Optics Communications 357 (2015) 86–94

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Optics Communications

http://d0030-40

n CorrUnivers

E-mshalabysobayya

1 OAlexand

journal homepage: www.elsevier.com/locate/optcom

Hybrid direct-detection differential phase shift keying-multipulsepulse position modulation techniques for optical communicationsystems

Ahmed E. Morra a,b,d,n, Hossam M.H. Shalaby b,1, Salem F. Hegazy c,d, Salah S.A. Obayya d

a Faculty of Electronic Engineering (FEE), Menoufia University, Menouf 32952, Egyptb Egypt-Japan University of Science and Technology (E-JUST), Alexandria 21934, Egyptc National Institute of Laser Enhanced Sciences, Cairo University, Giza 12613, Egyptd Zewail City of Science and Technology, Sheikh Zayed District, Giza 12588, Egypt

a r t i c l e i n f o

Article history:Received 25 July 2015Received in revised form26 August 2015Accepted 27 August 2015Available online 5 September 2015

Keywords:DD-DBPSKDD-DQPSKMPPMOptical amplifier noise limited systems

x.doi.org/10.1016/j.optcom.2015.08.08118/& 2015 Elsevier B.V. All rights reserved.

esponding author at: Faculty of Electronicity, Menouf 32952, Egypt. Fax: þ20 48366071ail addresses: ahmed.morra@el-eng.menofia.e@ieee.org (H.M.H. Shalaby), shegazy@zewailci@zewailcity.edu.eg (S.S.A. Obayya).n leave from the Electrical Engineering Deparria 21544, Egypt.

a b s t r a c t

In this paper, a hybrid differential phase shift keying-multipulse pulse position modulation (DPSK–MPPM)technique is proposed in order to enhance the receiver sensitivity of optical communication systems. Bothbinary and quadrature formats are adopted in the proposed systems. Direct-detection DPSK schemes that arebased on an asymmetric Mach–Zehnder interferometer with a novel ultrafast discrete delay unit are presentedto simplify the receiver implementation. Expressions for the bit-error rate (BER) of the proposed hybridmodulation techniques are derived taking into account the effect of the optical amplifier noise. Under theconstraints of the same transmitted data rate, bandwidth, and average received optical signal-to-noise ratio, theBER performances of the proposed schemes are then evaluated numerically and compared with that of tra-ditional differential binary phase shift keying (DBPSK), differential quadrature phase shift keying (DQPSK), andMPPM schemes and with that of recent hybrid schemes. Furthermore, a comparison between the proposedsystems and the traditional ones is held in terms of the bandwidth-utilization efficiency. Our results reveal thatthe proposed hybrid schemes are more energy-efficient and have higher receiver sensitivity compared with thetraditional ones while improving the bandwidth-utilization efficiency. The proposed DPSK–MPPM system isready to accommodate adjustable (or variable) bit rates, by virtue of the programmable delay integrated to thereceiver system.

& 2015 Elsevier B.V. All rights reserved.

1. Introduction

The sensitivity of the receiver is one of the most important issuesfor many optical communication systems. Higher receiver sensitivityimplies less number of transmitted signal photons per bit at the samebit-error rate (BER) [1]. Among the preeminent modulation schemesof optical communication systems featuring high receiver sensitivitiesare differential binary phase shift keying (DBPSK) and differentialquadrature phase shift keying (DQPSK) [2]. On the other hand, DQPSKis one of the most popular receivers for multilevel phase-modulatedoptical communication systems and is more bandwidth efficient thanDBPSK. Optical differential phase shift keying (DPSK) signals can bedirectly detected using an asymmetric Mach–Zehnder interferometer.

Engineering (FEE), Menoufia6.du.eg (A.E. Morra),ty.edu.eg (S.F. Hegazy),

tment, Alexandria University,

This simplifies the receiver implementation and avoid the need foroptical local oscillators and microwave carrier recovery circuits.

Recently, several ideas for optical hybrid-modulation systems havebeen suggested so as to enhance the sensitivity of the receiver. Liuet al. presented a combination of m-ary pulse position modulation(PPM) or m-ary frequency-shift keying (FSK) with additional polar-ization and/or phase modulation [1,3]. The first experimental realiza-tion was then carried out in [4] of hybrid polarization-multiplexed-2PPM-quadrature phase-shift keying (PM-2PPM-QPSK ) modulationfor long-haul transmission at a data rate of 42.8 Gbit/s. As a good stepto improve the performance of both traditional binary phase shiftkeying (BPSK) and multipulse pulse position modulation (MPPM)techniques in optical fiber communications, Selmy et al. proposedhybrid BPSK–modified MPPM, which surpasses the traditionalBPSK and MPPM techniques [5]. A hybrid orthogonal frequency-divi-sion multiplexing-pulse-position modulation (OFDM-PPM) techniquewas then proposed in [6] for free-space optical communications(FSO). Furthermore, Shi et al. proposed a hybrid polarization-division-multiplexed quadrature phase-shift keying-MPPM (PDM-QPSK-MPPM) for FSO [7].

A.E. Morra et al. / Optics Communications 357 (2015) 86–94 87

In an attempt to increase further the receiver sensitivity of opticalcommunication systems, in this paper, we propose hybrid differentialphase shift keying-multipulse pulse position modulation (DPSK–MPPM) techniques. The key idea here is to use the sensitivity- andspectrally‐ efficient DPSK scheme along with an energy-efficientmodulation scheme, such as MPPM [8], in order to integrate the ad-vantages of both schemes. We study the implementation and evaluatethe performance of both DBPSK and DQPSK formats. This is the firsttime that a hybrid modulation scheme for optical communicationsystems is based on direct-detection DPSK (DD-DPSK). This sig-nificantly simplifies the receiver implementation as there is no longerneed for optical local oscillators or microwave carrier recovery circuits.

To evaluate the performance of the proposed modulationtechniques, we derive expressions for the achieved bit-error rate(BER), under the assumption of optical amplifier-noise limitedsystems (which is realistic for long-haul optical fiber commu-nication systems [2]). In addition, we compare the performance ofthe proposed modulation techniques to that of traditional DBPSK,DQPSK, and MPPM techniques. Different design parameters suchas BER and bandwidth-utilization efficiency, are addressed in ourcomparisons, under the same conditions of data rate, bandwidth,and average received optical signal-to-noise ratio.

The rest of the paper is organized as follows. The system descrip-tion and receiver model are presented in Section 2. Section 3 is de-voted for the derivation of a BER expression for the proposed hybridsystems. Optical amplifier-noise limited systems are assumed duringour derivation. In Section 4, we compare the performance of theproposed hybrid systems to that of traditional systems, under thesame conditions of transmission data rate, bandwidth, and averagereceived optical signal-to-noise ratio. Also, we compare the perfor-mance of our systems to some of similar hybrid systems in the lit-erature. Finally, our conclusions are given in Section 5.

2. Hybrid DPSK–MPPM system model

In this section we describe the proposed hybrid DPSK–MPPMsystem model, including both the transmitter and the receiver. Inaddition, we give an example of the transmitted hybrid signal.

2.1. Transmitter side and signal example

Our proposed hybrid transmitter is shown in Fig. 1. The trans-mitter sends data symbols within time frames. Each time frame

Fig. 1. Block diagram of the hybrid transmitter.

Fig. 2. An example of the transmitted signal of a hybrid DBPSK–MPPM scheme with

has a duration T and is composed of M disjoint slots. Coherentoptical pulses (each of pulsewidth T M/τ = ) are signalled within n

slots of each time frame. A block of ⎢⎣ ⎥⎦ plog Mn2( ) + bits are trans-

mitted each time frame, where

⎧⎨⎩pn

nfor DBPSK,

2 for DQPSK. 1=

( )

The first N log Mn2( )= ⌊ ⌋ bits are encoded using the MPPM scheme.

These bits would identify the positions of the n pulses within theframe. Each MPPM optical pulse is then DBPSK or DQPSK modu-lated using an additional q bits, where q¼1 in the case of DBPSKand q¼2 in the case of DQPSK. That is, compared with traditionalDPSK, instead of transmitting a consecutive stream of DPSK pulses(each with a relatively low power), we transmit less number ofhigher power DPSK pulses. The positions of these pulses withinthe frames are identified using more data bits. An example of thetransmitted signal of a hybrid DBPSK–MPPM scheme with M¼4and n¼2 is shown in Fig. 2.

2.2. Receiver side

Figs. 3 and 4 show the receiver sides of both DBPSK–MPPM andDQPSK–MPPM techniques, respectively. The received signal is firstsplit into two branches using a 3-dB coupler. The lower branch iscomposed of a traditional direct-detection MPPM receiver in orderto identify the positions of the received n pulses within the frame.In the upper branch, the DPSK data is directly detected.

The DD-DBPSK receiver is implemented using the asymmetricMach–Zehnder interferometer with balanced detection [2]. As shownin Fig. 3, the received optical signal is further splitted into two portionswith one portion subject to programmable discrete delay based on thepositions of the previous and current signal slots being compared. InSection 2.2.1, we present a novel ultrafast delay unit (see the sche-matic diagram in Fig. 5) capable of applying discrete optical delays atswitching speeds up to 40–50 Gb/s (as fast as symbol rates) [9,10]. Ifthe previous and current signal slots being compared exist in the sameframe, the delay is m m2 1 τ( − ) , where m M0, 1, , 21 ∈ { … − } andm m m M1, 2, , 12 1 1∈ { + + … − } are the positions of the previousand current signal slots, respectively. On the other hand, if the pre-vious and current signal slots being compared exist in different frames,the delay is M m m1 2 τ( − + ) , where m m M, 0, 1, , 11 2 ∈ { … − } are thepositions of the previous and current signal slots, respectively. Itshould be noticed that the signal processing and decision circuitry setthe value of the binary control for the ultrafast discrete delay unitdepending on the value of the required delay.

It is worth mentioning that the output of DBPSK receiver de-pends on the phase difference between any two neighboringpulses and is used by the decision circuit to determine the DBPSKbit. It should be noticed that the delay by two time frames in theupper branch is to guarantee the availability of information aboutboth m1 and m2 from the lower branch.

It should be noticed that the demodulation of DD-DQPSK, asshown in Fig. 4, is done in a similar way to DD-DBPSK except for

M¼4 and n¼2. The phase differences due to DBPSK modulation are also shown.

Fig. 4. Receiver of the hybrid DQPSK–MPPM technique adopting asymmetric Mach–Zehnder interferometer.

Fig. 3. Receiver of the hybrid DBPSK–MPPM technique adopting asymmetric Mach–Zehnder interferometer.

A.E. Morra et al. / Optics Communications 357 (2015) 86–9488

that DD-DQPSK demodulation needs the received optical signal tobe split through two asymmetric interferometers with phase dif-ference of /2π .

2.2.1. Phase- and polarization-preserving ultrafast discrete delayunit

In this subsection, we present a novel ultrafast discrete delayunit capable of preserving the state of polarization (SOP) and thephase of the input pulse. Consider a linearly polarized optical pulsefed into an electro-optic (EO) modulator whose two operationalstates; either to leave the SOP unchanged or to flip it to the or-thogonal state [11]. The EO modulator is followed by a highly bi-refringent polarization-maintaining single-mode (PMSM) fiber oflength L oriented such that its slow and fast axes are preciselyaligned with the two possible SOPs emerging from the EO mod-ulator. It is well known that, by virtue of its highly asymmetricstructure or refractive-index [12], PMSM fiber allows guiding two

principal SOP of monochromatic light at strict timing and phaserelations without significant distortion. This feature highlights themerit of the PMSM fiber as a precise optical delay line preservingthe phase information. Therefore, this simple apparatus can switchbetween two possible delay times; either L v/s g

slowτ = correspond-

ing to the group velocity of the slow axis vgslow , or L v/f g

fastτ = cor-

responding to the group velocity of the fast axis vgfast , based on the

binary control of the EO modulator (set by the signal processingand decision circuitry as shown in Figs. 3 and 4).

Now consider a series of K of such delay stage with each oneequipped with PMSM fiber segment of length R-multiples of that ofthe preceding one (see the schematic diagram in Fig. 5). The fast andslow axes of all fiber segments and the EO modulators are alignedtogether, so that the manipulation of the SOP along the cascadedstages can assign the delay time of the emerging optical pulse to beone of the 2K choices Rf i

K i01τ{ ∑ =

− ; Rs f iK i

11τ τ+ ∑ =

− ; R R1s f iK i

21τ τ+ ( + ∑ )=

− ;

Fig. 6. Timing diagram for propagation through 1-, 2-, 3-, and 4-stages PMSM fi-bers when R¼2. The red-dashed lines denote the fast-axis propagation and theblue-solid lines denote slow-axis propagation. The slope of the red-dashed and theblue-solid lines are the group velocities for fast-axis and slow-axis propagations,respectively. Notice the exponential increase of the number of possible delay stepswith the number of sequential stages.

Fig. 5. Schematic diagram for K stages of the proposed ultrafast discrete delay unit.At a stage i, an input pulse is delayed based on the setting of the EO modulatoreither by Ri

fτ (fast-axis propagation) or by Risτ (slow-axis propagation). The K

binary inputs of the EO modulators therefore program the delay system to one of2K time-delay states.

A.E. Morra et al. / Optics Communications 357 (2015) 86–94 89

R R1 s f iK i

21τ τ( + ) + ∑ =

− ; R R R R1 ; ;s f iK i

s iK i2

31

01τ τ τ+ ( + + ∑ ) … ∑ }=

−=− . For

an optical pulse, input to the system at time t0, it can be then posi-tioned at 2K different time instants, where the first time instant is att Rf i

K i0 0

1τ+ ∑ =− .

In general, this train of time instants is separated either byfixed time interval s fτ τ( − ) or by variable intervals which arefunctions of the parameter R. However, a fixed time interval

s fτ τ( − ) can be realized between all delay times under the condi-tion R¼2, as depicted in Fig. 6. This condition can be interpreted inanalogy to the binary numbering system as there are only twopossible operational states per stage.

An advantage with the proposed discrete delay system is the re-latively short optical fiber required to realize optical delays, comparedwith other methods utilizing the wavelength tuning and chromaticdispersion [13]. To clarify this point, let us elaborate a quantitativeexample. To make an optical pulse span of 1.5 ns delay interval at stepsof 0.1 ns, if a PMSM fiber with differential group delay about 29.3 ps/mnear the wavelength 1550 nm [14] is used, a 51.19 m total fiber lengthis required along a number of 4 stages with the fiber length of the firststage about 3.41 m. The short fiber length serves the delay system bylimiting the pulse broadening effects caused by dispersion. Hence,there is no need for pre- and post-compensators used to recover thepulse width in other delay control systems utilizing much longer op-tical fibers [13].

Another advantage is the capability of the system to manipulatehigh-rates of optical pulses. Because each stage can switch betweentwo operational states independent from the neighboring stages,

different optical pulses can be simultaneously handled while se-quentially propagating along the system. Therefore, the rate of theproposed system is determined, in principle, by the switching rate ofthe used EO modulators. Fortunately, current technologies offer aplethora of ultrafast EO modulators. For example, recent advances ofGaAs-, silicon-, and photonic-crystal-based EO modulator can reachdata rates up to 40–50 Gbit/s [9,10,15].

One more advantage is that the optical pulse emerging fromPMSM fiber has a well defined polarization and phase with respectto the input. It is easy thereby to compensate for the polarizationand phase changes using two additional EO modulators. Thisfeature is essential for time division schemes that require ex-tracting the phase information in a subsequent measurementsystem (like the scheme presented in this paper). It worth men-tioning that by integrating this tunable optical delay unit to thereceiver system, the proposed DPSK–MPPM system is ready tooperate at adjustable (or variable) data rates.

3. Bit error rate analysis of proposed hybrid modulationtechniques in optical amplifier-noise limited channels

In this section we develop an expression for the BER of theproposed hybrid modulation techniques. In our analysis, we as-sume optical amplifier-noise limited systems. As seen from Figs. 3and 4, the BER of the hybrid system depends on both current andprevious frames. We obtain an upper bound of the BER of theproposed hybrid modulation techniques by considering the worstcase scenario. That is, we assume that all the n positions are in-correctly decoded whenever an MPPM frame is incorrectly de-tected. This upper bound can be written as

⎜ ⎟

⎡⎣⎢

⎛⎝

⎞⎠

⎤⎦⎥

N pN

p

qp q

p

BER1

BER2

SER

1 SER SER2

BER

1 SER 1 SER BER ,2

Hybrid MPPMcurrent

MPPMcurrent

MPPMcurrent

MPPMprevious

DPSK

MPPMcurrent

MPPMprevious

DPSK( )( )

( )

≤+

+

+ − + ( − )

+ − −( )

where SERMPPMcurrent and SERMPPM

previous are the symbol-error rates (SERs) ofMPPM data in both current and previous frames, respectively,BERMPPM

current is the bit-error rate (BER) of MPPM data in current frame,and BERDPSK is the bit-error rate (BER) of DBPSK or DQPSK data bitson top of the current MPPM frame. The MPPM BER is given by [16]

BER12

22 1

SER3MPPM

N

N MPPM≤− ( )

It should be noticed that in the case of incorrect detection of thecurrent MPPM frame, the DPSK data bits on top of current MPPMframe will be decoded incorrectly with probability 1/2 but in thecase of incorrect detection of the previous MPPM frame withcorrect detection of current MPPM frame, only the first q DPSKdata bits on top of current MPPM frame will be decoded in-correctly with probability 1/2. Noticing that SERMPPM

current=

SER SERMPPMprevious def

MPPM= , the last inequality can be simplified to

⎜ ⎟

⎡⎣⎢

⎛⎝

⎞⎠

⎤⎦⎥

N pN

p

qq

p

BER1

BER2

SER

1 SER SER2

BER

1 SER BER ,4

Hybrid MPPM MPPM

MPPM MPPM DPSK

MPPM DPSK

( )

( )

≤+

+

+ − −

+ −( )

To confirm that the last upper bound is tight, we obtain a lower boundof the BER of the proposed modulation techniques by considering thebest case scenario. That is, we assume that only the last position of the

A.E. Morra et al. / Optics Communications 357 (2015) 86–9490

n positions is incorrectly decoded whenever a current MPPM frame isincorrectly detected and incorrect detection of the previous MPPMframe does not affect the first q DPSK data bits on top of currentMPPM frame. This lower bound can be written as

⎡⎣⎢

⎤⎦⎥ 5N p

Nq

pBER 1 BER2

SER 1 SER BER ,Hybrid MPPM MPPM MPPM DPSK( )( )

≥+

+ + −

where SERMPPM is given by [17] with slight modifications:

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎛⎝⎜⎜

⎞⎠⎟⎟⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎡

⎣⎢⎢⎢

⎛⎝⎜⎜

⎛⎝⎜⎜

⎞⎠⎟⎟⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟

⎤

⎦⎥⎥⎥

nm

M nl

pP

PP

PP

PP

pP dP

SER

1

1 11

,

6

MPPMl

M n

m

nmin

n

m

min

n

n m

min

n

M n l

min

n

l

min

n

l

l mm

min

n

1 1 0 1 2

1 2 0 2

0 2 0 2 2

( )

( )

∫∑ ∑σ

σ σ

σ σ σ

= −

× −

× − + −

( )

=

−

=

∞

− − −

+

where Pmin denotes the minimum power in symbol signal slots and n2σ

is the variance per dimension of complex zero-mean white Gaussiannoise in each polarization. p1(·) denotes the probability-density func-tion (pdf) of the power in a signal slot, which follows a noncentral chi-squared χ2 distribution with noncentrality parameter A MP n/av

2 = ,where Pav denotes the average received optical power. Similarly, p0(·)denotes the pdf of the power in a non-signal slot, which follows a χ2

distribution. In addition, P0(·) and P1(·) denote the corresponding cu-mulative distributions to p0 and p1, respectively. For any P 0min ≥ , p1(·)and p0(·) are given by

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟

pP P

Ae I P

A

pP

Pe

k

12

2 /2,

7

min

n

mink

P Ak min

n

min

n

min

n

kP

k

1 2 2

/4 1/2/2

/2 1 2

0 2

2

/2 1/2

/2

min n

min n

2 2

2

σ σ

σσ

Γ

=

=( ) ( )

σ

σ

−−( + )

−

−−

respectively, where Ic(·) is the cth order modified Bessel function of thefirst kind, and k is the number of degrees of freedom, where k¼4 in anon-polarized receiver and k¼2 in a polarized receiver. Next, BERDPSKcan be found in [2] with slight modifications. For the case of DBPSK,we have

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪⎡⎣⎢⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎥

⎡

⎣⎢⎢

⎤

⎦⎥⎥

⎡

⎣⎢⎢

⎤

⎦⎥⎥

8

e

eMn

P

BER

12

for a polarized receiver,

12

18

for a non polarized receiver.

DBPSK

Mn

Pav

n

Mn

Pav

n av

n

2 2

2 22

( )

( )( )σ

=

+ −

σ

σ

−

−

It is worth citing here the BER of traditional DBPSK [2]:

⎧

⎨⎪⎪

⎩⎪⎪

⎛⎝⎜⎜

⎞⎠⎟⎟

e

eP

BER

12

for a polarized receiver,

12

18

for a nonpolarized receiver. 9

DBPSKtraditional

P

P av

n

/2

/22

av n

av n

2

2

σ

=+

− ( )

σ

σ

−

−

While, for the case of DQPSK, we have [2]

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪ ⎛⎝⎜

⎞⎠⎟ 10

Q a b e I ab

Q a b e I ab

I abe

ba

ab

BER

,12

for a polarized receiver,

,12

8for a non polarized receiver,

DQPSK

a b

a b

a b

2 2 /20

2 2 /20

1 2 2 /2

( )

=

( ) − ( )

( ) − ( )

+( )

− −

−( + )

−( + )

−( + )

where Q ,(· ·) is the Marcum Q function,

⎧

⎨⎪⎪

⎩⎪⎪

a

P M

n

P

21 1/2 for hybrid receiver,

21 1/2 for traditional receiver,

11

av

n

av

n

2

2

σ

σ

=

( − )

( − )( )

and

⎧

⎨⎪⎪

⎩⎪⎪

b

P M

n

P

21 1/2 for hybrid receiver,

21 1/2 for traditional receiver.

12

av

n

av

n

2

2

σ

σ

=

( + )

( + )( )

4. Numerical results

In this section we compare between the performance of po-larized systems adopting the proposed hybrid modulation tech-niques and that adopting traditional DBPSK, DQPSK, and MPPMtechniques. Our comparisons are made under the same averagereceived optical signal-to-noise ratio for both the proposed andthe traditional systems. The average received optical signal-to-noise ratio (OSNRav) is given by [2]

⎧

⎨⎪⎪

⎩⎪⎪

OSNR

P PS B

P PS B

2for a polarized receiver,

4 2for a non polarized receiver,

13

av

av

n

av

n o

av

n

av

n o

2

2

s

s

σ

σ

=

=

= −( )

where Snsis the spectral density of the received spontaneous

emission per polarization and Bo is the optical bandwidth of thereceived optical filter. In addition, all systems under comparisonsare assumed to have the same transmission data rate Rb. Fur-thermore, we assume that all systems have the same receiverbandwidth, except for traditional DQPSK systems (because thecomparison with traditional DQPSK systems cannot be made un-der the same Rb and receiver bandwidth simultaneously). Thus, weassume that traditional DQPSK system has the same Rb but half thereceiver bandwidth of other systems under comparison. Thismight lead to different frame parameters (n and M) in order to beable to satisfy these conditions:

⎧

⎨

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

RM

p

M

1for traditional DBPSK and DQPSK,

logfor traditional MPPM system,

logfor proposed hybrid systems,

14

b

Mn

Mn

2

2

( )

( )

τ

τ

τ

=⌊ ⌋

⌊ ⌋ +

( )

where the pulsewidth τ is held fixed to keep the above constrainton the receiver bandwidth.

To verify that the upper bound is tight, we plot both the lowerand the upper bounds for the proposed DBPSK–MPPM system inFig. 7 where M¼22 and n¼6. One can notice that the lower andthe upper bounds are very close to each other. This emphasizesthat the upper bound is tight to the exact BER expression. There-fore, all the following results are obtained using the BER upperbound expression in Eq. (4).

In Figs. 7 and 8 we plot the bit-error rates (BERs) of proposedhybrid DPSK–MPPM and traditional DPSK systems versus averagereceived optical signal-to-noise ratio. Of course n should be increasedby increasing M in order to keep the constraint on transmission rate

5 6 7 8 9 10 11 12 13 14 1510−12

10−10

10−8

10−6

10−4

10−2

100

OSNRav in dB

Bit−error rate (BER)

Fig. 7. Average bit-error rate versus average received optical signal-to-noise ratiofor both proposed DBPSK–MPPM and traditional DBPSK systems.

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2010−12

10−10

10−8

10−6

10−4

10−2

100

OSNRav in dB

Bit−error rate (BER)

Hybrid DQPSK−MPPM (M=8 n=2)Hybrid DQPSK−MPPM (M=14 n=3)Hybrid DQPSK−MPPM (M=20 n=4)Polarized Traditional DBPSKPolarized Traditional DQPSK

Fig. 8. Average bit-error rate versus average received optical signal-to-noise ratio forproposed DQPSK–MPPM system, traditional DBPSK, and traditional DQPSK systems.

10 15 20 25 300.5

1

1.5

2

2.5

3

M

OSNRav improvement over DBPSK in dB Hybrid DBPSK−MPPM

Hybrid DQPSK−MPPM

Fig. 9. Proposed systems receiver sensitivity improvement over a traditionalDBPSK system at BER 10 9= − .

A.E. Morra et al. / Optics Communications 357 (2015) 86–94 91

fixed. It can be seen from the figures that the performance of thehybrid systems improves as M increases. Indeed, the energy efficiencyof the systems improves by increasing M.

Also, it can be seen that the proposed systems perform better thanthe corresponding traditional DBPSK systems. Specifically from Fig. 7,for the proposed DBPSK–MPPM systemwithM¼22 and n¼6, there isan improvement of about 1.8 dB at BER 10 9= − when compared topolarized DBPSK system. Also it can be seen from Fig. 8 that for theproposed DQPSK–MPPM system with M¼20 and n¼4, there is animprovement of about 2.4 dB at BER 10 9= − when compared to thepolarized DBPSK system.

The reason behind this improvement can be explained as fol-lows. In the case of transmitting the same data rate at the samebandwidth and average received optical signal-to-noise ratio, hy-brid systems have higher peak power per slot as compared tocorresponding traditional DBPSK systems. This leads to a highersignal-to-noise ratio and improved BER. It should also be noticedfrom Fig. 8 that the proposed DQPSK–MPPM system outperformstraditional DQPSK system but under the condition that traditionalDQPSK system receiver bandwidth is half the receiver bandwidthof proposed DQPSK–MPPM system.

Although traditional DBPSK system outperforms traditional DQPSKsystem [2], on the contrary it can be seen from Figs. 7 and 8 that the

proposed DQPSK–MPPM system performs better than the proposedDBPSK–MPPM system. Specifically we notice that there is an im-provement of about 1.6 dB at BER 10 3= − for the proposed DQPSK–MPPM system (of M¼8 and n¼2) when compared with DBPSK–MPPM system (of M¼8 and n¼3). The reason behind this improve-ment is because hybrid DQPSK–MPPM system has higher peak powerper slot as compared to corresponding DBPSK–MPPM system in thecase of transmitting the same data rate at the same bandwidth andaverage received optical signal-to-noise ratio. But this improvement isreduced to 0.5 dB at BER 10 9= − when increasing the average receivedoptical signal-to-noise ratio. The reason behind this improvement re-duction is because the influence of noise is reduced by increasingaverage received optical signal-to-noise ratio until a certain point.After this point, the situation reverses and becomes similar to tradi-tional systems; DBPSK–MPPM system performs better than DQPSK–MPPM system.

Fig. 9 shows the receiver sensitivity improvement of the pro-posed systems over traditional DBPSK system at BER 10 9= − as afunction of M, in the case of transmitting the same data rate at thesame bandwidth. For all the values of M, the proposed systemssurpass the traditional DBPSK system. Clearly, the improvementincreases gradually with increasing M, until reaching its saturationat M¼18 for proposed DBPSK–MPPM system and M¼20 for pro-posed DQPSK–MPPM system.

In Figs. 10 and 11, we plot the bit-error rates of proposed hybridand traditional MPPM systems versus average received optical signal-to-noise ratio. It can be seen from the figures that, under the aboveconditions, the hybrid systems perform better than correspondingtraditional MPPM systems. Specifically, from Fig. 10 we notice thatthere is an improvement of about 2.2 dB at BER 10 9= − for hybridDBPSK–MPPM system (of M¼16 and n¼3) when compared withtraditional MPPM system (ofM¼16 and n¼5). From Fig. 11, we noticethat there is an improvement of about 1.5 dB at BER 10 9= − for hybridDQPSK–MPPM system (of M¼36 and n¼3) when compared withtraditional MPPM system (of M¼36 and n¼5). Again, the aforemen-tioned improvements in the receiver sensitivity when transmitting thesame data rate at the same bandwidth and average received opticalsignal-to-noise ratio is because the hybrid systems have a higher peakpower per slot when compared to traditional MPPM system.

It is worth noticing that our proposed systems outperform tradi-tional systems at BER 10 3= − , where the forward-error correction(FEC) schemes are commonly used. Specifically from Fig. 7, for theproposed DBPSK–MPPM system with M¼22 and n¼6, there is an

5 6 7 8 9 1010−12

10−10

10−8

10−6

10−4

10−2

Bit−error rate (BER)

OSNRav in dB

Traditional MPPM (M=26 n=4)Traditional MPPM (M=36 n=5)Hybrid DQPSK−MPPM (M=22 n=2)Hybrid DQPSK−MPPM (M=36 n=3)

Fig. 11. Average bit-error rate versus average received optical signal-to-noise ratiofor both hybrid DQPSK–MPPM and traditional MPPM systems.

3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

log2(M)

Bandwidth−utilization efficiency

Hybrid DBPSK−MPPMHybrid DQPSK−MPPMTraditional MPPM

n=4

Fig. 12. Bandwidth-utilization efficiency as a function of Mlog2 .

0 100 200 300 400 5000

0.5

1

1.5

2

n

Bandwidth−utilization efficiency

Traditional MPPM

Hybrid DBPSK−MPPM

Hybrid DQPSK−MPPM

M=1024

Fig. 13. Bandwidth-utilization efficiency as a function of n.

5 6 7 8 9 10 11 12 13 14 1510−12

10−10

10−8

10−6

10−4

10−2

100

OSNRav in dB

Bit−error rate (BER)

Traditional MPPM (M=8 n=4)

Traditional MPPM (M=16 n=5)

Hybrid DBPSK−MPPM (M=8 n=2)

Hybrid DBPSK−MPPM (M=16 n=3)

Fig. 10. Average bit-error rate versus average received optical signal-to-noise ratiofor both hybrid DBPSK–MPPM and traditional MPPM systems.

A.E. Morra et al. / Optics Communications 357 (2015) 86–9492

improvement of about 0.5 dB at BER 10 3= − when compared to thepolarized DBPSK system. This improvement increases to about 1 dB atBER 10 4= − . Also it can be seen from Fig. 8 that for the proposedDQPSK–MPPM systemwithM¼20 and n¼4, there is an improvementof about 1.9 dB at BER 10 3= − when compared to the polarized DBPSKsystem. Although our proposed systems surpass traditional systems atFEC limit, our proposed systems perform very well at BER 10 9= −

without the need of FEC schemes as seen from Figs. 7, 8, 10, and 11.Clearly, without implementing FEC schemes, the proposed systemscould achieve the required BER.

It should be mentioned that although the proposed hybridsystems increase the peak power per slot, this increase would notresult in crossing the threshold of nonlinear effects in optical fi-bers. Specifically, from Figs. 7 and 10, for the proposed DBPSK–MPPM systems with M¼22 and n¼6 and with M¼16 and n¼3,the peak power levels are 1.9 dBm and 1.8 dBm, respectively atBER 10 9= − . That is, stimulated Brillouin scattering (SBS) thresholdof 2 dBm, which is the dominant nonlinear process, is not reached

by these peak power levels [18]. Practically, the SBS threshold canreach higher power values (between 5 and 10 dBm) by core sizevariations along the fiber and other inhomogeneities. As a result,the proposed system would not suffer from the nonlinear effects.

Another key performance indicator is the bandwidth-utilizationefficiency (BWUE). It can be defined as

⎧

⎨⎪⎪⎪

⎩⎪⎪⎪

⎢⎣⎢

⎥⎦⎥

⎢⎣ ⎥⎦BWUE

p

M

M

logfor proposed hybrid systems,

logfor traditional MPPM system.

15

Mn

Mn

2

2

( )

( )=

+

( )

In addition to sensitivity improvement over the traditional systems,the proposed systems would improve the bandwidth-utilization effi-ciency by carrying more bits in the same transmission time duration.In Fig. 12, we plot bandwidth-utilization efficiency versus Mlog2 un-der a fixed value of n¼4 for the proposed and traditional MPPMsystems. Clearly, increasing M results in a gradual decrease of band-width-utilization efficiency until reaching its saturation at large valuesof M. Also, in Fig. 13 we plot bandwidth-utilization efficiency versus n

A.E. Morra et al. / Optics Communications 357 (2015) 86–94 93

under a fixed value of M¼1024 for the proposed and traditionalMPPM systems. On the contrary, increasing nwould result in a gradualincrease of bandwidth-utilization efficiency.

It should be noticed from Figs. 12 and 13 that the proposed systemsfurther enhance the bandwidth-utilization efficiency of traditionalDBPSK BWUE 100%DBPSK( = ) under certain values of M and n andfurther enhance the bandwidth-utilization efficiency of MPPM sys-tems for all values of M and n. In order to reach the value of band-width-utilization efficiency of traditional DQPSK systemsBWUE 200%DQPSK( = ), hybrid DQPSK–MPPM systems need to use largevalues of M and n. That is, traditional DQPSK system is more band-width efficient than hybrid DQPSK–MPPM system. However, the re-ceiver of the latter is more sensitive than traditional DQPSK receiver.

Finally, we compare the performance of non-polarized pro-posed DBPSK–MPPM system with that of the hybrid polarization-division-multiplexed quadrature phase-shift keying-m-ary pulse-position modulation (PQ–mPPM) system [1,3] and with that of thehybrid BPSK–modified MPPM system [5]. The comparison is madeunder the same data rate for fixed bandwidth and received opticalsignal-to-noise ratio.

Practically, the optical bandwidth in typical measurements isequal to B 12.5 GHzref = , corresponding to 0.1 nm at 1550 nmcarrier wavelength [2,19,20]. That is, a traditional optical signal-to-noise ratio OSNRref is defined as

OSNRP

S B2 16ref

av

n refs

=( )

To convert the signal-to-noise ratio per bit (SNRb) used in [1,3] toOSNRref, the following relation is used [19,20]

OSNRRB

SNR2

,17

refb

refb=

( )

where Rb is the signal bit rate. In order to make a fair comparisonwith the results in [1,3], the optical bandwidth of the receivedoptical filter Bo is set equal to the signal bit rate Rb¼2.5 Gb/s, samevalue used in [1,3].

In Fig. 14 we plot the BER versus OSNRref for the proposed andPQ–mPPM systems. Although the PQ–16PPM system has higherpeak power than the proposed systems, it can be seen from Fig. 14that the proposed systems nearly have the same performance asthe PQ–16PPM system at the FEC limit of BER 10 3= − , however

−8 −6 −4 −2 0

10−8

10−6

10−4

10−2

OSNRref in dB

Bit−error rate (BER)

PQ−16PPMHybrid DBPSK−MPPM (M=8 n=1)Hybrid DBPSK−MPPM (M=16 n=2)Hybrid DBPSK−MPPM (M=18 n=2)

Fig. 14. Average bit-error rate versus OSNRref for both hybrid DBPSK–MPPM andPQ–16PPM systems.

the proposed systems perform better than the correspondingPQ–16PPM system at BER 10 9= − . Specifically, for the proposedDBPSK–MPPM system with M¼8 and n¼1, there is an improve-ment of about 1.7 dB at BER 10 9= − when compared to the PQ–16PPM system. The reason behind this improvement is that theDD-DBPSK receiver, which is used in the proposed system, sur-passes the polarization-multiplexed QPSK receiver, which is usedin the PQ–mPPM system [2,20]. Clearly, without implementing FECschemes, the proposed systems would achieve the required BER.Furthermore, our proposed systems are more bandwidth efficientthan PQ–mPPM system. It is worth mentioning that the proposedDBPSK–MPPM system with M¼8 and n¼1 has nearly the sameperformance as the proposed DBPSK–MPPM systems with M¼16and n¼2 and with M¼18 and n¼2 because all of these systemshave nearly the same peak power.

In Fig. 15, we plot the BER versus OSNRav for the proposed andhybrid BPSK–modified MPPM systems [5]. It can be seen from thefigure that there is a little improvement of about 0.7 dB at BER 10 9= −

of the hybrid BPSK–modified MPPM system over the correspondingproposed DBPSK–MPPM system. The higher peak power is not thereason for this improvement (as both systems have the same peakpower) but because coherent BPSK receiver, which is used in theBPSK–modified MPPM system, gives slightly better performance thanDD-DBPSK receiver, used in the proposed system. Furthermore, theproposed DBPSK–MPPM system has the same bandwidth-utilizationefficiency as that of the BPSK–modified MPPM system. However, theBPSK–modified MPPM system is less bandwidth efficient than that ofthe proposed DQPSK–MPPM system.

Not to mention that the receivers of the proposed systems aresimpler than those of the BPSK–modified MPPM and PQ–mPPMreceivers as the former are based on direct-detection technologies.However, a limitation that may be seen with the proposed DPSK–MPPM receiver is the need for a fast tunable time delay, whichincreases the complexity and cost of the demodulation processrelative to the traditional direct-detection DPSK receivers. Whilethis statement may be accurate for the fixed-rate DPSK receiver,the structure of variable-rate DPSK receiver cannot also dispensewith a programmable time-delay unit to accommodate differentkinds of data traffic [21] (yet in such a case ultrafast switching ofthe time delay is not a requirement).

2 3 4 5 6 7 8 9

10−8

10−6

10−4

10−2

OSNRav in dB

Bit−error rate (BER)

Hybrid 6−BPSK 22−PPMHybrid DBPSK−MPPM (M=22 n=6)

Fig. 15. Average bit-error rate versus average OSNR for both hybrid DBPSK–MPPMand BPSK–modified MPPM systems.

A.E. Morra et al. / Optics Communications 357 (2015) 86–9494

5. Conclusions

Hybrid DPSK–MPPM techniques have been proposed for opticalcommunication systems in order to increase the receiver sensi-tivity. Simple detection mechanisms, based on direct-detectionDPSK receivers with a novel ultrafast discrete delay unit, havebeen proposed and studied. The bit error rates of the proposedsystems have been derived and compared numerically to that ofcorresponding systems adopting traditional DPSK, and MPPMtechniques. In our derivation, the effect of optical amplifier noisehas been taken into account. The comparisons have been per-formed under the constraints of the same transmitted data rates,bandwidth, and average received optical signal-to-noise ratio. Inaddition, the bandwidth-utilization efficiencies for the proposedand the traditional systems are studied. It turned out that theproposed modulation techniques are more power efficient thantraditional ones and have improved BERs and receiver sensitivitiesand still improve the bandwidth-utilization efficiencies.

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