Abstract

We review recent progresses on digital self-coherent detection of differential phase-shift keyed (DPSK) signal using orthogonal differential direct detection followed by high-speed analog-to-digital conversion and digital signal processing (DSP). Techniques such as data-aided multi-symbol phase estimation for receiver sensitivity enhancement, unified detection scheme for multi-level DPSK signals, and optical field reconstruction are described. The availability of signal field information brings the possibility to compensate for some linear and nonlinear transmission impairments through further DSP. An adaptive DSP algorithm for simultaneous electronic polarization de-multiplexing and polarization-mode dispersion compensation is also presented.

©2008 Optical Society of America

1. Introduction

Optical transmission system based on self-homodyne differential phase-shift keying (DPSK) [1–4] has emerged as an attractive vehicle for supporting high-speed optical transport networks by offering lower requirements on optical signal-to-noise ratio (OSNR) and higher tolerance to system impairments such as certain fiber nonlinear effects as compared to traditional on-off-keying (OOK) based systems. Multilevel DPSK formats such as differential quadrature phase-shift keying (DQPSK) additionally offer high spectral efficiency and high tolerance to chromatic dispersion (CD), polarization-mode dispersion (PMD), and optical filtering, particularly when polarization-division multiplexing (PMUX) is also applied. Self-homodyne DPSK signals are received by differential direct detection that does not need an optical local oscillator (OLO) as required in coherent detection [5–8]. To generate coherent gain without the actual presence of a physical OLO, self-coherent detection was recently proposed, based either optical signal processing [9–11] or digital signal processing (DSP) [12,13]. With the help of high-speed analog-to-digital conversion (ADC) and DSP following orthogonal differential direct detection, the phase and even the field of a received optical signal can be digitally reconstructed [12,13]. Adaptive equalization of transmission impairments such as nonlinear phase noise, CD, and PMD could then be subsequently performed, in a similar way as digital coherent detection [14–16]. Such DSP-assisted self-homodyne detection is herein referred to as digital self-coherent detection (DSCD). These new capabilities bring opportunities to make transport systems more versatile, flexible, and ultimately cost-effective. With advances in high-speed electronic circuits, digital coherent and self-coherent detections are expected to find a wide range of applications to meet the ever-increasing demand of capacity upgrade and cost reduction in future optical networks.

This paper is organized as follows. In Section 2, we describe the architecture of DSCD. Section 3 briefly discusses a data-aided multi-symbol phase estimation (MSPE) scheme for receiver sensitivity enhancement [17–19]. Section 4 presents the detection of multi-level DPSK signals [19]. The reconstruction of signal field and compensation of transmission impairments are discussed in Section 5. Section 6 presents a dual-polarization version of DSCD for electronic polarization de-multiplexing and PMD compensation (PMDC). A simple adaptive DSP algorithm for simultaneous electronic polarization de-multiplexing and PMDC is also presented. Section 7 concludes this paper.

 figure: Fig. 1.

Fig. 1. Schematic DSCD architecture based on orthogonal differential direct-detection followed by ADC and DSP. OA: optical pre-amplifier; OF: optical filter; ODI: optical delay interferometer; BD: balanced detector; ADC: analog-to-digital converter.

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2. Architecture of digital self-coherent detection

A schematic DSCD architecture is shown in Fig. 1. The optical complexity of the DSCD is similar to that of conventional direct-detection for differential quadrature phase-shift keying (DQPSK). The received signal, r(t)=|r(t)|exp[j·ϕ(t)], is first split into two branches that are connected to a pair of optical delay interferometers (ODIs) with orthogonal phase offsets θ and θ-π/2, where θ is an arbitrary phase value. Note that the phase orthogonality is assumed to be guaranteed, e.g., via the design reported in Ref. [20]. This simplifies the control of the pair of ODIs to a single phase control. The delay in each of the ODI, τ, is set to be approximately T/sps, where T is the signal symbol period and sps is the number of samples per symbol of the analog-to-digital converters (ADCs) that convert the two detected analog signal waveforms, referred to as the I and Q components, to digitized waveforms uI(t) and uQ(t), which follow

u(t)=uI(t)+j·uQ(t)=ej·θr(t)·r*(tτ).

In the special case with sps=1, the delay in the orthogonal ODI pair equals to the symbol period, and the I and Q decision variables for an m-ary DPSK signal can be directly obtained by setting θ=π/m, as to be discussed later. Any demodulator phase error ϕe=θ-π/m can be readily compensated by using the following simple electronic demodulator error compensation (EDEC) process [21]

u(t)ej·ϕeu(t).

3. Receiver sensitivity enhancement via data-aided MSPE

There is a well-known differential-detection penalty in receiver sensitivity for DPSK as compared to PSK. This penalty can be substantially reduced by using a data-aided MSPE that utilizes the previously recovered data symbols to recursively extract a new phase reference that is more accurate than that provided by the immediate past symbol alone, and its analog implementations have been proposed for optical DQPSK [17], DQPSK/ASK [18], and m-ary DPSK [19]. The MSPE concept was recently extended to the digital domain in Refs. [19] and [21]. An improved complex decision variable for m-ary DPSK can be written as [19]

x(n)=u(n)+p=1N{wpejpπ/mu(n)q=1p[u(nq)·ejΔϕ(nq)]}

where u(n) is the directly detected complex decision variable for the n-th symbol, m is the number of phase states of the m-ary DPSK signal, N is the number of past decisions used in the MSPE process, w is a forgetting factor, and Δϕ(n-q)=ϕ(n-q)-ϕ(n-q-1) is the optical phase difference between the (n-q)-th and the (n-q-1)-th symbols, which can be estimated based on the past decisions. For optical DQPSK, using recovered I and Q data tributaries, cI and cQ, we have [19]

exp[j·Δϕ(n)]=cI(n)cQ(n)¯·(1)cI(n)¯+j·cI(n)cQ(n)·(1)cI(n)¯,

where ⊕ denotes XOR logic operation.

One advantage of the digital implementation is that w can be conveniently set to 1, and N can be small (e.g., <5) to obtain most of the sensitivity enhancement [19]. The computational complexity of the data-aided MSPE, in terms of the number of complex multiplications and additions, increases roughly linearly with N. Note that in digital coherent detection, carrier phase estimation, instead of the MSPE, is needed [8,22,23].

 figure: Fig. 2.

Fig. 2. Measured BER performance of the 40-Gb/s DQPSK signal received with and without the data-aided MSPE [21].

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In a recent 40-Gb/s DQPSK experiment with offline DSP, the benefits of the MSPE and EDEC were confirmed. Figure 2 shows the BER performance with the data-aided MSPE activated in both back-to-back and nonlinear transmission configurations [21]. At BER=10-3, the MSPE improves the back-to-back receiver sensitivity by 0.5 dB and 1 dB with N=1 and N=3, respectively. The forgetting factor w was set to 1. The performance difference between 215-1 and 27-1 patterns is negligible. The achieved back-to-back sensitivity is -41.5 dBm for BER=10-3, which is close to that obtained with coherent-detection QPSK (-42 dBm for BER=10-3) [8]. After transmission over the 320-km fiber link, the signal performance was severely degraded by nonlinear phase noise and polarization-dependent frequency shift (PDFS) of the demodulator. Remarkably, with the combined use of EDEC and MSPE, the required OSNR for BER=10-3 is reduced by 3.2 dB, indicating the improved performance of DSCD over conventional differential direct detection that uses binary decision circuitries.

It is worth mentioning that the MSPE scheme can be applied to advanced modulation formats that involve simultaneous differential-phase and amplitude modulation, such as DQPSK/ASK [18]. For quadrature amplitude modulation (QAM), such as 16-QAM, coherent detection, rather than differential detection, is usually used. In digital coherent detection, the decision-feedback aided carrier phase estimation [22] is effectively equivalent to the data-aided MSPE used here for DSCD.

4. Detection of m-ary DPSK

The DSCD can be used to receive high spectral-efficiency m-ary DPSK signals [19]. An mary DPSK signal has log2(m) binary data tributaries that are usually obtained from m/2 decision variables associated with m/4 ODI pairs having the following orthogonal phase offsets, (πm,πmπ2),(3πm,3πmπ2),,((m21)πm,πm) . With DSP, the last (m/2-2) decision variables can be derived by linear combinations of the first two decision variables, uI and uQ. This dramatically reduces the optical complexity associated with the detection of m-ary DPSK. The decision variables associated with phase offset πp/m (p=3,5,…,m/2-1), can be expressed as

v(πpm)=cos(p1mπ)uIsin(p1mπ)uQ.

Similarly, we can express their orthogonal counterparts as

v(πpmπ2)=sin(p1mπ)uI+cos(p1mπ)uQ.

The data tributaries of an m-ary DPSK signal can then be retrieved by [19].

c1=cI=[u(πm)>0],c2=cQ=[u(πmπ2)>0],
c3=[u(πm+π4)>0][u(πmπ4)>0],
clog2(m)=[u(3mπ)>0][u(7mπ)>0][u(m21mπ)>0]
    [u(3mππ2)>0][u(7mπ2)>0][u(m21mππ2)>0].

When the data-aided MSPE is applied, uI and uQ need to be replaced with their corresponding improved decision variables. In effect, the complex decision variable u(n) or x(n) contains complete information on the differential phase between adjacent symbols, and is sufficient statistic, allowing to derive all the required decision variables. Note that a similar approach based on analog signal processing, rather than DSP, was reported in Ref. [9]. The above formulas form the basis of a simple yet universal DSCD receiver platform for m-ary DPSK using only one pair of orthogonal demodulators as shown in Fig. 1.

5. Reconstruction of signal optical field and compensation of transmission impairments

5.1 Field reconstruction principle

The optical phase difference between adjacent sampling locations can be obtained from

ej·[ϕ(t)ϕ(tτ)]=u(t)ej·θu(t)ej·θ.

With the differential phase information being available, a digital representation of the received signal field can be obtained by

r(t0+n·τ)=r(t0+n·τ)ej·ϕ(t0)m=1nej·Δϕ(t0+m·τ),

where t0 is an arbitrary reference time, ϕ(t0) is a reference phase that can be set to 0, and the amplitude of the receiver signal can be obtained by an additional intensity detection branch [12] or approximated as below [13]

r(t0+n·τ)u(t0+n·τ)·u(t0+n·τ+τ)14.

We note, however, that care needs to be taken at sampling locations where the signal amplitude is close to zero, particularly when the sampling resolution is limited [12,13]. In addition, the required digitization resolution is higher in DSCD than in digital coherent receiver.

When the inter-symbol interference caused by distortions such as dispersion and PMD is reasonably small, synchronous sampling with sps=1 may be used and the signal amplitude may be approximated as a constant. Note that DSCD can be designed to be polarization-independent to readily receive a single-polarization signal in an arbitrary polarization state, while digital coherent detection requires accurate polarization alignment between the signal and the OLO or polarization diversity. Once the received optical signal field is digitally available, advanced signal processing techniques, similar to those used in digital coherent receivers, may be applied to mitigate transmission impairments.

5.2 Reconstruction of signal constellation

Recently, in a proof-of-concept experiment, DSCD was shown to accurately reconstruct the constellation diagrams of a 40-Gb/s DQPSK signal and a 60-Gb/s 8ary-DPSK signal, and reveal quality degradations due to amplified spontaneous emission (ASE) noise and fiber nonlinearity [24]. Figure 3 shows the experimental setup. A tunable laser locked at 1553 nm was used as the CW source. A 40-Gb/s return-to-zero (RZ) DQPSK signal was generated by modulating the CW source through a nested LiNbO3 Mach-Zehnder modulator (MZM) driven by the two 20-Gb/s data tributaries, followed by pulse carver, which is an x-cut LiNbO3 MZM driven sinusoidally at 20 GHz. The RZ pulses had a duty-cycle of 50%. The 20-Gb/s drive signals were generated by suitably multiplexing 10-Gb/s pseudo-random bit sequences (PRBSs) of length up to 215-1. To generate 8ary-DPSK, an additionally phase modulator, driven by another 20-Gb/s signal whose peak-to-peak amplitude is ~¼Vπ was used. The generated RZ-DQPSK signal or RZ-8ary-DPSK signal was then optionally transmitted over a transmission link consisting of a pre dispersion compensation module (DCM) providing -510 ps/nm dispersion, 4 80-km SSMF spans, each of which was followed by a 2-stage EDFA having a DCM inserted between its two stages, and post-DCM that compensated the overall dispersion to about zero. The span dispersion was under-compensated by 33, 37, 56, and 40 ps/nm (at 1550 nm), respectively, for the four spans. The span losses ranged from 18 to 21 dB. The power launched into each span can be varied for evaluating signal distortions under different conditions of ASE noise and fiber nonlinearity. After fiber transmission, the signal was sent into an optical pre-amplifier, followed by a bandpass filter with a 3-dB bandwidth of 0.3 nm.

 figure: Fig. 3.

Fig. 3. Experimental setup for reconstructing the constellation diagrams of a 40-Gb/s RZ-DQPSK and a 60-Gb/s RZ-8ary-DPSK signal using DSCD [24]. Inset shows simultaneously measured I/Q eye diagrams of a 40-Gb/s RZ-DQPSK signal. Time scale: 20 ps/division.

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The received signal was detected by a DSCD setup with offline DSP. The I/Q waveforms were then digitized at a sampling rate of 40 Gsamples/s using two 8-bit ADCs embedded within a Tektronix TDS6154C real-time oscilloscope. Care was taken to ensure that the two digitized waveforms were temporally aligned within 2 ps. The ADCs had low-pass filter characteristics with a cutoff frequency of about 15 GHz. The sampled I/Q waveforms were recorded and processed offline to reconstruct signal constellation diagrams under various link conditions.

From the digitized waveforms I(t) and Q(t), we can obtain the differential phase between adjacent symbols. The amplitude of the receiver signal can be obtained by an intensity detection branch [12] or approximated from I(t) and Q(t) [13]. Figure 4 shows the reconstructed differential-phase constellation diagrams of the 40-Gb/s DQPSK signal at different optical signal-to-noise ratios (OSNRs). Each constellation contains about 5,000 symbols. As expected, the variance of the differential-phase distribution, σ 2 Δϕ, increased with the decrease of OSNR. Figure 4 also shows the measured differential-phase variance σ 2 Δϕ as a function of OSNR. The dashed line is calculated using the following relation [24]

σΔϕ212NEB·(0.1nm·OSNR0.1nm)1,

where the noise effective bandwidth of the monitor NEB is determined by the optical bandpass filter to be 0.3 nm. The measured σ 2 Δϕ is in excellent agreement with the calculated one over an OSNR range from 10 dB to 25 dB. For OSNR>25 dB, the intrinsic differential-phase variance due to imperfect modulation starts to affect the measurement.

 figure: Fig. 4.

Fig. 4. Measured differential-phase constellation diagrams of the 40-Gb/s DQPSK signal at OSNR=35 dB (left) and 21 dB (center) and measured differential-phase variance as a function of OSNR (right). The dashed line is calculated.

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Figure 5 shows the reconstructed differential-phase constellations of the 40-Gb/s DQPSK signal after the 320-km SSMF transmission at different signal powers. The presence of the Gordon-Mollenauer nonlinear phase noise [25] becomes apparent at 6-dBm and 10-dBm signal powers, which corresponds to mean nonlinear phase shifts of 0.8 and 2 rad., respectively. Figure 5 also shows a reconstructed differential-phase constellation diagram of the 60-Gb/s RZ-8ary-DPSK signal. The modulator bandwidth limitation induced phase pattern dependence is more pronounced than in DQPSK, indicating that care needs to be taken in the modulation of multi-level DPSK formats.

 figure: Fig. 5.

Fig. 5. Measured differential-phase constellations of the 40-Gb/s DQPSK signal after transmission with 6 dBm (left) and 8 dBm (center) signal launch powers, and measured differential-phase constellation diagram of a 60-Gb/s 8ary-DPSK signal (right).

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5.3 Electronic dispersion compensation

With the availability of signal field, electronic dispersion compensation (EDC) may be performed to restore the original signal via, e.g., a multi-stage digital finite impulse response (FIR) filter that approximates the inverse function of the dispersion experienced by the signal during fiber transmission. EDC with DSCD was reported, both experimentally [12] and numerically [13], in typical optically repeated transmission links with the consideration of ASE noise and fiber nonlinearity. We note, however, that special care needs to be taken at sampling locations where the signal amplitude is close to zero [12,13]. For example, the effective sampling resolution needs to be sufficiently high.

5.4 Compensation of nonlinear phase noise

In optical fiber transmission, phase modulated signals may be degraded by the Gordon-Mollenauer nonlinear phase noise [25] resulting from the interaction between the self-phase modulation (SPM) and the ASE noise. It was found that the Gordon-Mollenauer nonlinear phase noise can be substantially compensated by a lumped post compensation process [26], which can be achieved by replacing the directly measured complex decision variable, u(n), with a compensated complex variable ν(n)

v(n)=u(n)·exp{j·12cNL·[P(n)P(n1)]},

where cNL is the average nonlinear phase shift experienced by the signal over the fiber transmission, P(n) is the normalized power of the n-th symbol, and the factor of ½ is for the 50% under-compensation that was found to be optimum in the lumped post-compensation scheme [26]. Post nonlinear phase noise compensation was recently demonstrated in digital coherent detection [27,28] and DSCD [29].

6. Dual-polarization digital self-coherent detection

6.1 Architecture

Polarization multiplexing provides a straightforward way to double spectral efficiency, relax transmitter/receiver bandwidth requirement, and increase signal tolerance to CD and PMD. To receive a polarization-multiplexed DPSK signal, polarization diversity is needed for DSCD. Figure 6 shows the schematic of a dual-polarization DSCD. The received optical signal is first split by a PBS into two orthogonally polarized components, which are demodulated by two orthogonal ODI pairs, and detected and sampled according to the single-polarization DSCD architecture described previously. Figure 6 also shows an alternative implementation where four PBSs are placed after a single orthogonal ODI pair. The optical fields of these two polarization components are then reconstructed, and used to recover the fields of the original polarization components.

 figure: Fig. 6.

Fig. 6. Schematic of two dual-polarization DSCD configurations for receiving a polarization-multiplexed DPSK signal using two orthogonal ODI pairs (upper) and one shared ODI pair (lower). PBS: polarization beam splitter.

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6.2 Simultaneous electronic polarization de-multiplexing and PMDC

Due to fiber birefringence, the two orthogonal polarization components of the optical signal as reconstructed at the receiver after fiber transmission are generally not the original polarization components of the polarization-multiplexed signal, so electronic polarization de-multiplexing (EPDMUX) is needed to recover the original polarization components. In addition, fiber birefringence induced signal polarization changes are usually time varying due to fluctuations in ambient temperature and mechanical stress, so adaptive EPDMUX is needed. In the presence of PMD, signal is further distorted. We discuss below how simultaneous EPDMUX and PMDC may be realized with DSCD.

Figure 7 illustrates the polarization evolution of a polarization-multiplexed optical signal in a typical fiber transmission link having PMD. Under the first-order PMD assumption, the two orthogonal polarization components reconstructed in the DSCD, Ex’ and Ey’, can be expressed as

[ExEy]=T·[ExEy]=P·R2·PMD(ω)·R1·[ExEy],

where Ex and Ey are the original polarization components at the transmitter, matrix T represents the polarization transformation of the fiber link, R1 is the rotation matrix associated with the projection of the original signal on the principle state of polarization (PSP) axes of the fiber PMD, R2 is the rotation matrix associated with the projection of the signal components along the PMD PSP axes of the fiber PMD on the polarization axes of the PBS(s) used in the receiver, PMD(ω) is the PMD matrix, and P is a matrix representing the addition phase delay between the two reconstructed fields after the polarization beam splitting at the receiver.

 figure: Fig. 7.

Fig. 7. Polarization evolution of an optical signal over a typical fiber transmission link having PMD. “‖” and “⊥” represent the orientations of the two PSP axes of the fiber PMD.

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Using the notations shown in Fig. 7, the above matrixes can be further expressed as

R1=[cos(θ1)sin(θ1)sin(θ1)cos(θ1)],PMD(Δf)=[100ej(2π·Δf·τDGD+δϕPMD)],
R2=[cos(θ2)sin(θ2)sin(θ2)cos(θ2)],P=[100ej·δϕPBS],

where θ 1 and θ 2 are rotation angles as illustrated in Fig. 7, τDGD is the PMD-induced differential group-delay (DGD) between the two PSP axes, δϕPMD is the phase delay caused by fiber PMD or birefringence, Δf is the frequency offset from the center frequency of the signal, and δϕPBS is the addition phase delay between the two reconstructed fields after the polarization beam splitting. When the polarization transformation matrix is known, the original signal polarization components can then be derived from the reconstructed polarization components through

[ExEy]=T1·[Ex(t)Ey(t)]=R11·PMD1(Δf)·R21·P1[ExEy].

Using Equations (14) and (15), the original signal polarization components can be expressed in the time domain as

[Ex(t)Ey(t)]=[cos(θ1)[cos(θ2)Ex(t)+sin(θ2)Ey(t)ej·δϕPBS]sin(θ1)[sin(θ2)Ex(t+τDGD)+cos(θ2)Ey(t+τDGD)ej·δϕPBS]ej·δϕPMDsin(θ1)[cos(θ2)Ex(t)+sin(θ2)Ey(t)ej·δϕPBS]+cos(θ1)[sin(θ2)Ex(t+τDGD)+cos(θ2)Ey(t+τDGD)ej·δϕPBS]ej·δϕPMD].

In general, there are five parameters that specify the polarization transformation matrix, θ 1, τDGD, δϕPMD, θ 2, δϕPBS, and they need to be determined. When PMD is sufficiently small, e.g., the PMD-induced DGD is much smaller than the signal symbol period, τDGD may be set to zero, leaving four parameters to be determined. Since these parameters are generally time varying, it is needed to find the values of these parameters dynamically. For high-speed optical signal, parallelization in signal processing is needed to lower the speed requirement for EPDMUX and electronic PMDC. Figure 8 shows a parallel DSP arrangement with a multiplexer and demultiplexer pair and multiple (M) processing units (PUs) each operating on a block-by-block basis. Overlap of data processed by adjacent PUs is needed to address the PMD induced inter-symbol interference.

 figure: Fig. 8.

Fig. 8. A parallel structure of the DSP circuit for EPDMUX and electronic PMDC.

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Figure 9 shows the block diagram of a PU. The PU inputs two blocks of samples that represent the two reconstructed optical fields, and outputs two blocks of samples that represent the original signal polarization components. The block size is N. Note that the field reconstruction process can share the same parallel structure used for EPDMUX and PMDC. Since the changes of parameters θ 1, τDGD, δϕPMD, and θ 2 are generally much slower than the signal symbol rate, a feed-forward path is used to estimate the best-guess values of these four parameters through a search process, and provide them to a real-time path. For example, the search process can be based on a global search that samples all possible sets of values of the matrix parameters, computes the corresponding Ex and Ey values for each set according to Eq. (16), and finds the set of best-guess values that give the minimized variances of |Ex(t)|2 and/or |Ey(t)|2 since each of the original signal polarization components is of DPSK format, which is has a constant amplitude characteristics. In effect, this is similar to the constant modulus algorithm (CMA) widely used in blind equalization of wireless DPSK signals [30], and recently used in digital self-coherent receivers [31]. The feed-forward path constantly updates the best-guess values at a speed that is sufficient to track the physical changes of these parameters (e.g., 10 kHz). To save computational effort, a new set of best guess values can be obtained from those that are the nearest neighbors (in a multi-dimensional space constructed by these parameters) of the preceding set of best guess values.

The real time path uses the best guess values provided by the feed-forward path, computes Ex and Ey values for each of a set of possible δϕPBS values, and finds the Ex and Ey values that gives the minimized variance of |Ex(t)|2 and/or |Ey(t)|2. Note that in DSCD, δϕPBS needs to be found in real time (on a block by block basis) since there is an uncertainty in the relative phase difference between the reconstructed signal fields Ex’ and Ey’, as indicated in Eq. (9). For digital coherent detection, the OLO provides a common phase reference for both polarization components, so δϕPBS can be advantageously estimated in the feed-forward path to save computational effort. Simultaneous EPDMUX and PMDC have recently been demonstrated with digital coherent detection through offline DSP [14–16].

 figure: Fig. 9.

Fig. 9. Block diagram of a processing unit for EPDMUX and electronic PMDC.

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7. Conclusion

We have reviewed recent progresses on digital self-coherent detection. Techniques such as data-aided multi-symbol phase estimation (MSPE) for receiver sensitivity enhancement, unified detection of multi-level DPSK signals, and optical field reconstruction have been briefly discussed. Adaptive DSP methods for the compensation of linear and nonlinear transmission impairments, PMD in particular, are also described. With real-time implementations on the horizon [32–34], digital self-coherent detection and digital coherent detection in general are expected to find interesting applications in future high-speed optical transport systems.

Acknowledgments

The authors wish to thank Y. K. Chen, A. R. Chraplyvy, C. R. Giles, and R. W. Tkach for their support.

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15. C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan; “Wavelength division multiplexing (WDM) and polarization mode dispersion (PMD) performance of a coherent 40Gbit/s dual-polarization quadrature phase shift keying (DP-QPSK) transceiver,” in Proceedings of Optical Fiber Communication Conference2007, Post-deadline Paper PDP16.

16. C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.

17. D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005). [CrossRef]  

18. X. Liu, “Receiver sensitivity improvement in optical DQPSK and DQPSK/ASK through data-aided multi-symbol phase estimation,” in Proceedings of European Conference on Optical Communications 2006, Paper We2.5.6, 2006. [CrossRef]  

19. X. Liu, “Generalized data-aided multi-symbol phase estimation for improving receiver sensitivity in direct-detection optical m-ary DPSK,” Opt. Express 15, 2927–2939 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-6-2927 [CrossRef]   [PubMed]  

20. C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005. [CrossRef]  

21. X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.4.5, 2006.

22. Y. Cai and A. N. Pilipetskii, “Comparison of Two Carrier Phase Estimation Schemes in Optical Coherent Detection Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OMP5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OMP5.

23. G. Goldfarb and G. Li, “BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing,” Opt. Express 14, 8043–8053 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8043 [CrossRef]   [PubMed]  

24. X. Liu and S. Chandrasekhar, “Measurement of constellation diagrams for 40-Gb/s DQPSK and 60-Gb/s 8ary-DPSK using sampled orthogonal differential direct-detection”, in Proceedings of European Conference on Optical Communications 2007, Paper 7.2.7, 2007

25. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. 15, 1351–1353 (1990). [CrossRef]   [PubMed]  

26. X. Liu, X. Wei, R. E. Slusher, and C. J. McKinstrie, “Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation,” Opt. Lett. 27, 1616–1618 (2002). [CrossRef]  

27. K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol 22, 779–783 (2004). [CrossRef]  

28. G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, “Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation,” in Proceedings of European Conference on Optical Communications 2006, Post-deadline Paper Th4.3.4, 2006.

29. N. Kikuchi, K. Mandai, and S. Sasaki, “Compensation of non-linear phase-shift in incoherent multilevel receiver with digital signal processing,” in Proceedings of European Conference on Optical Communications 2007, Paper 9.4.1, 2007..

30. D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28, 1867–1875 (1980). [CrossRef]  

31. S. J. Savory, V. Mikhailov, R. I. Killey, and P. Bayvei, “Digital coherent receivers for uncompensated 42.8Gb/s transmission over high PMD fibre,” in Proceedings of European Conference on Optical Communications 2007, Paper 10.4.1, 2007.

32. T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006). [CrossRef]  

33. A. Leven, N. Kaneda, A. Klein, U.-V. Koc, and Y.-K. Chen, “Real-time implementation of 4.4 Gbit/s QPSK intradyne receiver using field programmable gate array,” Electron. Lett. 42, 1421–1422 (2006). [CrossRef]  

34. A. Leven, N. Kaneda, U. -V. Koch, and Y. -K. Chen, “Coherent Receivers for Practical Optical Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThK4. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OThK4.

References

  • View by:

  1. R. C. Giles and K. C. Reichmann, “Optical self-homodyne DPSK transmission at 1-Gbit/s and 2-Gbit/s over 86km of fiber,” Electron. Lett. 23, 1180–1181 (1987).
    [Crossref]
  2. C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. 10, 281–293 (2004).
    [Crossref]
  3. A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23, 115–130 (2005).
    [Crossref]
  4. K.-P. Ho, Phase-modulated optical communication systems, (Springer, New York, 2005).
  5. F. Derr, “Coherent optical QPSK intradyne system: Concept and digital receiver realization,” J. Lightwave Technol. 10, 1290–1296 (1992).
    [Crossref]
  6. M. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16, 674–676 (2004).
    [Crossref]
  7. R. Noe, “PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing,” IEEE Photon. Technol. Lett. 17, 887–889 (2005).
    [Crossref]
  8. K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 11, 563–570 (2006).
  9. M. Nazarathy, Y. Yadin, M. Orenstein, Y. Lize, L. Christen, and A. Willner, “Enhanced Self-Coherent Optical Decision-Feedback-Aided Detection of Multi-Symbol M-DPSK/PolSK in Particular 8-DPSK/BPolSK at 40 Gbps,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JWA43. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-JWA43.
  10. M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Willner, “Self-coherent decision-feedback-directed 40 Gbps DQPSK Receiver,” IEEE Photon. Technol. Lett. 19, 828–839 (2007).
    [Crossref]
  11. M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Wilner, “Self-coherent optical detection of multisymbol differential phase-shift-keyed transmission,” J. Lightwave Technol. (accepted for publication).
  12. N. Kikuchi, K. Mandai, S. Sasaki, and K. Sekine, “Proposal and first experimental demonstration of digital incoherent optical field detector for chromatic dispersion compensation,” in Proceedings of European Conference on Optical Communications2006, Post-deadline Paper Th4.4.4.
  13. X. Liu and X. Wei, “Electronic Dispersion Compensation Based on Optical Field Reconstruction with Orthogonal Differential Direct-Detection and Digital Signal Processing,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OTuA6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OTuA6.
  14. G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, “Efficient Mitigation of Fiber Impairments in an Ultra-Long Haul Transmission of 40Gbit/s Polarization-Multiplexed Data, by Digital Processing in a Coherent Receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP17. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP17.
  15. C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan; “Wavelength division multiplexing (WDM) and polarization mode dispersion (PMD) performance of a coherent 40Gbit/s dual-polarization quadrature phase shift keying (DP-QPSK) transceiver,” in Proceedings of Optical Fiber Communication Conference2007, Post-deadline Paper PDP16.
  16. C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.
  17. D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005).
    [Crossref]
  18. X. Liu, “Receiver sensitivity improvement in optical DQPSK and DQPSK/ASK through data-aided multi-symbol phase estimation,” in Proceedings of European Conference on Optical Communications 2006, Paper We2.5.6, 2006.
    [Crossref]
  19. X. Liu, “Generalized data-aided multi-symbol phase estimation for improving receiver sensitivity in direct-detection optical m-ary DPSK,” Opt. Express 15, 2927–2939 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-6-2927
    [Crossref] [PubMed]
  20. C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005.
    [Crossref]
  21. X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.4.5, 2006.
  22. Y. Cai and A. N. Pilipetskii, “Comparison of Two Carrier Phase Estimation Schemes in Optical Coherent Detection Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OMP5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OMP5.
  23. G. Goldfarb and G. Li, “BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing,” Opt. Express 14, 8043–8053 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8043
    [Crossref] [PubMed]
  24. X. Liu and S. Chandrasekhar, “Measurement of constellation diagrams for 40-Gb/s DQPSK and 60-Gb/s 8ary-DPSK using sampled orthogonal differential direct-detection”, in Proceedings of European Conference on Optical Communications 2007, Paper 7.2.7, 2007
  25. J. P. Gordon and L. F. Mollenauer, “Phase noise in photonic communications systems using linear amplifiers,” Opt. Lett. 15, 1351–1353 (1990).
    [Crossref] [PubMed]
  26. X. Liu, X. Wei, R. E. Slusher, and C. J. McKinstrie, “Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation,” Opt. Lett. 27, 1616–1618 (2002).
    [Crossref]
  27. K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol 22, 779–783 (2004).
    [Crossref]
  28. G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, “Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation,” in Proceedings of European Conference on Optical Communications 2006, Post-deadline Paper Th4.3.4, 2006.
  29. N. Kikuchi, K. Mandai, and S. Sasaki, “Compensation of non-linear phase-shift in incoherent multilevel receiver with digital signal processing,” in Proceedings of European Conference on Optical Communications 2007, Paper 9.4.1, 2007..
  30. D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28, 1867–1875 (1980).
    [Crossref]
  31. S. J. Savory, V. Mikhailov, R. I. Killey, and P. Bayvei, “Digital coherent receivers for uncompensated 42.8Gb/s transmission over high PMD fibre,” in Proceedings of European Conference on Optical Communications 2007, Paper 10.4.1, 2007.
  32. T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
    [Crossref]
  33. A. Leven, N. Kaneda, A. Klein, U.-V. Koc, and Y.-K. Chen, “Real-time implementation of 4.4 Gbit/s QPSK intradyne receiver using field programmable gate array,” Electron. Lett. 42, 1421–1422 (2006).
    [Crossref]
  34. A. Leven, N. Kaneda, U. -V. Koch, and Y. -K. Chen, “Coherent Receivers for Practical Optical Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThK4. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OThK4.

2007 (2)

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Willner, “Self-coherent decision-feedback-directed 40 Gbps DQPSK Receiver,” IEEE Photon. Technol. Lett. 19, 828–839 (2007).
[Crossref]

X. Liu, “Generalized data-aided multi-symbol phase estimation for improving receiver sensitivity in direct-detection optical m-ary DPSK,” Opt. Express 15, 2927–2939 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-6-2927
[Crossref] [PubMed]

2006 (4)

G. Goldfarb and G. Li, “BER estimation of QPSK homodyne detection with carrier phase estimation using digital signal processing,” Opt. Express 14, 8043–8053 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8043
[Crossref] [PubMed]

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 11, 563–570 (2006).

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
[Crossref]

A. Leven, N. Kaneda, A. Klein, U.-V. Koc, and Y.-K. Chen, “Real-time implementation of 4.4 Gbit/s QPSK intradyne receiver using field programmable gate array,” Electron. Lett. 42, 1421–1422 (2006).
[Crossref]

2005 (2)

R. Noe, “PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing,” IEEE Photon. Technol. Lett. 17, 887–889 (2005).
[Crossref]

A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23, 115–130 (2005).
[Crossref]

2004 (3)

C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. 10, 281–293 (2004).
[Crossref]

M. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16, 674–676 (2004).
[Crossref]

K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol 22, 779–783 (2004).
[Crossref]

2002 (1)

1992 (1)

F. Derr, “Coherent optical QPSK intradyne system: Concept and digital receiver realization,” J. Lightwave Technol. 10, 1290–1296 (1992).
[Crossref]

1990 (1)

1987 (1)

R. C. Giles and K. C. Reichmann, “Optical self-homodyne DPSK transmission at 1-Gbit/s and 2-Gbit/s over 86km of fiber,” Electron. Lett. 23, 1180–1181 (1987).
[Crossref]

1980 (1)

D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28, 1867–1875 (1980).
[Crossref]

Achiam, Y.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
[Crossref]

Adamczyk, O.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
[Crossref]

Bayvei, P.

S. J. Savory, V. Mikhailov, R. I. Killey, and P. Bayvei, “Digital coherent receivers for uncompensated 42.8Gb/s transmission over high PMD fibre,” in Proceedings of European Conference on Optical Communications 2007, Paper 10.4.1, 2007.

Bhandare, S.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
[Crossref]

Bigo, S.

G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, “Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation,” in Proceedings of European Conference on Optical Communications 2006, Post-deadline Paper Th4.3.4, 2006.

G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, “Efficient Mitigation of Fiber Impairments in an Ultra-Long Haul Transmission of 40Gbit/s Polarization-Multiplexed Data, by Digital Processing in a Coherent Receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP17. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP17.

Buhl, L. L.

C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005.
[Crossref]

X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.4.5, 2006.

Cai, Y.

Y. Cai and A. N. Pilipetskii, “Comparison of Two Carrier Phase Estimation Schemes in Optical Coherent Detection Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OMP5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OMP5.

Calabro, S.

D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005).
[Crossref]

Cappuzzo, M. A.

C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005.
[Crossref]

Centanni, J.

X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.4.5, 2006.

Chandrasekhar, S.

X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.4.5, 2006.

X. Liu and S. Chandrasekhar, “Measurement of constellation diagrams for 40-Gb/s DQPSK and 60-Gb/s 8ary-DPSK using sampled orthogonal differential direct-detection”, in Proceedings of European Conference on Optical Communications 2007, Paper 7.2.7, 2007

Charlet, G.

G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, “Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation,” in Proceedings of European Conference on Optical Communications 2006, Post-deadline Paper Th4.3.4, 2006.

G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, “Efficient Mitigation of Fiber Impairments in an Ultra-Long Haul Transmission of 40Gbit/s Polarization-Multiplexed Data, by Digital Processing in a Coherent Receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP17. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP17.

Chen, E. Y.

C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005.
[Crossref]

Chen, Y. -K.

A. Leven, N. Kaneda, U. -V. Koch, and Y. -K. Chen, “Coherent Receivers for Practical Optical Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThK4. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OThK4.

Chen, Y.-K.

A. Leven, N. Kaneda, A. Klein, U.-V. Koc, and Y.-K. Chen, “Real-time implementation of 4.4 Gbit/s QPSK intradyne receiver using field programmable gate array,” Electron. Lett. 42, 1421–1422 (2006).
[Crossref]

Christen, L.

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Willner, “Self-coherent decision-feedback-directed 40 Gbps DQPSK Receiver,” IEEE Photon. Technol. Lett. 19, 828–839 (2007).
[Crossref]

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Wilner, “Self-coherent optical detection of multisymbol differential phase-shift-keyed transmission,” J. Lightwave Technol. (accepted for publication).

M. Nazarathy, Y. Yadin, M. Orenstein, Y. Lize, L. Christen, and A. Willner, “Enhanced Self-Coherent Optical Decision-Feedback-Aided Detection of Multi-Symbol M-DPSK/PolSK in Particular 8-DPSK/BPolSK at 40 Gbps,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JWA43. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-JWA43.

de Man, E.

C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.

de Waardt, H.

C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.

de Wardt, H.

D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005).
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Doerr, C. R.

C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005.
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X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.4.5, 2006.

Duthel, T.

C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.

Fludger, C. R.

C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.

Giles, R. C.

R. C. Giles and K. C. Reichmann, “Optical self-homodyne DPSK transmission at 1-Gbit/s and 2-Gbit/s over 86km of fiber,” Electron. Lett. 23, 1180–1181 (1987).
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Gill, D. M.

C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005.
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Gnauck, A. H.

A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23, 115–130 (2005).
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C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005.
[Crossref]

X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.4.5, 2006.

Godard, D. N.

D. N. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28, 1867–1875 (1980).
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Goldfarb, G.

Gomez, L. T.

C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005.
[Crossref]

Gordon, J. P.

Gottwald, E.

D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005).
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K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol 22, 779–783 (2004).
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Hoffmann, S.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
[Crossref]

Ibrahim, S.K.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
[Crossref]

Jansen, S.

D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005).
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Kahn, J. M.

K.-P. Ho and J. M. Kahn, “Electronic compensation technique to mitigate nonlinear phase noise,” J. Lightwave Technol 22, 779–783 (2004).
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Kaneda, N.

A. Leven, N. Kaneda, A. Klein, U.-V. Koc, and Y.-K. Chen, “Real-time implementation of 4.4 Gbit/s QPSK intradyne receiver using field programmable gate array,” Electron. Lett. 42, 1421–1422 (2006).
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A. Leven, N. Kaneda, U. -V. Koch, and Y. -K. Chen, “Coherent Receivers for Practical Optical Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThK4. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OThK4.

Kang, I.

X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.4.5, 2006.

Khoe, G.

D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005).
[Crossref]

Khoe, G. D.

C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.

Kikuchi, K.

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 11, 563–570 (2006).

Kikuchi, N.

N. Kikuchi, K. Mandai, S. Sasaki, and K. Sekine, “Proposal and first experimental demonstration of digital incoherent optical field detector for chromatic dispersion compensation,” in Proceedings of European Conference on Optical Communications2006, Post-deadline Paper Th4.4.4.

N. Kikuchi, K. Mandai, and S. Sasaki, “Compensation of non-linear phase-shift in incoherent multilevel receiver with digital signal processing,” in Proceedings of European Conference on Optical Communications 2007, Paper 9.4.1, 2007..

Killey, R. I.

S. J. Savory, V. Mikhailov, R. I. Killey, and P. Bayvei, “Digital coherent receivers for uncompensated 42.8Gb/s transmission over high PMD fibre,” in Proceedings of European Conference on Optical Communications 2007, Paper 10.4.1, 2007.

Kilper, D.

X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.4.5, 2006.

Klein, A.

A. Leven, N. Kaneda, A. Klein, U.-V. Koc, and Y.-K. Chen, “Real-time implementation of 4.4 Gbit/s QPSK intradyne receiver using field programmable gate array,” Electron. Lett. 42, 1421–1422 (2006).
[Crossref]

Koc, U.-V.

A. Leven, N. Kaneda, A. Klein, U.-V. Koc, and Y.-K. Chen, “Real-time implementation of 4.4 Gbit/s QPSK intradyne receiver using field programmable gate array,” Electron. Lett. 42, 1421–1422 (2006).
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Koch, U. -V.

A. Leven, N. Kaneda, U. -V. Koch, and Y. -K. Chen, “Coherent Receivers for Practical Optical Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThK4. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OThK4.

Laperle, C.

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan; “Wavelength division multiplexing (WDM) and polarization mode dispersion (PMD) performance of a coherent 40Gbit/s dual-polarization quadrature phase shift keying (DP-QPSK) transceiver,” in Proceedings of Optical Fiber Communication Conference2007, Post-deadline Paper PDP16.

Leven, A.

A. Leven, N. Kaneda, A. Klein, U.-V. Koc, and Y.-K. Chen, “Real-time implementation of 4.4 Gbit/s QPSK intradyne receiver using field programmable gate array,” Electron. Lett. 42, 1421–1422 (2006).
[Crossref]

A. Leven, N. Kaneda, U. -V. Koch, and Y. -K. Chen, “Coherent Receivers for Practical Optical Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThK4. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OThK4.

Li, G.

Liu, X.

X. Liu, “Generalized data-aided multi-symbol phase estimation for improving receiver sensitivity in direct-detection optical m-ary DPSK,” Opt. Express 15, 2927–2939 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-6-2927
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M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Willner, “Self-coherent decision-feedback-directed 40 Gbps DQPSK Receiver,” IEEE Photon. Technol. Lett. 19, 828–839 (2007).
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C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. 10, 281–293 (2004).
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X. Liu, X. Wei, R. E. Slusher, and C. J. McKinstrie, “Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation,” Opt. Lett. 27, 1616–1618 (2002).
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X. Liu and S. Chandrasekhar, “Measurement of constellation diagrams for 40-Gb/s DQPSK and 60-Gb/s 8ary-DPSK using sampled orthogonal differential direct-detection”, in Proceedings of European Conference on Optical Communications 2007, Paper 7.2.7, 2007

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Wilner, “Self-coherent optical detection of multisymbol differential phase-shift-keyed transmission,” J. Lightwave Technol. (accepted for publication).

X. Liu and X. Wei, “Electronic Dispersion Compensation Based on Optical Field Reconstruction with Orthogonal Differential Direct-Detection and Digital Signal Processing,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OTuA6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OTuA6.

X. Liu, “Receiver sensitivity improvement in optical DQPSK and DQPSK/ASK through data-aided multi-symbol phase estimation,” in Proceedings of European Conference on Optical Communications 2006, Paper We2.5.6, 2006.
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X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.4.5, 2006.

Lize, Y.

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Willner, “Self-coherent decision-feedback-directed 40 Gbps DQPSK Receiver,” IEEE Photon. Technol. Lett. 19, 828–839 (2007).
[Crossref]

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Wilner, “Self-coherent optical detection of multisymbol differential phase-shift-keyed transmission,” J. Lightwave Technol. (accepted for publication).

M. Nazarathy, Y. Yadin, M. Orenstein, Y. Lize, L. Christen, and A. Willner, “Enhanced Self-Coherent Optical Decision-Feedback-Aided Detection of Multi-Symbol M-DPSK/PolSK in Particular 8-DPSK/BPolSK at 40 Gbps,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JWA43. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-JWA43.

Maaref, N.

G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, “Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation,” in Proceedings of European Conference on Optical Communications 2006, Post-deadline Paper Th4.3.4, 2006.

Mandai, K.

N. Kikuchi, K. Mandai, and S. Sasaki, “Compensation of non-linear phase-shift in incoherent multilevel receiver with digital signal processing,” in Proceedings of European Conference on Optical Communications 2007, Paper 9.4.1, 2007..

N. Kikuchi, K. Mandai, S. Sasaki, and K. Sekine, “Proposal and first experimental demonstration of digital incoherent optical field detector for chromatic dispersion compensation,” in Proceedings of European Conference on Optical Communications2006, Post-deadline Paper Th4.4.4.

Mardoyan, H.

G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, “Efficient Mitigation of Fiber Impairments in an Ultra-Long Haul Transmission of 40Gbit/s Polarization-Multiplexed Data, by Digital Processing in a Coherent Receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP17. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP17.

G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, “Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation,” in Proceedings of European Conference on Optical Communications 2006, Post-deadline Paper Th4.3.4, 2006.

McGhan, D.

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan; “Wavelength division multiplexing (WDM) and polarization mode dispersion (PMD) performance of a coherent 40Gbit/s dual-polarization quadrature phase shift keying (DP-QPSK) transceiver,” in Proceedings of Optical Fiber Communication Conference2007, Post-deadline Paper PDP16.

McKinstrie, C. J.

Mikhailov, V.

S. J. Savory, V. Mikhailov, R. I. Killey, and P. Bayvei, “Digital coherent receivers for uncompensated 42.8Gb/s transmission over high PMD fibre,” in Proceedings of European Conference on Optical Communications 2007, Paper 10.4.1, 2007.

Mollenauer, L. F.

Nazarathy, M.

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Willner, “Self-coherent decision-feedback-directed 40 Gbps DQPSK Receiver,” IEEE Photon. Technol. Lett. 19, 828–839 (2007).
[Crossref]

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Wilner, “Self-coherent optical detection of multisymbol differential phase-shift-keyed transmission,” J. Lightwave Technol. (accepted for publication).

M. Nazarathy, Y. Yadin, M. Orenstein, Y. Lize, L. Christen, and A. Willner, “Enhanced Self-Coherent Optical Decision-Feedback-Aided Detection of Multi-Symbol M-DPSK/PolSK in Particular 8-DPSK/BPolSK at 40 Gbps,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JWA43. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-JWA43.

Noe, R.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
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R. Noe, “PLL-free synchronous QPSK polarization multiplex/diversity receiver concept with digital I&Q baseband processing,” IEEE Photon. Technol. Lett. 17, 887–889 (2005).
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O’Sullivan, M.

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan; “Wavelength division multiplexing (WDM) and polarization mode dispersion (PMD) performance of a coherent 40Gbit/s dual-polarization quadrature phase shift keying (DP-QPSK) transceiver,” in Proceedings of Optical Fiber Communication Conference2007, Post-deadline Paper PDP16.

Orenstein, M.

M. Nazarathy, Y. Yadin, M. Orenstein, Y. Lize, L. Christen, and A. Willner, “Enhanced Self-Coherent Optical Decision-Feedback-Aided Detection of Multi-Symbol M-DPSK/PolSK in Particular 8-DPSK/BPolSK at 40 Gbps,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JWA43. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-JWA43.

Peveling, R.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
[Crossref]

Pfau, T.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
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Pilipetskii, A. N.

Y. Cai and A. N. Pilipetskii, “Comparison of Two Carrier Phase Estimation Schemes in Optical Coherent Detection Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OMP5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OMP5.

Porrmann, M.

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
[Crossref]

Reichmann, K. C.

R. C. Giles and K. C. Reichmann, “Optical self-homodyne DPSK transmission at 1-Gbit/s and 2-Gbit/s over 86km of fiber,” Electron. Lett. 23, 1180–1181 (1987).
[Crossref]

Renaudier, J.

G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, “Efficient Mitigation of Fiber Impairments in an Ultra-Long Haul Transmission of 40Gbit/s Polarization-Multiplexed Data, by Digital Processing in a Coherent Receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP17. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP17.

G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, “Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation,” in Proceedings of European Conference on Optical Communications 2006, Post-deadline Paper Th4.3.4, 2006.

Salsi, M.

G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, “Efficient Mitigation of Fiber Impairments in an Ultra-Long Haul Transmission of 40Gbit/s Polarization-Multiplexed Data, by Digital Processing in a Coherent Receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP17. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP17.

Sasaki, S.

N. Kikuchi, K. Mandai, S. Sasaki, and K. Sekine, “Proposal and first experimental demonstration of digital incoherent optical field detector for chromatic dispersion compensation,” in Proceedings of European Conference on Optical Communications2006, Post-deadline Paper Th4.4.4.

N. Kikuchi, K. Mandai, and S. Sasaki, “Compensation of non-linear phase-shift in incoherent multilevel receiver with digital signal processing,” in Proceedings of European Conference on Optical Communications 2007, Paper 9.4.1, 2007..

Savory, S. J.

S. J. Savory, V. Mikhailov, R. I. Killey, and P. Bayvei, “Digital coherent receivers for uncompensated 42.8Gb/s transmission over high PMD fibre,” in Proceedings of European Conference on Optical Communications 2007, Paper 10.4.1, 2007.

Schmidt, E. -D.

C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.

Schulien, C.

C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.

Sekine, K.

N. Kikuchi, K. Mandai, S. Sasaki, and K. Sekine, “Proposal and first experimental demonstration of digital incoherent optical field detector for chromatic dispersion compensation,” in Proceedings of European Conference on Optical Communications2006, Post-deadline Paper Th4.4.4.

Slusher, R. E.

Sun, H.

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan; “Wavelength division multiplexing (WDM) and polarization mode dispersion (PMD) performance of a coherent 40Gbit/s dual-polarization quadrature phase shift keying (DP-QPSK) transceiver,” in Proceedings of Optical Fiber Communication Conference2007, Post-deadline Paper PDP16.

Taylor, M.

M. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16, 674–676 (2004).
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Tran, P.

G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, “Efficient Mitigation of Fiber Impairments in an Ultra-Long Haul Transmission of 40Gbit/s Polarization-Multiplexed Data, by Digital Processing in a Coherent Receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP17. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP17.

G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, “Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation,” in Proceedings of European Conference on Optical Communications 2006, Post-deadline Paper Th4.3.4, 2006.

van den Borne, D.

C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.

D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005).
[Crossref]

Villeneuve, B.

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan; “Wavelength division multiplexing (WDM) and polarization mode dispersion (PMD) performance of a coherent 40Gbit/s dual-polarization quadrature phase shift keying (DP-QPSK) transceiver,” in Proceedings of Optical Fiber Communication Conference2007, Post-deadline Paper PDP16.

Wei, X.

C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. 10, 281–293 (2004).
[Crossref]

X. Liu, X. Wei, R. E. Slusher, and C. J. McKinstrie, “Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation,” Opt. Lett. 27, 1616–1618 (2002).
[Crossref]

X. Liu and X. Wei, “Electronic Dispersion Compensation Based on Optical Field Reconstruction with Orthogonal Differential Direct-Detection and Digital Signal Processing,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OTuA6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OTuA6.

Willner, A.

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Willner, “Self-coherent decision-feedback-directed 40 Gbps DQPSK Receiver,” IEEE Photon. Technol. Lett. 19, 828–839 (2007).
[Crossref]

M. Nazarathy, Y. Yadin, M. Orenstein, Y. Lize, L. Christen, and A. Willner, “Enhanced Self-Coherent Optical Decision-Feedback-Aided Detection of Multi-Symbol M-DPSK/PolSK in Particular 8-DPSK/BPolSK at 40 Gbps,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JWA43. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-JWA43.

Wilner, A.

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Wilner, “Self-coherent optical detection of multisymbol differential phase-shift-keyed transmission,” J. Lightwave Technol. (accepted for publication).

Winzer, P. J.

A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23, 115–130 (2005).
[Crossref]

C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005.
[Crossref]

Wong-Foy, A.

C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005.
[Crossref]

Wuth, T.

C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.

Xu, C.

C. Xu, X. Liu, and X. Wei, “Differential phase-shift keying for high spectral efficiency optical transmissions,” IEEE J. Sel. Top. Quantum Electron. 10, 281–293 (2004).
[Crossref]

Yadin, Y.

M. Nazarathy, Y. Yadin, M. Orenstein, Y. Lize, L. Christen, and A. Willner, “Enhanced Self-Coherent Optical Decision-Feedback-Aided Detection of Multi-Symbol M-DPSK/PolSK in Particular 8-DPSK/BPolSK at 40 Gbps,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JWA43. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-JWA43.

Zhang, Z.

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan; “Wavelength division multiplexing (WDM) and polarization mode dispersion (PMD) performance of a coherent 40Gbit/s dual-polarization quadrature phase shift keying (DP-QPSK) transceiver,” in Proceedings of Optical Fiber Communication Conference2007, Post-deadline Paper PDP16.

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[Crossref]

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 11, 563–570 (2006).

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[Crossref]

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Willner, “Self-coherent decision-feedback-directed 40 Gbps DQPSK Receiver,” IEEE Photon. Technol. Lett. 19, 828–839 (2007).
[Crossref]

T. Pfau, S. Hoffmann, R. Peveling, S. Bhandare, S.K. Ibrahim, O. Adamczyk, M. Porrmann, R. Noe, and Y. Achiam, “First Real-Time Data Recovery for Synchronous QPSK Transmission With Standard DFB Lasers,” IEEE Photon. Technol. Lett. 18, 1907–1909 (2006).
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Other (18)

X. Liu and S. Chandrasekhar, “Measurement of constellation diagrams for 40-Gb/s DQPSK and 60-Gb/s 8ary-DPSK using sampled orthogonal differential direct-detection”, in Proceedings of European Conference on Optical Communications 2007, Paper 7.2.7, 2007

C. R. Doerr, D. M. Gill, A. H. Gnauck, L. L. Buhl, P. J. Winzer, M. A. Cappuzzo, A. Wong-Foy, E. Y. Chen, and L. T. Gomez, “Simultaneous reception of both quadratures of 40-Gb/s DQPSK using a simple monolithic demodulator,” in Proceedings of Optical Fiber Communication Conference 2005, Post-deadline Paper PDP12, 2005.
[Crossref]

X. Liu, S. Chandrasekhar, A. H. Gnauck, C. R. Doerr, I. Kang, D. Kilper, L. L. Buhl, and J. Centanni, “DSP-enabled compensation of demodulator phase error and sensitivity improvement in direct-detection 40-Gb/s DQPSK,” in Proceedings of European Conference on Optical Communications 2006, post-deadline paper Th4.4.5, 2006.

Y. Cai and A. N. Pilipetskii, “Comparison of Two Carrier Phase Estimation Schemes in Optical Coherent Detection Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OMP5. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OMP5.

A. Leven, N. Kaneda, U. -V. Koch, and Y. -K. Chen, “Coherent Receivers for Practical Optical Communication Systems,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OThK4. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OThK4.

G. Charlet, N. Maaref, J. Renaudier, H. Mardoyan, P. Tran, and S. Bigo, “Transmission of 40Gb/s QPSK with coherent detection over ultra long haul distance improved by nonlinearity mitigation,” in Proceedings of European Conference on Optical Communications 2006, Post-deadline Paper Th4.3.4, 2006.

N. Kikuchi, K. Mandai, and S. Sasaki, “Compensation of non-linear phase-shift in incoherent multilevel receiver with digital signal processing,” in Proceedings of European Conference on Optical Communications 2007, Paper 9.4.1, 2007..

S. J. Savory, V. Mikhailov, R. I. Killey, and P. Bayvei, “Digital coherent receivers for uncompensated 42.8Gb/s transmission over high PMD fibre,” in Proceedings of European Conference on Optical Communications 2007, Paper 10.4.1, 2007.

K.-P. Ho, Phase-modulated optical communication systems, (Springer, New York, 2005).

M. Nazarathy, Y. Yadin, M. Orenstein, Y. Lize, L. Christen, and A. Willner, “Enhanced Self-Coherent Optical Decision-Feedback-Aided Detection of Multi-Symbol M-DPSK/PolSK in Particular 8-DPSK/BPolSK at 40 Gbps,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JWA43. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-JWA43.

M. Nazarathy, X. Liu, L. Christen, Y. Lize, and A. Wilner, “Self-coherent optical detection of multisymbol differential phase-shift-keyed transmission,” J. Lightwave Technol. (accepted for publication).

N. Kikuchi, K. Mandai, S. Sasaki, and K. Sekine, “Proposal and first experimental demonstration of digital incoherent optical field detector for chromatic dispersion compensation,” in Proceedings of European Conference on Optical Communications2006, Post-deadline Paper Th4.4.4.

X. Liu and X. Wei, “Electronic Dispersion Compensation Based on Optical Field Reconstruction with Orthogonal Differential Direct-Detection and Digital Signal Processing,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper OTuA6. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OTuA6.

G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo, “Efficient Mitigation of Fiber Impairments in an Ultra-Long Haul Transmission of 40Gbit/s Polarization-Multiplexed Data, by Digital Processing in a Coherent Receiver,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP17. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP17.

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan; “Wavelength division multiplexing (WDM) and polarization mode dispersion (PMD) performance of a coherent 40Gbit/s dual-polarization quadrature phase shift keying (DP-QPSK) transceiver,” in Proceedings of Optical Fiber Communication Conference2007, Post-deadline Paper PDP16.

C. R. Fludger, T. Duthel, D. van den Borne, C. Schulien, E. -D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, and H. de Waardt, “10×111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK Transmission over 2375 km Employing Coherent Equalisation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP22. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP22.

D. van den Borne, S. Jansen, G. Khoe, H. de Wardt, S. Calabro, and E. Gottwald, “Differential quadrature phase shift keying with close to homodyne performance based on multi-symbol phase estimation,” IEE Seminar on Optical Fiber Comm. and Electronic Signal Processing, ref. No. 2005–11310 (2005).
[Crossref]

X. Liu, “Receiver sensitivity improvement in optical DQPSK and DQPSK/ASK through data-aided multi-symbol phase estimation,” in Proceedings of European Conference on Optical Communications 2006, Paper We2.5.6, 2006.
[Crossref]

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Figures (9)

Fig. 1.
Fig. 1. Schematic DSCD architecture based on orthogonal differential direct-detection followed by ADC and DSP. OA: optical pre-amplifier; OF: optical filter; ODI: optical delay interferometer; BD: balanced detector; ADC: analog-to-digital converter.
Fig. 2.
Fig. 2. Measured BER performance of the 40-Gb/s DQPSK signal received with and without the data-aided MSPE [21].
Fig. 3.
Fig. 3. Experimental setup for reconstructing the constellation diagrams of a 40-Gb/s RZ-DQPSK and a 60-Gb/s RZ-8ary-DPSK signal using DSCD [24]. Inset shows simultaneously measured I/Q eye diagrams of a 40-Gb/s RZ-DQPSK signal. Time scale: 20 ps/division.
Fig. 4.
Fig. 4. Measured differential-phase constellation diagrams of the 40-Gb/s DQPSK signal at OSNR=35 dB (left) and 21 dB (center) and measured differential-phase variance as a function of OSNR (right). The dashed line is calculated.
Fig. 5.
Fig. 5. Measured differential-phase constellations of the 40-Gb/s DQPSK signal after transmission with 6 dBm (left) and 8 dBm (center) signal launch powers, and measured differential-phase constellation diagram of a 60-Gb/s 8ary-DPSK signal (right).
Fig. 6.
Fig. 6. Schematic of two dual-polarization DSCD configurations for receiving a polarization-multiplexed DPSK signal using two orthogonal ODI pairs (upper) and one shared ODI pair (lower). PBS: polarization beam splitter.
Fig. 7.
Fig. 7. Polarization evolution of an optical signal over a typical fiber transmission link having PMD. “‖” and “⊥” represent the orientations of the two PSP axes of the fiber PMD.
Fig. 8.
Fig. 8. A parallel structure of the DSP circuit for EPDMUX and electronic PMDC.
Fig. 9.
Fig. 9. Block diagram of a processing unit for EPDMUX and electronic PMDC.

Equations (20)

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u ( t ) = u I ( t ) + j · u Q ( t ) = e j · θ r ( t ) · r * ( t τ ) .
u ( t ) e j · ϕ e u ( t ) .
x ( n ) = u ( n ) + p = 1 N { w p e jp π / m u ( n ) q = 1 p [ u ( n q ) · e j Δ ϕ ( n q ) ] }
exp [ j · Δ ϕ ( n ) ] = c I ( n ) c Q ( n ) ¯ · ( 1 ) c I ( n ) ¯ + j · c I ( n ) c Q ( n ) · ( 1 ) c I ( n ) ¯ ,
v ( πp m ) = cos ( p 1 m π ) u I sin ( p 1 m π ) u Q .
v ( πp m π 2 ) = sin ( p 1 m π ) u I + cos ( p 1 m π ) u Q .
c 1 = c I = [ u ( π m ) > 0 ] , c 2 = c Q = [ u ( π m π 2 ) > 0 ] ,
c 3 = [ u ( π m + π 4 ) > 0 ] [ u ( π m π 4 ) > 0 ] ,
c log 2 ( m ) = [ u ( 3 m π ) > 0 ] [ u ( 7 m π ) > 0 ] [ u ( m 2 1 m π ) > 0 ]
        [ u ( 3 m π π 2 ) > 0 ] [ u ( 7 m π 2 ) > 0 ] [ u ( m 2 1 m π π 2 ) > 0 ] .
e j · [ ϕ ( t ) ϕ ( t τ ) ] = u ( t ) e j · θ u ( t ) e j · θ .
r ( t 0 + n · τ ) = r ( t 0 + n · τ ) e j · ϕ ( t 0 ) m = 1 n e j · Δ ϕ ( t 0 + m · τ ) ,
r ( t 0 + n · τ ) u ( t 0 + n · τ ) · u ( t 0 + n · τ + τ ) 1 4 .
σ Δ ϕ 2 1 2 NEB · ( 0.1 nm · OSNR 0.1 nm ) 1 ,
v ( n ) = u ( n ) · exp { j · 1 2 c NL · [ P ( n ) P ( n 1 ) ] } ,
[ E x E y ] = T · [ E x E y ] = P · R 2 · PMD ( ω ) · R 1 · [ E x E y ] ,
R 1 = [ cos ( θ 1 ) sin ( θ 1 ) sin ( θ 1 ) cos ( θ 1 ) ] , PMD ( Δ f ) = [ 1 0 0 e j ( 2 π · Δ f · τ DGD + δ ϕ PMD ) ] ,
R 2 = [ cos ( θ 2 ) sin ( θ 2 ) sin ( θ 2 ) cos ( θ 2 ) ] , P = [ 1 0 0 e j · δ ϕ PBS ] ,
[ E x E y ] = T 1 · [ E x ( t ) E y ( t ) ] = R 1 1 · PMD 1 ( Δ f ) · R 2 1 · P 1 [ E x E y ] .
[ E x ( t ) E y ( t ) ] = [ cos ( θ 1 ) [ cos ( θ 2 ) E x ( t ) + sin ( θ 2 ) E y ( t ) e j · δϕ PBS ] sin ( θ 1 ) [ sin ( θ 2 ) E x ( t + τ DGD ) + cos ( θ 2 ) E y ( t + τ DGD ) e j · δϕ PBS ] e j · δϕ PMD sin ( θ 1 ) [ cos ( θ 2 ) E x ( t ) + sin ( θ 2 ) E y ( t ) e j · δϕ PBS ] + cos ( θ 1 ) [ sin ( θ 2 ) E x ( t + τ DGD ) + cos ( θ 2 ) E y ( t + τ DGD ) e j · δϕ PBS ] e j · δϕ PMD ] .

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