In this chapter we consider the use of coherent optical transmission systems using phase/amplitude modulation formats such as BPSK, QPSK and 16-QAM for the Line Signal (LS). In this case, the Line Signal (LS) cannot be detected with standard direct detection-based receiver but a coherent receiver must be used.

The remainder of this chapter is organized as follows: after an introduction on coherent receivers, we present the simulation results obtained for the same case study introduced in the previous chapter.

3.1 Coherent Detection

An important goal of a long-haul optical fiber system is to transmit the highest data throughput over the longest distance without signal regeneration. Given constraints on the bandwidth imposed by optical amplifiers and ultimately by the fiber itself, it is important to maximize spectral efficiency, measured in bit/s/Hz. But given constraints on signal power imposed by fiber nonlinearity, it is also important to maximize power (or Signal-to-Noise Ratio) efficiency, i.e., to minimize the required average transmitted energy per bit (or the required Signal-to-Noise Ratio per bit). Most current systems use binary modulation formats, such as On-Off Keying or Differential Phase-Shift Keying, which encode one bit per symbol. Given practical constraints on filters for Dense Wavelength-Division Multiplexing (DWDM), these are able to achieve spectral efficiencies of 0.8 bit/s/Hz per polarization. Spectral efficiency limits for various detection and modulation methods have been studied in the linear and nonlinear regimes. Non-Coherent Detection and differentially Coherent Detection offer good power efficiency only at low spectral efficiency, because they limit the degrees of

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freedom available for encoding of information. The most promising detection technique for achieving high spectral efficiency while maximizing power (or SNR) efficiency, is Coherent Detection with polarization multiplexing, as symbol decisions are made using the In-phase (I) and Quadrature (Q) signals in the two field polarizations, allowing information to be encoded in all the available degrees of freedom. When the outputs of an optoelectronic down converter are sampled at Nyquist rate, the digitized waveform retains full information of the electric field, which enables compensation of transmission impairments by Digital Signal Processing (DSP). A DSP-based receiver is highly advantageous because adaptive algorithms can be used to compensate time-varying transmission impairments. Advanced Forward Error-Correction coding can also be implemented. Moreover, digitized signals can be delayed, split and amplified without degradation in signal quality. DSP-based receivers are ubiquitous in Wireless and Digital Subscriber Line (DSL) systems at lower data rates. In such systems, computationally intensive techniques have been demonstrated, such as Orthogonal Frequency-Division Multiplexing (OFDM) with Multiple-Input-Multiple-Output (MIMO) transmission in a real-time 1 Gbit/s wireless link. Continued hardware improvements will enable deployment of DSP-based coherent optical systems in the next few years.

Experimental results in coherent optical communication have been promising. Kikuchi demonstrated polarization-multiplexed 4-ary quadrature-amplitude modulation (4-QAM) transmission at 40 Gbit/s with a channel bandwidth of 16 GHz (2.5 bit/s/Hz). This experiment used a high-speed sampling oscilloscope to record the output of a homodyne down converter. DSP was performed offline because of the unavailability of sufficiently fast processing hardware. The first demonstration of real-time coherent detection occurred in 2006, when an 800 Mbit/s 4-QAM signal was coherently detected using a receiver with 5-bit Analog-to-Digital Converters (ADC) followed by a Field Programmable Gate Array. In 2007, feed forward carrier recovery was demonstrated in

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real time for 4-QAM at 4.4 Gbit/s. Savory showed the feasibility of digitally compensating the Chromatic Dispersion (CD) in 6,400 km of Single Mode Fiber (SMF) without inline Dispersion Compensating Fiber (DCF), with only 1.2 dB Optical-Signal-to-Noise Ratio (OSNR) penalty at 42.8 Gbit/s. Coherent detection of large QAM constellations has also been demonstrated. For example, 16-ary transmission at 40 Gbit/s using an Amplitude-Phase-Shift Keying (APSK) format was shown by Sekine et al. In 2007, Hongo et al demonstrated 64-QAM transmission over 150 km of Dispersion-Shifted Fiber.

This Section provides an overview of detection and modulation methods, with emphasis on coherent detection. The paragraph is organized as follows: in a first part we review signal detection methods, including non-coherent, differentially coherent and coherent detection. We compare these techniques and the modulation formats they enable. In next section, we compare the Bit-Error Ratio (BER) performance of different modulation formats in the presence of additive white Gaussian noise (AWGN).

Notation

In this chapter, we represent optical signal and noise electric fields as complex-valued,

baseband quantities, which are denoted as Esubscipt

( )

t . In all subsequent sections,

photocurrents are represented as real pass-band signals as Isubscipt

( )

t . After we derive the

canonical model for a coherent receiver, we write all signals and noises as complex-valued baseband quantities, with the convention that the output of the optoelectronic down-converter is denoted by y , the transmitted symbol as x , the output of the linear

equalizer as _{!x , and the phase de-rotated output prior to symbol decisions as}ˆx. Signals

that occupy one polarization only are represented as scalars and are written in italics as shown; while dually polarized signals are denoted as vectors and are written in bold

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face, such as yk . Unless stated otherwise, we employ a linear

( )

x, y basis for

decomposing dually polarized signals.

3.1.1 Optical Detection Methods

3.1.1.1 Non-‐Coherent Detection a)

b)

Figure 3.1 Noncoherent receivers for (a) amplitude-‐shift modulation (ASK) and (b) binary frequency-‐shift keying (FSK).

In Non-Coherent Detection, a receiver computes decision variables based on a measurement of signal energy. An example of Non-Coherent Detection is direct

detection of On-Off Keying (OOK) using a simple photodiode (Figure 3.1(a)). To encode

more than one bit per symbol, multi-level Amplitude-Shift Keying (ASK), also known as Pulse-Amplitude Modulation, can be used. Another example of Non-Coherent Detection is Frequency-Shift Keying (FSK) with wide frequency separation between the

carriers. Figure 3.1(b) shows a Non-Coherent receiver for binary FSK.

The limitations of Non-Coherent detection are:

i. Detection based on energy measurement allows signals to encode only one

Degree Of Freedom (DOF) per polarization per carrier, reducing spectral efficiency and power efficiency;

ii. The loss of phase information during detection is an irreversible transformation

that prevents full equalization of linear channel impairments like CD and PMD by linear filters. Although Maximum-Likelihood Sequence Detection (MLSD) can be

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used to find the best estimate of the transmitted sequence given only a sequence of received intensities, the achievable performance is suboptimal compared with optical or electrical equalization making use of the full electric field.

3.1.1.2 Differentially Coherent Detection

a)

b)

Figure 3.2 Differentially coherent phase detection of (a) 2-‐DPSK (b) M-‐DPSK, M >2

In differentially coherent detection, a receiver computes decision variables based on a measurement of differential phase between the symbol of interest and one or more reference symbol(s). In Differential Phase-Shift Keying (DPSK), the phase reference is provided by the previous symbol; in Polarization-Shift Keying (PolSK), the phase reference is provided by the signal in the adjacent polarization. A binary DPSK receiver is shown in Figure 3.2(a). Its output photocurrent is:

IDPSK

( )

t = R⋅ℜ Es

( )

t E

*

t− Ts

(

)

{

}

(3.1)

where Es(t) is the received signal, R is the Responsivity of each photodiode, and Ts is

the symbol period. This receiver can also be used to detect Continuous-Phase Frequency-Shift Keying (CPFSK), as the delay interferometer is equivalent to a

delay-and-multiply demodulator. A receiver for M-ary DPSK, M > 2 , can similarly be

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IDPSK , i

( )

t = 1 2R⋅ℜ Es

( )

t E * t− Ts

(

)

{

}

(3.2) IDPSK , q

( )

t = 1 2R⋅ℑ Es

( )

t E * t− Ts

(

)

{

}

(3.3)

A key motivation for employing Differentially Coherent Detection is that binary DPSK

has 2.8 dB higher sensitivity than Non-Coherent OOK at a BER of 10−9. However, the

constraint that signal points can only differ in phase allows only one DOF per polarization per carrier, the same as Non-Coherent Detection. As the photocurrents in Equations (3.1) to (3.3) are not linear functions of the E-field, linear impairments, such as CD and PMD, also cannot be compensated fully in the electrical domain after photodetection. A more advanced detector for M-ary DPSK is the multichip DPSK receiver, which has multiple DPSK receivers arranged in parallel, each with a different

interferometer delay that is an integer multiple of Ts. Since a multichip receiver

compares the phase of the current symbol to a multiplicity of previous symbols, the extra information available to the detector enables higher sensitivity. In the limit that the number of parallel DPSK receivers is infinite, the performance of multi-chip DPSK approaches coherent PSK. In practice, the number of parallel DPSK receivers required for good performance needs to be equal to the impulse duration of the channel divided

by Ts. Although multi-chip DPSK does not require a Local Oscillator (LO) laser, carrier

synchronization and polarization control, the hardware complexity can be a significant disadvantage.

3.1.1.3 Hybrid of Non-‐Coherent and Differentially Coherent Detection

A hybrid of Non-Coherent and Differentially Coherent Detection can be used to recover information from both amplitude and differential phase. One such format is

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Polarization-Shift Keying (PolSK), which encodes information in the Stokes parameter. If we let

E_x

( )

t = a_x

( )

t ejφx( )t _{and E}

y

( )

t = ay

( )

t e

jφy( )t_{be the E-fields in the two polarizations, the}

Stokes parameters are S1= ax

2_{− a}

y

2

, S2= 2axaycos

( )

δ , and S3= 2axaysin

( )

δ , where

δ t

( )

=φx

( )

t −φy

( )

t . A PolSK receiver is shown in Figure 3.3. The phase noise tolerance of

PolSK is evident by examining S1 to S3. Firstly, S1 is independent of phase. Secondly,

S2 and S3 depend on the phase difference φx(t)−φy(t). As φx(t) and φy(t) are both

corrupted by the same phase noise of the transmitter (TX) laser, their arithmetic

difference δ(t) is free of phase noise. In practice, the phase noise immunity of PolSK is

limited by the bandwidth of the photodetectors. It has been shown that 8-PolSK can

tolerate laser line-widths as large as ΔυTb≈ 0.01, which is about 100 times greater than

the phase noise tolerance of coherent 8-QAM. This was a significant advantage in the early 1990s, when symbol rates were only in the low GHz range. In modern systems, symbol rates of tens of GHz, in conjunction with tunable laser having line widths

< 100kHz, has diminished the advantages of PolSK. Recent results have shown that feed

forward carrier synchronization enables coherent detection of 16-QAM at _ΔυTb∼ 10

−5_,

which is within the limits of current technology. As systems are increasingly driven by the need for high spectral efficiency, polarization-multiplexed QAM is likely to be more attractive because of its higher sensitivity.

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3.1.1.4 Coherent Detection

The most advanced detection method is coherent detection, where the receiver computes decision variables based on the recovery of the full electric field, which contains both amplitude and phase information. Coherent detection thus allows the greatest flexibility in modulation formats, as information can be encoded in amplitude and phase, or alternatively in both In-phase (I) and Quadrature (Q) components of a carrier. Coherent detection requires the receiver to have knowledge of the carrier phase, as the received signal is demodulated by a LO that serves as an absolute phase reference. Traditionally, carrier synchronization has been performed by a Phase-Locked Loop (PLL). Optical systems can use:

i. An optical PLL (OPLL) that synchronizes the frequency and phase of the LO

laser with the TX laser;

ii. An electrical PLL where down-conversion using a free-running LO laser is

followed by a second-stage demodulation by an analog or digital electrical VCO whose frequency and phase are synchronized.

Use of an electrical PLL can be advantageous in duplex systems, as the transceiver may use one laser as both TX and LO. PLLs are sensitive to propagation delay in the feedback path, and the delay requirement can be difficult to satisfy. Feed-Forward (FF) carrier synchronization overcomes this problem. In addition, as a FF synchronizer uses both past and future symbols to estimate the carrier phase, it can achieve better performance than a PLL which, as a feedback system, can only employ past symbols. Recently, DSP has enabled polarization alignment and carrier synchronization to be performed in software. A coherent transmission system and its canonical model are

shown in Figure 3.4. At the transmitter, Mach-Zehnder (MZ) Modulators encode data

symbols onto an optical carrier and perform pulse shaping. If polarization multiplexing is used, the TX laser output is split into two orthogonal polarization components, which

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are modulated separately and combined in a Polarization Beam Splitter (PBS). We can write the transmitted signal as:

(3.4)

Where _{is the symbol period,} _{is the average transmitted power,} is the pulse

shape (e.g., non-return-to-zero (NRZ) or return-to-zero (RZ)) with the normalization

, and are the frequency and phase noise of the TX laser, and

is a complex vector representing the kth transmitted symbol.

a)

b)

Figure 3.4. Coherent transmission system (a) implementation, (b) system model

Etx

( )

t = Etx, 1 E_{tx, 2} ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = Pt xkb t

(

− kTs

)

e j(ωst+φs( )t)

∑

T

_s

P

_t b t

( )

b t

( )

∫

2 dt= T_s

ω

_s φ_s

( )

t xk = x⎡⎣ 1, k, x2, k⎤⎦ T 2×1

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We assume that symbols have normalized energy: E x⎡⎣ ⎤⎦ =1. For single-polarization 2

transmission, we can set the unused polarization component x_{2, k} to zero.

The channel consists of NA spans of fiber, with inline amplification and DCF after each

span. In the absence of nonlinear effects, we can model the channel as a 2× 2 matrix:

h t

( )

= h11

( )

t h12

( )

t h₂₁

( )

t h₂₂

( )

t ⎡ ⎣ ⎢ ⎤ ⎦ ⎥↔F H11

( )

ω H12

( )

ω H₂₁

( )

ω H₂₂

( )

ω ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = H ω

( )

, (3.5)

Where hij

( )

t denote the response of the i th

output polarization due to an impulse applied at _jth input polarization of the fiber. The choice of reference polarizations at the transmitter and receiver is arbitrary. Equation (3.5) can describe CD, all orders of PMD, Polarization-Dependent Loss (PDL), optical filtering effects and sampling time error. In addition, a coherent optical system is corrupted by AWGN, which includes

i. Amplified spontaneous emission (ASE) from inline amplifiers;

ii. Receiver LO shot noise;

iii. Receiver thermal noise.

In the canonical transmission model, we model the cumulative effect of these noises by an equivalent noise source n t

( )

= n⎡⎣ ₁

( )

t ,n₂

( )

t ⎤⎦T referred to the input of the receiver. The E-field at the output of the fiber is E_s

( )

t = E⎡⎣ _{s, 1}

( )

t , E_{s, 2}

( )

t ⎤⎦T, where:

Es, l

( )

t = Pr xm, kclm

(

t− kTs

)

e j(ωst+φs( )t)+ E sp, l

( )

t m=1 2

∑

k

∑

(3.6)

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propagation loss, Pr= Pt, is the average received power, clm t( )= b t

( )

⊗ hlm

( )

t , is a

normalized pulse shape, and Esp, l

( )

t is ASE noise in the polarization. Assuming the NA

fiber spans are identical and all inline amplifiers have gain G and spontaneous emission factor nsp, the two-sided Power Spectral Density (PSD) of Esp, l

( )

t is

S_E

sp

( )

f = NAnsp!ωs

(

G−1

)

G W Hz

[

]

(3.7)

The first stage of a coherent receiver is a dual-polarization optoelectronic down-converter that recovers the baseband-modulated signal. In a digital implementation, the

analog outputs are low-pass filtered and sampled at 1 T = M KTs, where M K is a

rational oversampling ratio. Channel impairments can then be compensated digitally before symbol detection.

3.1.1.4.1 Single-‐Polarization Down-‐Converter

a) b)

Figure 3.5.Single-‐polarization down-‐converter employing a (a) heterodyne and (b) homodyne design.

We first consider a single-polarization down-converter, where the LO laser is aligned in

the lth polarization. Down-conversion from optical pass-band to electrical baseband can

be achieved in two ways:

i. In a homodyne receiver, the frequency of the LO laser is tuned to that of the TX

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ii. In a heterodyne receiver, the LO and TX lasers differ by an intermediate frequency (IF), and an electrical LO is used to downconvert the IF signal to baseband.

Both implementations are shown in Figure 3.5. Although we show the optical hybrids as 3

- dB fiber couplers, the same networks can be implemented in free-space optics using 50 50 beam-splitters. Since a beam-splitter has the same transfer function as a fiber coupler, there is no difference in their performances.

In the heterodyne down-converter of Figure 3.5(a), the optical frequency bands around

ωLO+ωIF and ωLO−ωIF both map to the same IF. In order to avoid DWDM crosstalk

and to avoid excess ASE from the unwanted image band, optical filtering is required before the down-converter. The output current of the balanced photodetector in Figure 3.5(a) is:

I_{het, l}

( )

t = R E

(

₁

( )

t 2− E₂

( )

t 2

)

= 2Rℑ E

{

_{s, l}

( )

t E_{LO, l}*

( )

_t

}

_{+ I}

sh, l

( )

t (3.8)

Where ELO, l

( )

t = PLO, le

j(ωLOt+φLO( )t)

is the E -field of the LO laser, and P_{LO, l}, ωLO and

φLO

( )

t are its power, frequency and phase noise. Ish, l

( )

t is the LO shot noise. Assuming

PLO≫ Ps, Ish, l

( )

t has a two-sided PSD of SIsh

( )

f = qRPLO A

2

Hz.A2/Hz.

Substituting Equation (3.6) into Equation (3.8), we get:

I_{het , l}

( )

t = 2R P_{LO, l} P_r⎡⎣y_li

( )

t sin

( )

ω_IFt + y_lq

( )

t cos

( )

ω_IFt ⎤⎦+ E_{sp, l}'

t

( )

{

}

+ Ish, l

( )

t (3.9)

where ωIF=ωs−ωLOis the IF, φ

( )

t =φs

( )

t −φLO

( )

t is the carrier phase, and yli(t) and

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yl 0(t)= xm, kclm

(

t− kTs

)

e iφ t( ) m=1 2

∑

k

∑

(3.10)

The term 2R PLO, rEsp, l

'

t

( )

in Equation (8) is sometimes called LO-spontaneous beat

noise, and Esp,l '

( )

_t _{= ℑ E} sp,l

( )

t e − j(ωLOt+φLO( )t)

{

}

has a two-sided PSD of 1 2SEsp

( )

f . It can

similarly be shown that the currents at the outputs of the balanced photodetectors in the homodyne down-converter (Figure 3.5(b)) are:

Ihom,l,i

( )

t = ℜ E1

( )

t 2 − E₂

( )

t 2

{

}

= R P_LO,l

(

P_ry_li

( )

t + E_sp,li'

( )

_t

)

_{+ I} sh,li

( )

t (3.11) Iho,l,q

( )

t = ℜ E3

( )

t 2 − E4

( )

t 2

{

}

= R PLO,l Prylq

( )

t + Esp,lq '

( )

_t

(

)

+ Ish,lq

( )

t (3.12) Where E_{sp, li}'

( )

_t _{and E} sp, lq

'

( )

_t _{are white noises with two-sided PSD of}1

2SEsp

( )

f ;Ish, li

( )

t

and Ish, lq

( )

t are white noises with two–sided PSD of

1

2SIsh

( )

f . Since it can be shown

that thermal noise is always negligible compared to shot noise and ASE noise, we have neglected this term in Equations (3.11) and (3.12). In long-haul systems, the PSD of LO-spontaneous beat noise is typically much larger than that of LO shot noise; such systems are thus ASE-limited. Conversely, unamplified systems do not have ASE, and are therefore LO shot-noise-limited. If one were to demodulate Equation (3.9) by an electrical LO at ωIF, as shown in Figure 3.5(a), the resulting baseband signals Ihet , l, i

( )

t

and Ihet , l, q

( )

t will be the same as Equations (3.11) and (3.12) for the homodyne

down-converter in Figure 3.5(b), with all noises having the same PSD’s. Hence, the heterodyne

and the two-quadrature homodyne down-converters have the same performance. A difference between heterodyne and homodyne down-conversion only occurs when the

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transmitted signal occupies one quadrature (e.g. 2-PSK) and the system is LO shot-noise- limited, as this enables the use of a single-quadrature homodyne down-converter that has the optical front-end of Figure 3.5(a), but has ω_s=ω_LO. Its output photocurrent its

2R P_{LO, l} P_ry_lq

( )

t + E_{sp, l}'

t

( )

⎡⎣ ⎤⎦+ Ish, l

( )

t . Compared to Equation (3.12), the signal term

is doubled (four times the power), while the shot noise power is only increased by two, thus yielding a sensitivity improvement of 3 dB compared to heterodyne or two-quadrature homodyne down-conversion. This case is not of practical interest in this thesis, however, as long haul systems are ASE-limited, not LO shot-noise-limited. Also, for good spectral and power efficiencies, modulation formats that encode information in both I and Q are preferred. Hence, there is no performance difference between a homodyne and a heterodyne down-converter provided optical filtering is used to reject image-band ASE for the heterodyne down-converter. Since the two down-converters in

Figure 3.5 ultimately recover the same baseband signals, we can combine Equations. (3.11)

and (3.12) and write a normalized, canonical equation for their outputs as:

yl(t)= xm, kclm

(

t− kTs

)

e iφ t( )_{+ n} l

( )

t m=1 2

∑

k

∑

(3.13)

Where nl

( )

t is complex white noise with a two-sided PSD of:

Snn

( )

f = N0= Ts γs (3.14)

Is the Signal-to-Noise Ratio (SNR) per symbol. The values of γs for homodyne and

heterodyne down-converters in different noise regimes are shown in Table 1. For the shot-noise limited regime using a heterodyne or two-quadrature homodyne

down-converter, γs is simply the number of detected photons per symbol. We note that

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baseband signals recovered in Figure 3.5. For the remainder of this thesis, it is understood that all complex arithmetic operations are ultimately implemented using these real and imaginary signals.

The advantages of heterodyne down-conversion are that it uses only one balanced photodetector and has a simpler optical hybrid. However, the photocurrent in Equation

(3.9) has a bandwidth of ωIF+ BW , where BW is the signal bandwidth (Figure 3.6(a)). To

avoid signal distortion caused by overlapping side lobes ωIF needs to be sufficiently

large. Typically,ωIF ≈ BW , thus a heterodyne down-converter requires a balanced

photodetector with at least twice the bandwidth of a homodyne down-converter, whose

output photocurrents in Equations (3.11) and (3.12) only have bandwidths of BW (Figure

3.6(b)). This extra bandwidth requirement is a major disadvantage. In addition, it is also

difficult to obtain electrical mixers with baseband bandwidth as large as the IF. A summary of homodyne and heterodyne receivers is given in Table 2. A comparison of carrier synchronization options is given in Table 3.

a) b)

Figure 3.6. Spectrum of a (a) heterodyne and (b) homodyne down-‐converter measured at the output of the balanced photodetector.

3.1.1.4.2 Dual-‐Polarization Down-‐Converter

In the single-polarization down-converter, the LO needed to be in the same polarization as the received signal. One-way to align the LO polarization with the received signal is

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with a Polarization Controller (PC). There are several drawbacks with this: first, the received polarization can be time-varying due to random birefringence, so polarization tracking is required. Secondly, PMD causes the received Stokes vector to be frequency-dependent. When a single-polarization receiver is used, frequency-selective fading occurs unless PMD is first compensated in the optical domain. Thirdly, a single-polarization receiver precludes the use of single-polarization multiplexing to double the spectral efficiency.

A dual-polarization down-converter is shown inside the receiver of Figure 3.4(a). The LO

laser is polarized at ₄₅! relative to the PBS, and the received signal is separately demodulated by each LO component using two single-polarization down-converters in parallel, each of which can be heterodyne or homodyne. The four outputs are the I and Q

of the two polarizations, which has the full information ofEs

( )

t . CD and PMD are linear

distortions that can be compensated quasi-exactly by a linear filter. The lossless transformation from the optical to the electrical domain also allows the receiver to emulate non-coherent and differentially coherent detection by nonlinear signal processing in the electrical domain (Figure 3.7). In long-haul transmission where ASE is

the dominant noise source, these receivers have the same performance as those in Figure

3.1, Figure 3.2 and Figure 3.3. A summary of the detection methods discussed in this section

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a) b)

c)

Figure 3.7.Emulating (a) direct detection, (b) 4-‐DPSK detection and (c) PolSK detection with optoelectronic down-‐ conversion followed by non-‐linear signal processing in the electronic domain. The signals Ex(t) and Ey(t) are the complex-‐valued analog outputs described by Equation(3.13) for each polarization. We note that in the case of the heterodyne down-‐converter, the non-‐ linear operations shown can be performed at the IF output(s) of the balanced photoreceiver.

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3.2 Simulation studies for Phase-‐Shift Keying (PSK)-‐modulated LSs.

This section shows the simulation setup and the simulation results when we consider a

LS with a BPSK and QPSK modulation.

3.2.1 BPSK Scenario Simulation Setup

The figure Figure 3.8 shows the VPI scheme used for the simulations.

Figure 3.8 VPI block diagram

Where the difference with the OOK simulation setup is only the LS transmitter: now we

consider the LS with a BPSK modulation. Figure 3.9 shows the implementation of BPSK

transmitter. The transmitter consists of laser source, followed by a lithium niobate dual-drive phase modulator. The modulator performs phase modulation (PM) and was dual-driven at twice the switching voltage by a non-return-to-zero (NRZ) data stream in a push-pull configuration and biased at the transmission null point. This method produced phase modulation with near-perfect 180 degrees phase shift. A digital “1” is represented by a phase change in the optical carrier between the consecutive data bits, while the signal optical power is always kept constant.

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Figure 3.9 Implementation of BPSK transmitter

3.2.2 BPSK Scenario Design Parameters

Table 3.1 and Table 3.2 show the parameters used for the simulations.

Transmitters Parameters

TX Type IQ_SD MZs

Line Signal Bit Rate 10Gbit/s

Line Signal Modulation Format BPSK

Monitor Signal Bit Rate 20Mbit/s

Monitor Signal Modulation Format OOK

Laser Emission Frequency 193.1 THz

Laser Average Power 1.0 mW

Low Pass Filter Transfer Function Off

MZs Insertion Loss 2.0 dB Extinction Ratio 35 dB _ DC V_π 3 V _ RF V_π 3 V

Mach-Zehnder Overmodulator Extinction Ratio 0.4dB

Optical Signal-to-Noise Ratio [2 24]÷

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Receiver Parameters

Local Oscillator Emission Frequency 193.1 THz

Local Oscillator Sample Rate 160 GHz

Local Oscillator Average Power 1.0 mW

Photodiode Responsivity 1.0 A/W

Photodiode Model PIN

Photodiode Dark Current 0 A

Photodiode Shot Noise ON

Low Pass Transfer Function Rectangular

Low Pass Bandwidth 0.75 10 Gb/s 7.5 GHz⋅ =

Table 3.2 BPSK receiver Parameters

3.2.3 BPSK Scenario Simulation Results

Figure 3.10. BER curves of the MS (@20 Mb/s) and of the LS (@10Gb/s) when it is simulated using different PRBS of

order N = 7, N = 8, N = 9 and N=17 respectively.Figure 3.10 shows the BER of the LS and Monitor Signal (MS) for the parameters shown in Table 3.1 and Table 3.2. The red line represents the

BER of the LS for a PRBS 217_{-1. The other curves represent the BER of the Monitor}

Signal (MS) when the PRBS order of the LS varies in the range [7, 8, 9, 17].

Differently from the OOK case, where the LS is modulated with BPSK, it is not necessary to use any coding technique for the LS. This can be simply explained by the fact that for BPSK, only the phase of the optical carrier is modulated, leaving the intensity unchanged. Since the OOK MS receiver is insensitive to phase variations, and the envelope of the LS constant, no LS encoding is needed. This is an important aspect since the use of line coding has a price in terms of effective bandwidth and spectrum efficiency.

Figure 3.11 shows the optical spectrum of the BPSK LS. Figure 3.12 shows the eye diagram

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Figure 3.10. BER curves of the MS (@20 Mb/s) and of the LS (@10Gb/s) when it is simulated using different PRBS of order N = 7, N = 8, N = 9 and N=17 respectively.

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Figure 3.12. Eye Diagram of MS when the LS is simulated using an uncoded PRBS of order N=7, N=8, N=9 and N=17 respectively.

Figure 3.13 shows the relation between the BER of MS and the BER of LS in this scenario.

Figure 3.13 BER of MS VS BER of LS

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3.2.4 QPSK Scenario Simulation Setup

The Figure 3.14 shows the VPI scheme used for the simulations.

The QPSK transmitter comprises continuous wave (CW) laser source, optical power splitter, two-phase modulators, optical phase shifter, an optical power combiner and a

clock modulator as shown in Figure 3.15. The optical signal from a CW laser source is split

into two portions. The phases of the signals, one of which is phase shifted by _{π 2} with

respect to the other, are encoded with two independent NRZ data streams at _{B 2} and

then recombined. The output signal is a regular QPSK signal. Then the signal is

remodulated with the clock synchronized frequency = B 2

(

)

with the data streams. The

resultant QPSK signal has an NRZ-like intensity waveform with all marks and 50% duty ratio, while the data are encoded in the optical phase of each NRZ pulse.

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Figure 3.15 QPSK transmitter configuration

Figure 3.16 shows the implementation of QPSK transmitter.

Figure 3.16 VPI implementation of QPSK transmitter

Roberto Proietti 5/14/14 7:59 AM

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3.2.5

QPSK Scenario Design Parameters

Table 3.3 and Table 3.4 show the parameters used for the QPSK scenario simulations.

Transmitter Parameters

LS Symbol Rate 10GB

LS Bit Rate 20Gb/s

LS Modulation Format QPSK

MS Bit Rate 20Mb/s

MS Modulation Format OOK

MZs Insertion Loss 2.0 dB Extinction Ratio 35 dB _ DC V_π _{3 V} _ RF V_π _{3 V}

Optical Signal-to-Noise Ratio [2 24]÷

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Receiver Parameters

Table 3.4 QPSK receiver parameters

3.2.6 QPSK Scenario Simulation Results

Based on the above study for BPSK, we can expect similar results and conclusion in the

case where the LS is QPSK modulated. Figure 3.17shows the BER of the LS and MS for

the parameters shown in Table 3.3 and in Table 3.4. The red line represents the BER of the

LS when a PRBS 217_{-1 is used. The other curves represent the BER of the MS when the}

PRBR order of the LS varies in the range [7, 8, 9, 17].

As for the BPSK case, since the photodiode is insensitive to phase modulation, also for QPSK it is not necessary to use any line coding technique. Figure 3.18 shows the eye diagram of the MS in this scenario.

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Figure 3.17. BER curves of the MS (@20 Mb/s) and of the LS (@10Gb/s) when it is simulated using different PRBS of order N = 7, N = 8, N = 9 and N=17 respectively.

Figure 3.18. Eye Diagram of MS when the LS is simulated using an uncoded PRBS of order N=7, N=8, N=9 and N=17 respectively.

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Figure 3.19 BER of MS VS BER of LS

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3.3 Simulation studies for Quadrature Amplitude Modulated

(QAM) LSs.

This section describes and shows the simulation results when we consider the LS with 16-QAM modulation format. Note that we do not consider 4-QAM format since it is equivalent to the QPSK case being 4-QAM equivalent to a QPSK signal rotated of π/4.

3.3.1 16-‐QAM Scenario Simulation Setup

The Figure 3.20 shows the VPI scheme used for the simulations.

In VPI is not present a transmitter that implements only the 16 QAM modulation format, but there is a universal transmitter intended for optical M-QAM M-PSK D-M-PSK C-M-QAM and arbitrary constellation signal generation using different transmitter architectures. This transmitter supports 2, 4, 16, 32, 64, 128, 256 QAM; 2, 4, 8, 16, 32, 64, 128, 256 PSK/DPSK/CQAM and arbitrary constellation formats. The mQAM transmitter generates an optical QAM signal using four different transmitter architectures: a pair of single drive MZMs (IQ_SD); pair of dual drive MZMs (IQ_DD); single dual drive MZM (SingleMZM_DD); sequential amplitude and phase modulators

(AM_PM), (Figure 3.21). The transmitter incorporates Mach-Zehnder modulators, a laser

source, a random number generator and a Coder Driver module performing bit sequence encoding and generating the driving signals for the selected transmitter architecture.

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Figure 3.21 Transmitter architectures available in mQAM transmitter

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3.3.2 16-‐QAM Scenario Design Parameters

Table 3.5 and Table 3.6 show the parameters used for the 16-QAM simulations.

Transmitter Parameters

TX Type IQ_SD (Pair of Single Drive MZs)

LS Symbol Rate 10 GBd

LS Bit Rate 40 Gbit/s

LS Modulation Format 16-QAM

MS Bit Rate 20 Mbit/s

MS Modulation Format OOK

MZs Insertion Loss 2.0 dB Extinction Ratio 35 dB _ DC V_π 3 V _ RF V_π 3 V

Optical Signal-to-Noise Ratio [2 - 24] dB

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Receiver Parameters

Table 3.6 16-‐QAM receiver parameter

3.3.3 16-‐QAM Scenario Simulations Results

Proceeding in a similar way as with the OOK, BPSK and QPSK modulation formats, we simulate the case where the LS is modulated with 16-QAM. Note that, differently from BPSK and QPSK, a 16-QAM modulated signal presents both phase and amplitude modulation. Therefore, without proper line-coding, it is unlikely to receive correctly the

Monitor Signal, for the same reasons explained in Chapter 2 for the OOK case. Figure 3.23

shows the BER of the LS and MS for the parameters shown in Table 3.5 and Table 3.6. The

red line represents the BER of the LS when a PRBS 217_{-1 is used. The blue, green and}

light blue curves represent the BER of the MS when the PRBS order of the LS is 7, 8, and 9 respectively. The purple curve represents the BER of the MS when the 8B/10B

line coding is applied to the PRBS 217_{-1 used for the LS.}

The Coder and Modulator Driver within the 16-QAM transmitter encode the input bit sequence for 16-QAM modulation format and generates the driving signals for the optical transmitter respectively. The transmitter is composed by a CW laser and a I/Q modulator based on the nested MZM structure including a pair of single drive MZMs

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(IQ_SD). In the 16-QAM modulation format, a logical symbol is transmitted using in-phase (I) and quadrature (Q) components of the optical signal. The set of points on the IQ plane corresponding to a whole set of logical symbols is a constellation. For each symbol, a region is defined on the IQ plane, so that, when a signal sample is received, a decision on the received symbol is made based on the region where the sample falls into. The driving signals for the modulators are generated as in-phase (I) and quadrature (Q) component signals. It is convenient to consider a pair of I and Q components as a complex symbol IQ = I + j ⋅Q . The initial bit sequence b is first divided into its odd (I) and even (Q) parts

Ij= b2⋅ j−1,Qj= b2⋅ j , and IQ symbols are formed as:

IQk 16−QAM ₌ 22−l ₂_{⋅ I} 2⋅ k−1( )+l−1

(

)

+ l=1 2

∑

22−l ₂_⋅Q 2⋅ k−1( )+l−1

(

)

l=1 2

∑

22₋₁ (3.15)

For that reason, the previous Matlab script used for encoding the LS in OOK case must be modified. Starting from two different PRBS (N=17) sequences, the script encodes these sequences separately, obtaining therefore two different encoded sequences completely independent of each other. Finally we apply the two encoded sequences on the in-phase and in-quadrature inputs of the 16-QAM coder. Unfortunately, differently from the OOK case, the 8B/10B coding does not seem to have any effect on the quality of the received MS, which is completely corrupted by the interference caused by the LS within the bandwidth of the MS receiver. This result is somehow expected since 8B/10B line coding is designed for a binary alphabet.

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Figure 3.23 BER curves of the MS (@20 Mb/s) and of the LS (@10GBd) when it is simulated using uncoded PRBSs of order N=7, N=8 and N=9 and when the LS is coded with the 8B/10B Code.

To overcome this issue, we tried then to decrease the bit rate of the MS and increase its Extinction Ratio. The outcomes of this analysis are reported in Figure 3.24Figure 3.25 Figure 3.26Figure 3.27.

Figure 3.24 BER curves of: a)MS (@20 Mb/s) and of LS (@10GBd) when it is simulated using the 8B10B Code and the E.R. is equal to 0.4, 0.6, 0.8, 1.0;

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Figure 3.25 MS (@10 Mb/s) and of LS (@10GBd) when it is simulated using the 8B10B Code and the E.R. is equal to 0.4, 0.6, 0.8, 1.0;

Figure 3.26 MS (@5 Mb/s) and of LS (@10GBd) when it is simulated using the 8B10B Code and the E.R. is equal to 0.4, 0.6, 0.8, 1.0;

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Figure 3.27 MS (@2 Mb/s) and of LS (@10GBd) when it is simulated using the 8B10B Code and the E.R. is equal to 0.4, 0.6, 0.8, 1.0;

The conclusion is that only by reducing the bit-rate of the Monitor Signal it is possible to improve the BER of the MS, even though the correlation between the two BER curves is much weaker compared to the other modulation formats. Looking at the above figures, it

seems that only the purple curve in Figure 3.26 can be used (this is obtained for 5Gb/s and

ER=0.8). In fact, while the blue curve in Figure 3.27 obtained for 2Mb/s and ER=0.4, does

not present an error floor like in the other cases, the blue and red curve are too far apart (six decades difference for OSNR = 10 dB). We tried then to raise a little the bit-rate of

the MS to see whether we could bring the two curves closer. Figure 3.28 shows the results.

The green curve obtained for 3Mb/s and ER=0.4 seems to represent the best result for a 10 Gb 16QAM-modulated LS.

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Figure 3.28. BER of MS @2Mb/s, @3Mb/s, @4Mb/s, @5Mb/s and BER of LS (@10GBd) when it is simulated using the 8B10B Code. The E.R. is equal to 0.4.

We also tried to use an ER smaller then 0.4 dB to see if we can bring the MS BER blue curve in Figure 3.28 closer to the LS BER curve, while still avoiding the error floor that

shows up as the bit-rate increases (see green BER curve in Figure 3.28 for 3 Mb/s and the

ER=0.4). The Figure 3.29 shows the results when we decrease the value of ER.

Figure 3.29 BER of MS @2Mb/s with an ER=0.4, ER=0.35, ER=0.30, ER=0.25, ER=0.20 and ER=0.15 and BER of LS (@10GBd) when it is simulated using the 8B10B Code.

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Now the purple curve obtained for 2Mb/s and ER=0.15 seems to represent the best result for a 10 Gb 16QAM-modulated LS. The relation between the BER curve of the MS and the BER curve of the LS is shown in Figure 3.30.

Figure 3.30 BER of supervisor signal @2Mb/s VS BER of LS @10GBd when it is simulated using the 8B10B Code. The value of Extinction Ratio is 0.15 dB

Finally, we show the eye diagram of the MS in this scenario (

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Figure 3.31 Eye Diagram of MS when the LS is simulated using a 8B/10B sequence; the MS bit-‐rate and the LS symbol-‐ rate are equal to 2Mb/s and 10Gb/s respectively; the ER=0.15.

Figure 3.32 Optical Spectrum of the 16-‐QAM Line Signal@10Gb/s; the in-‐phase and in-‐quadrature components of the 16-‐QAM signal coded with two different 8B10B sequences.

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Table 3.7 summarizes the optimum combination of the design parameters when the LS is modulated as a 16-QAM and we use a 8B/10B Code.

Optimum Design Parameters

Line Code 8B/10B

LS Modulation Format 16-QAM

LS Baud Rate 10GBd

LS Bit Rate 40Gbit/s

MS Modulation Format OOK

MS Bit Rate 2Mbit/s

Overmodulation Extinction Ratio 0.15 dB

Table 3.7 Optimum Design Parameters

3.4 Conclusions

In this chapter we presented the simulation results for the Impairments Monitoring Technique based on Overmodulation when the LS is modulated in phase and/or amplitude (i.e. BPSK, QPSK, 16-QAM). Differently from the OOK case, analyzed in Chapter 2, since the photodiode is insensitive to phase modulation, for the cases in which the LS is phase modulated (i.e. BPSK, QPSK, 8-PSK), it is not necessary to use any line coding technique. Vice versa, a line coding is still necessary for the amplitude and phase modulation, i.e. 16-QAM modulation format. In this case, the best coding for the implementation of the Impairments Monitoring Technique is the 8B/10B coding with a LS symbol rate equal to 10 GBd, a MS equal to 2 Mb/s and an Extinction Ratio of the overmodulation equal to 0.15 dB. The other line coding technique, i.e. 9B/10B, analyzed in Chapter 2, do not seem to be suitable for 16 QAM, probably because its capability to carve the spectrum at low frequency is not as effective as for 8B/10B coding and because, overall, those coding techniques are designed for binary signals and not for multilevel modulation formats. It would be interesting to explore the possibility

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to design a new coding technique tailored for multilevel modulation formats, but this goes beyond the scope of this thesis.

Table of Contents

Chapter 3

3 Coherent Detection Scenario

3.1

Coherent Detection

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3.1.1 Optical Detection Methods

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