbol carries the information of six bits. The first two bits d1k and d2k ,which are differentially encoded by a DQPSK differential encoder to enable resolv-ing the quadrant ambiguity of the carrier synchronization at the receiver, are equalwithin each quadrant and depicted in the corners of the constellation diagram. Thelast four bits b3k ...b6k are arranged as rotation symmetric, so a quadrant ambiguityat the receiver has also no impact on the information recovery of these data bits. Thesymbols have 10 different amplitudes and 52 different phases. Due to the high num-ber of different phase states, only an IQ transmitter seems to be feasible for signalgeneration. For the conventional IQ transmitter, the in-phase and quadrature drivingsignals have eight levels each.

Like for Square 16QAM, the symbols should be rearranged by a Square QAMcoder for Square 64QAM to produce a symbol assignment that allows for the usageof simple level generators to generate the 8-ary electrical in-phase and quadratureelectrical driving signals. When rearranging the bits as indicated by the arrows inFig. 2.21, the first, third and fifth bits are sorted in chronologically increasing orderwith increasing signal levels in the in-phase arm, and in the same way the second,fourth and sixth bits with increasing signal levels in the quadrature arm. The re-sulting constellation diagram with re-assigned symbols behind the Square 64QAMcoder is shown in Fig. 2.22.

1111

1110

1101

0010

1011

0100

0011

0110

1001

1100

0111

0001

1000 0000

0101

1010 1010

1011 1001

1000

0110

0111 0101

0100 1110

1111 1101

1100

1100 1110

1111 1101

0000 0010

0011 0001

1000 1010

1011 1001

0011 0001

0000 0010

1111 1101

1100 1110

0111 0101

0100 0110

0111

0110

0101

1011

1010

1001

1000

0011

0010

0001

0000

01 11

00 10

0100

{ }3 4 5 6, , ,c c c c

i

q{ }1 2,c c

Fig. 2.22 Symbol assignment after the Square 64QAM coder, optimized for the Square 64QAMlevel generator

2.6 Enhanced IQ Transmitter 47

When denoting the input bits as{d1k , d2k , b3k , b4k , b5k , b6k

}, and the output bits

as{c1k , c2k , c3k , c4k , c5k , c6k

}, the logical circuit of the Square 64QAM coder can

be described as follows:

c3k = d1k b3k b4k + d2k b3k b4k + d2k b3k b4k + d1k d2k b4k + d1k d2k b3k , (2.50)

c4k = d1k d2k b4k + d1k d2k b3k + d1k d2k b3k + d1k b3k b4k + d2k b3k b4k , (2.51)

c5k = d1k d2k b5k + d1k d2k b6k + d2k b5k b6k + d1k d2k b6k + d1k b5k b6k , (2.52)

c6k = d1k b5k b6k + d1k d2k b5k + d1k d2k b6k + d1k d2k b5k + d2k b5k b6k . (2.53)

The first two bits do not change, so it holds true that c1k = d1k and c2k = d2k .The output bits c1k , c3k and c5k serve as inputs for the Square 64QAM level gen-erator in the in-phase arm, and the remaining three bits as inputs for the levelgenerator in the quadrature arm. The Square 64QAM level generators must gen-erate 8-ary electrical driving signals with the appropriate amplitude levels, whichcan be deducted from (2.46) and (2.47). The normalized symbol coordinates in(2.46) and (2.47) are given as ik {1,5/7,3/7,1/7, 1/7, 3/7, 5/7, 1} andqk {1,5/7,3/7,1/7, 1/7, 3/7, 5/7, 1} and can be related to the data bitsusing the bit mappings illustrated in Fig. 2.21 and Fig. 2.22.

2.6.4 Enhanced IQ Transmitter

When the conventional IQ transmitter is used, the number of levels of the electricaldriving signals required for a particular modulation format is equal to the numberof states of ik and qk , respectively. With the aim of further reducing the number ofstates of the electrical driving signals, a modified IQ transmitter configuration canbe employed, which is denoted here as enhanced IQ transmitter [17]. By replacingthe amplitude modulation in each arm with separate intensity and phase modula-tions, the necessary number of levels of the driving signals can be reduced to half incomparison with the conventional IQ configuration. To accomplish intensity modu-lation, a MZM can be used in each arm which is operated at the quadrature point.The negative values on the I-axis and the Q-axis are reached by varying the phasebetween 0 and , using phase modulators or MZMs operated at the minimum trans-mission point. Because the phase has to be varied only between 0 and , binarysignals are sufficient for phase modulation for any modulation format. This way, theeye spreading problem, arising with the generation of multi-level electrical drivingsignals, can be mitigated in practice.


The application of the enhanced IQ transmitter is of special interest for Square16QAM. Only binary driving signals are required here for all the modulators. Thisresults in a simpler electrical transmitter part without level generators, composed ofjust a 1 : 4 demultiplexer, the coders and the modulator drivers. In Fig. 2.23, theenhanced IQ transmitter is illustrated for Square 16QAM, composed of MZMs forintensity modulation and PMs for phase modulation here.

CW

MZM

MZM RZ

MZM

3dB

-90

3dB

IS

IS

IS

IS

PM

PM Square 16QAM

Sq

uar

e 16

QA

M

Co

der

Data

DQ

PS

K

Dif

fere

nti

al

En

cod

er

1:4

DE

MU

X

4kb

1kb

2kd

1kd

2kb

3kb ( )

MZMIu t

( )PMI

u t1k

c

2kc

3kc

4kc ( )

MZMQu t

( )PMQ

u t

Fig. 2.23 Enhanced IQ transmitter for Square 16QAM

When defining the electrical driving signals of the Mach-Zehnder modulators forthe non-ideal driving case in the in-phase and quadrature branches as

u IM Z M (t) = V +2V

k

[arcsin (|ik |) p (t kTS)

], (2.54)

uQM Z M (t) = V +2V

k

[arcsin (|qk |) p (t kTS)

], (2.55)

and with the driving signals of the phase modulators in both arms given by

u IP M (t) =V2

k

[(sign (ik)+ 1) p (t kTS)

], (2.56)

uQ P M (t) =V2

k

[(sign (qk)+ 1) p (t kTS)

], (2.57)

the field transfer function of the enhanced IQ transmitter can be expressed as

2.6 Enhanced IQ Transmitter 49

Eout (t)Ein(t)

=12

cos(

u IM Z M (t)2V

)e j

uIP M(t)

V

+ j12

cos(

uQM Z M (t)2V

)e j

uQ P M(t)

V

=12

aI (t) e jI (t) + j12

aQ(t) e jQ(t). (2.58)

The optical Square QAM output signal of the enhanced IQ transmitter for NRZpulse shape is

Es(t) =

Ps e j (s t+s ) a(t) e j(t), (2.59)

where the amplitude and phase of the normalized complex envelope follow from(2.58) by applying complex arithmetic and are given by

a(t) =12

a2I (t)+ a

2Q(t)+ 2aI (t)aQ(t) sin

(I (t) Q(t)

), (2.60)

(t) = arg {aI (t) cosI (t) aQ(t) sinQ(t),aI (t) sinI (t)+ aQ(t) cosQ(t)}. (2.61)

The rearrangement of the bits must be accomplished in a different way than forthe conventional IQ transmitter. Figure 2.24 illustrates how the symbols after thedifferential encoder must be rearranged for Square 16QAM within the enhanced IQtransmitter using a Square QAM coder.

0000

0001

0010

1110

0101

1001

1111

1011

0111

0011

1010

1101

0110 1100

1000

0100

0000

0001

0010

1110

0110

1010

1111

1011

0111

0011

1001

1101

0101 1100

1000

0100

{ }1 2 3 4, , ,d d b b

i

q{ }1 2 3 4, , ,c c c c

i

q

Fig. 2.24 Symbol reassignment within the Square 16QAM enhanced IQ transmitter

Only four symbols in the second and the fourth quadrant have to change theirpositions to generate a symbol assignment where the first bit d1k = c1k and thesecond bit d2k = c2k (both inverted) define if a phase shift of is performed bythe phase modulators in the in-phase and the quadrature arms, respectively. The


inverters can be saved, because the resulting rotation of does not matter at thereceiver when differentially quadrant encoding is employed. By the third bit c3kand the fourth bit c4k the intensity levels in the in-phase and quadrature arms arespecified as low or high, respectively.

Table 2.5 shows the truth table for symbol rearrangement. It also illustratesthe relation between the normalized symbol coordinates ik and qk , used in(2.54)(2.57), and the data bits

{d1k , d2k , b3k , b4k

}as well as the four output bits{

c1k , c2k , c3k , c4k}

of the Square 16QAM coder for the enhanced IQ transmitter.

Table 2.5 Truth table of the Square QAM coder and relation of the data bits and the normalizedsymbol coordinates ik and qk when using the enhanced IQ transmitter for Square 16QAM

d1k d2k b3k b4k c1k c2k c3k c4k ik qk

0 0 0 0 0 0 0 0 -1/3 -1/30 0 0 1 0 0 0 1 -1/3 -10 0 1 0 0 0 1 0 -1 -1/30 0 1 1 0 0 1 1 -1 -10 1 0 0 0 1 0 0 -1/3 1/30 1 0 1 0 1 1 0 -1 1/30 1 1 0 0 1 0 1 -1/3 10 1 1 1 0 1 1 1 -1 11 0 0 0 1 0 0 0 1/3 -1/31 0 0 1 1 0 1 0 1 -1/31 0 1 0 1 0 0 1 1/3 -11 0 1 1 1 0 1 1 1 -11 1 0 0 1 1 0 0 1/3 1/31 1 0 1 1 1 0 1 1/3 11 1 1 0 1 1 1 0 1 1/31 1 1 1 1 1 1 1 1 1

The logical circuit of the Square QAM coder for the enhanced Square 16QAMtransmitter is defined by (2.62) and (2.63). These relations can be easily derivedfrom the truth table given by Table 2.5. Both first bits do not change (so it holds truethat c1k = d1k and c2k = d2k ), and the third and fourth output bits are related to theinput bits as

c3k = d1k d2k b3k + d1k d2k b3k + d1k d2k b4k + d1k d2k b4k , (2.62)

c4k = d1k d2k b3k + d1k d2k b3k + d1k d2k b4k + d1k d2k b4k . (2.63)

The optical part of the enhanced IQ transmitter can be simplified by performingthe separate intensity and phase modulations in each arm with only one component.For this purpose, a dual-drive MZM can be used, driven simultaneously in the push-pull mode for intensity modulation and in the push-push mode for phase modulation.However, the driving signals for intensity and phase modulation must be electricallycombined in that case before being injected into the MZM inputs [16].

2.6 Tandem-QPSK Transmitter 51

2.6.5 Tandem-QPSK Transmitter

Another transmitter also requiring only binary electrical driving signals for Square16QAM is denoted as Tandem-QPSK transmitter throughout this book and can becomposed of an optical IQ modulator followed by a DQPSK modulator. The lattercan be implemented either with one more IQ modulator, or with two consecutivephase modulators, as depicted in Fig. 2.25.

CW

MZM

MZM RZ

MZM

3dB

-90

3dB

Square 16QAM

PM PM

IS

IS

IS

IS

Data

DQ

PS

K

Dif

fere

nti

al

En

cod

er

1:4

DE

MU

X

/2

4kb

1kb

2kd

1kd

2kb

3kb ( )Iu t

1( )PMu t

( )Qu t

2( )PMu t

Fig. 2.25 Optical Tandem-QPSK transmitter for Square 16QAM

Like for the enhanced IQ transmitter, the MZMs within the IQ modulator achievemodulation in intensity. This way, only positive values on the in-phase and quadra-ture axis are addressed. As regards Square 16QAM, the MZMs are driven by binaryelectrical signals, and a constellation composed of four symbols in the first quadrantis created. In a similar way to the enhanced IQ transmitter, the electrical drivingsignals of the MZMs are defined here as

u I (t) = V +2V

k

[arcsin

(i1k)

p (t kTS)], (2.64)

uQ(t) = V +2V

k

[arcsin

(q1k)

p (t kTS)], (2.65)

where i1k and q1k represent the normalized symbol coordinates in the first quadrant

of the constellation diagram and are directly related to the data bits b3k and b4k ,respectively. For the bit mapping depicted in Fig. 2.15a, i1k = 1(1/3) for b3k = 1(0)and q1k = 1(1/3) for b4k = 1(0). Operating the IQ modulator in this way has thesame effect as interfering a DQPSK signal with a CW wave, as proposed in [10].

With two consecutive phase modulators which perform phase shifts of and/2, respectively, the three other quadrants can be approached, thus creating a


complete Square QAM constellation. It is a beneficial side-effect of this transmittertype thatinitiated through signal generationthe resulting constellation is inher-ently symmetric in rotation as regards the data bits b3k and b4k , so that no additionalSquare QAM coder for symbol rearrangement is needed to constitute a rotation sym-metric symbol assignment which is required to handle the quadrant ambiguity at thereceiver. It should be noted that the differential encoder for the serial DQPSK trans-mitter must be employed when performing the quadrant shift with two consecutivephase modulators as shown in Fig. 2.25.

With the amplitude and phase modulation of the IQ modulator, aI QM (t) andI QM (t), defined by (2.17) and (2.18), respectively, and with the phase modulatordriving signals u P M1(t) and u P M2(t) given by (2.30) as for the serial DPSK trans-mitter (n = 1, 2), the optical output signal of the Tandem-QPSK transmitter forNRZ pulse shape can be described by

Es(t) =

Ps e j (s t+s ) aI QM (t) e jI QM (t) ej

u P M1(t)

V

e ju P M2

(t)V

. (2.66)

The Tandem-QPSK transmitter is a promising option for practically implement-ing Square 16QAM systems, since the driving signals are binary and the signalgeneration is well suited for creating rotation symmetric constellations.

2.6.6 Multi-Parallel MZM Transmitter

Another option for generating Square QAM signals, which has been recently pro-posed in [14, 15], is to use a multi-parallel MZM transmitter. Its setup for Square16QAM is illustrated in Fig. 2.26.

By arranging two IQ modulators in parallel, a Square 16QAM signal can be syn-thesized from two QPSK signals. The so-called large-amplitude QPSK is createdby the upper IQM and determines the quadrant to which the symbol is mapped.The small-amplitude QPSK is obtained after the attenuator in the lower branch(attenuation 6 dB) and fixes the position of a symbol within the quadrant. TheSquare 16QAM constellation is finally assembled by the combination of both QPSKsignals. All MZMs are operated at the minimum transmission point. The Square16QAM signal is generated by driving them only with binary electrical signals, sothat the transmitter is free from handling multi-level electrical driving signalsjustlike the enhanced IQ transmitter and the Tandem-QPSK transmitter. The Square16QAM transmitter shown in Fig. 2.26 is denoted as quad-parallel MZM transmit-ter because four MZMs are used in parallel.

Generally, a M-ary Square QAM signal can be created by a multi-parallel MZMtransmitter being composed of m/2 optical IQMs and accordingly m MZMs. Thepower attenuation in the n-th IQM branch must then be chosen as (n 1) 6 dB.

To generate the modulator driving signals, the same coders as those appropri-ate for the conventional IQ transmitter can be employed in the electrical part ofthe multi-parallel MZM transmitter. In Fig. 2.19, it is shown how the bit mapping

2.6 Multi-Parallel Transmitter 53

MZM

MZM RZ

MZM

3dB

-90

3dB

MZM

MZM

3dB

-90

3dB

3dB

IQ-Modulator 1

IQ-Modulator 2

3dB CW

IS

IS

IS

IS

Sq

uar

e 16

QA

M

Co

der

Data

DQ

PS

K

Dif

fere

nti

a l

En

cod

er

1:4

DE

MU

X

4kb

1kb

2kd

1kd

2kb

3kb

( )SI

u t

1kc

2kc

3kc

4kc

( )SQ

u t

( )LQ

u t

6dB

Square 16QAM

( )LI

u t

Fig. 2.26 Quad-parallel MZM transmitter for generation of Square 16QAM signals

after differential encoding must be rearranged by a Square QAM coder for Square16QAM to create a symbol assignment suitable for driving the four MZMs of thequad-parallel MZM transmitter. To create the large-amplitude QPSK, the MZMs inthe in-phase and

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