Advanced signaling technologies for high-speed digital fiber-optic links Andrew J. Stark,1 Pierre Isautier,2 Jie Pan,2 Sriharsha Kota Pavan,2 Mark Filer,3 Sorin Tibuleac,3 Robert Lingle, Jr.,4 Richard de Salvo,5 and Stephen E. Ralph2,* 1
Georgia Tech Research Institute, Electronic Systems Laboratory, 400 10th St. NW, Atlanta, Georgia 30332, USA
2
Georgia Institute of Technology, Department of Electrical and Computer Engineering, Atlanta, Georgia 30332, USA 3
ADVA Optical Networking, Norcross, Georgia 30092, USA 4 5
OFS Optics, Norcross, Georgia 30071, USA
Harris Corporation, Melbourne, Florida 32904, USA
*Corresponding author: [email protected] Received 23 May 2014; accepted 11 June 2014; posted 15 July 2014 (Doc. ID 212725); published 29 August 2014
We summarize the most recent research of the Georgia Tech Terabit Optical Networking Consortium and the state-of-the-art in fiber telecommunications. These results comprise high-capacity single-mode fiber systems with digital coherent receivers and shorter-reach multimode fiber links with vertical cavity surface emitting lasers. We strongly emphasize the capabilities that sophisticated digital signal processing and electronics add to these fiber-based data transport links. © 2014 Optical Society of America OCIS codes: (060.4510) Optical communications; (060.4080) Modulation; (060.4250) Networks. http://dx.doi.org/10.1364/AO.53.005824
1. Introduction
The communications infrastructure of the world has changed dramatically over the past decades in response to the staggering increase in traffic demands. Global IP traffic has increased by two orders of magnitude over the last two decades [1]. These high traffic demands have been supported by commensurate increases in both the short and long reach optical fiber link capacities. For example, wavelength division multiplexed (WDM) systems with single channel capacity of 200 Gb∕s and total capacity of 20 Tb∕s are commercially available for long reach applications [2]. The performance capabilities have 1559-128X/14/255824-17$15.00/0 © 2014 Optical Society of America 5824
APPLIED OPTICS / Vol. 53, No. 25 / 1 September 2014
been achieved through a careful combination of optical, electronic, and signal processing technologies. Optical link functionality has been dramatically enhanced by exploiting high-speed silicon CMOS circuits and algorithms. Optimized transport solutions invariably require maximizing the capacity of the optical components. Specifically, maximizing the bits/s/km per source and receiver unit. Historically, this is the trend observed in the telecom market as optical systems grew from OC48 (2.5 Gb∕s) to OC192 (10 Gb∕s) employing a single laser source and single receiver. Similarly, short reach systems using 850 nm technologies with directly modulated lasers have evolved from sub Gb/s to 10 Gb∕s thus maximizing the capacity of each source and receiver. Until recently these higher data rates were achieved by increases in the symbol rate
and receiver bandwidth while strictly employing On–Off keying (OOK) modulation. Most systems are deployed with digital signal processing (DSP) in the form of forward error correction (FEC) [3]. These economics continue today with longer reach (>10 km) systems being deployed at 100 Gb∕s per each C-band (∼1550 nm) laser wavelength [4] achieved using higher modulation formats and digital coherent receiver (DCR) technology. DCRs incorporate a stable but unlocked optical local oscillator (LO) at the receiver together with significant DSP within a Si-CMOS ASIC to recover the timing and symbol phase, to correct for chromatic dispersion (CD), to perform polarization alignment, and to mitigate other channel impairments [5]. Similar to the deployment of the EDFA and DWDM technology, DCRs have revolutionized modern high-capacity fiber links, now enabling capacity close to the Shannon limit. One hundred gigabit-per-second dual-polarization quadrature phase shift keying (100G PDM-QPSK) transceivers with DCR technology have been available for more than 5 years [6]. Separately, the 40G/100G fiber-optic cables Ethernet standard is nearing completion. Within this IEEE 802.3 bm standard effort are goals to define 100 Gb∕s operation over at least 100 m of multimode fiber (MMF) [7] utilizing 4 lanes of 25 Gb∕s on OM4 fiber (100GBASE-SR4). These systems will be deployed within data centers to interconnect thousands of servers. Existing 850 nm vertical cavity surface emitting laser (VCSEL) technology is limited to ∼20 GHz bandwidth (over the required temperature range) which yields maximum single channel OOK rates to ∼25 Gb∕s [8]. Importantly, these rates are achieved using limited FEC and both transmitter and receiver equalization filters to provide gain boost at higher frequencies. Four hundred gigabit-per-second standards efforts have begun within the IEEE 802.3 400 Gb∕s study group. These efforts will exploit 100 G technologies and aim to support 400G over 100 m of MMF and potentially implementing higher modulation formats. In this paper we review the work performed within the Georgia Institute of Technology Terabit Optical Networking Consortium—formerly the 100G Consortium—which was founded in 2008 by ADVA Optical Networking, OFS, Verizon, and Ciena and hosted at Georgia Tech to investigate solutions and challenges for 100 Gb∕s transport (100g.gatech.edu). Since its inception, the Consortium has been joined by Harris Corp, Avago, Oclaro, Optametra, Picometrix, Nistica, Agilent, and RSoft. Over the past 6 years the consortium has evolved beyond 100 G and has begun to addresses the challenges for 400 Gb∕s and 1 Tb∕s data rates in signal processing, hardware, and simulations. We highlight the most recent efforts in high-capacity single-mode fiber (SMF) systems employing DCRs emphasizing the capabilities added by the use of DSP. We also describe shorter reach VCSEL-based MMF link technologies that support 25 Gb∕s and
greater serial data rates again emphasizing the impact of signal processing and the eventual transition to higher level modulation. 2. Electronic-Optical Interface: Waveform Generation and Detection A. Transmitters and Modulation
Optical quadrature modulation is typically achieved with an integrated structure consisting of two independent Mach–Zehnder interferometers (MZI) nested within an outer third MZI, Fig. 1. The outer MZI ensures a π∕2 phase difference between the two arms. Each polarization requires one of these nested MZI structures. The single-polarization quadrature amplitude modulation (QAM) signal can be described as s ∞ 2Es X st a cos2πf c t T s m−∞ I;m − aQ;m sin2πf c tgt − mT s :
(1)
The complex symbol am aI;m jaQ;m takes values defined by the order of the QAM format and gt is the pulse shape (which may span more than one symbol). In optical systems, the pulse shape is primarily determined by the low-pass transfer function of the external modulator structure, the drive electronics, and by the optional use of return-to-zero (RZ) pulse carving. Additionally, optical channel filters and wavelength switches affect the pulse shape; the cascaded behavior of these components is an area of active research [9–12]. For a detailed description of the exact transmitter see [13]. For the work reported here (Section 3), no special signal processing was utilized to craft specific pulse shapes at the transmitter. An RZ carver was selectively utilized for different experiments; the RZ carver is comprised of a MZM driven with a sinusoidal clock synchronous to the data stream. RZ carving offers better transmission performance in certain link configurations [14]. Waveform generation for long-haul transport has evolved beyond NRZ/RZ to support “per wavelength”
Fig. 1. I∕Q modulator constructed from three nested MZIs. To achieve the required carrier coherence along the waveguide paths, this structure is general integrated in a single package. Return-tozero carving (dashed box) can be optionally achieved with an external (or integrated) MZI driven by the symbol clock signal. 1 September 2014 / Vol. 53, No. 25 / APPLIED OPTICS
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data rates greater than 1 Tb∕s. Strategies are typically separated into two main approaches: Nyquist-WDM and coherent orthogonal frequency division multiplexing (Co-OFDM). Both NyquistWDM and Co-OFDM seek to stack spectral content as tight as possible while minimizing inter-channel interference (ICI) and inter-symbol interference (ISI), necessary conditions to approach the Shannon limit. For Nyquist-WDM, the ideal spectral shape for each subchannel is rectangular with the channel spacing (Δf ) equal to the baud rate. That is, the pulse gt within each channel is a sinc shape in the time domain. In contrast, Co-OFDM produces a sincshaped carrier in the frequency domain (rectangular pulse in the time domain). In practical systems, the transmitter cannot produce gt to perfectly eliminate ISI and ICI; efforts to reduce the impact of ISI and ICI are areas of active research [15]. B.
Optical Coherent Receivers
Optical coherent receivers are directly analogous to wireless or wire-line radios: a LO is mixed with the received signal to down convert the waveform to (or near) baseband for demodulation. In the ideal homodyne case, a coherent receiver linearly translates the channel of interest into a complex electrical baseband waveform. The general structure of a polarization-diverse coherent optical receiver is depicted in Fig. 2. The complex envelope of the received optical signal field Es t plus noise Nt and LO ELO are first split into X and Y polarization. Next, the X and Y components of the received signal and LO are independently combined via a 90° optical hybrid. The optical hybrid allows the subsequent mixing to extract both the in-phase and the quadrature components of the X or Y polarization of Es t. The fouroutput 90° optical hybrid, Fig. 2, is described by the transfer matrix
2 p 1 − ϵI expfjϕI g 6 p 6E 7 6 ϵI 6 27 6 6 7 6 p 4 E3 5 6 1 − ϵQ expfjϕQ g 4 p E4 ϵQ Es N ; × ELO 2
E1
3
p ϵI p 1 − ϵI expfjϕI g p j ϵQ p j 1 − ϵQ expfjϕQ g
3 7 7 7 7 7 5
(2)
where ϵ1 and ϵ2 are the power transfer coefficients, and ϕI and ϕQ are the phase misalignments of the two paths of the optical combiner. After the squarelaw photodetectors with responsivity Rk, the electrical signals Sk t Rk jEk tj2 are of the form S1 R1 1 − ϵI jEs j2 jNj2 2 RefEs N g ϵI jELO j2 p 2 expfjϕI g ϵI 1 − ϵI RefEs ELO NELO g: (3) If the photodiodes are perfectly balanced (Rk R) and the optical combiners perfectly matched ϵI ϵQ 0.5; ϕI ϕQ 0 the receiver rejects all common-mode direct-detection photocurrents, yielding SI t 2R RefEs tELO NtELO g;
(4)
SQ t 2R ImfEs tELO NtELO g:
(5)
In an ideal homodyne receiver, ELO is both temporally static and a perfect phase reference to the incoming optical field. That is, ELO is phase-locked to Es t and the term ELO is a constant scalar, enabling the photocurrents SI and SQ to vary proportionally to the real (I, in-phase) and imaginary (Q, quadrature) parts of the received signal. The coherent receiver is therefore capable of detecting the complex envelope of the in-phase and quadrature components of two
Fig. 2. Polarization-diverse optical coherent receiver. The stages of the receiver are coherent detection, digitization, and DSP. The performance of the receiver is determined by the combined performance of each optical and electronic component as well as the signal processing algorithms. 5826
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linear polarization modes (albeit at an arbitrary orientation [16,17]). Frequency locking of the LO with the incoming signal carrier had been the conventional approach for coherent optical receivers. Today, modern high-speed DSP capabilities allow the equivalent functionality in the digital domain after high-speed sampling of the electrical signals. The first term inside the Ref•g and Imf•g parts of Eqs. (4) and (5) is the desired signal term. The second term is the LO-noise beat term (the only beat term of relevance—both the signal–noise and noise–noise beat terms are eliminated in ideal balanced detection). Because a coherent receiver operates as a linear transformation the statistics of the both the signal and noise optical fields are preserved in the conversion to an electrical waveform. In contrast, direct-detection receivers with one or more delay interferometers yield non-Gaussian noise statistics. The advantages of coherent detection compared to direct detection can be summarized in three points. a. The coherent receiver offers received signal gain proportional to the LO power, improving receiver sensitivity. b. The output electrical photocurrent is a linear transformation of the optical signal field (containing full phase and amplitude information). c. The coherent receiver enables DSP in the electronics domain. DSP techniques have advanced at a breathtaking pace in the past decade and have largely driven the exponential proliferation of wireless and mobile electronics. With the introduction of optical coherent receivers, DSP algorithms can fully compensate or mitigate nearly all channel impairments of a fiberoptic system in the purely electronic domain. C.
Signal Processing for Digital Transmission
For optical fiber channels, there are four primary processing steps that the signal processing engine must perform regardless of the signal modulation format, Fig. 2. In general order these steps are CD compensation, symbol timing recovery, polarization demultiplexing, and carrier phase recovery. We also perform sampling skew removal immediately after digitization and before CD equalization and leastmean square (LMS) equalization before symbol detection. This first step removes any subsample-rate offset between the four sampled channels using a high-precision fractionally spaced filter, determined by a careful measurement and calibration of the sampling behavior of the digital oscilloscope used as the sampler. After digitization and sampling skew removal the DSP must first compensate for the accumulated CD [18]. The transfer function H CD ω expfjλ20 DLω2 ∕4πcg
(6)
describes the dominant quadratic phase dependence of second-order dispersion. The value DL s∕m
represents the total accumulated dispersion that the filter compensates and is as large as 20; 000 ps∕nm or greater for long-haul systems. Since the single channel signal bandwidths are ∼30 GHz (0.27 nm) the transfer function is typically implemented in the frequency domain since the temporal delays can be 5000 ps (5000∕32.5 153.8 bit-periods at 32 Gbaud). Optimum CD compensation can be determined by maximizing the variance of the received signal. Dispersion compensation was managed using compensating fiber until the deployment of DCRs. To recover the symbol timing phase we implement the nondata-aided (NDA) feed-forward digital filter and square method [19]. This block of the DSP estimates the symbol time on each polarization independently by first squaring the symbols and then centering on the maximum eye opening. That is, the timing estimate returns 1 τˆ − arg 2π
LN−1 X m0
jxm1
j2
j2πm ; exp − N
(7)
which is the normalized phase between −1∕2 and 1∕2. In Eq. (7), xm are the message symbols, L is the number of symbols per frame, and N is the number of samples per symbol. The magnitude square operation is proportional to the instantaneous power and maximum at the maximum eye opening since the QPSK waveform will, with high probability, pass through regions of low power. Polarization demultiplexing in SMF links is a 2 × 2 MIMO process governed by the Jones matrix that describes the fiber and the alignments of the transmitter and receiver linearly polarized E-fields. For dual-polarization fiber transmission, the MIMO equalizer is arranged in a “butterfly” structure, Fig. 2, and adapts four sets of complex coefficients, bridging each of the possible paths from X and Y input to X and Y output, to jointly minimize the resulting error in the output [error, would be determined by the choice of updating rule—the constant modulus algorithm (CMA) is a common choice]. Convergence is assured to avoid false recovery at both X and Y outputs when constrained by the relationship ¯ hxx h¯ yx
h¯ xy u¯ −¯v h¯ yy
v¯ ; u¯
(8)
where u and v are complex-valued vectors with one element per equalizer tap. The complex conjugate operation also implies a time reversal of the vectors. The CMA is the classical choice for QPSK-based fiber transmission [20,21] for optimizing the polarization demux. However, CMA does not adapt optimally for modulation formats that are not constrained to a constant envelope. An alternate method of separating polarization uses independent component analysis (ICA). ICA is based on the observation that the two orthogonally polarized waveforms are statistically independent and uncorrelated. The 1 September 2014 / Vol. 53, No. 25 / APPLIED OPTICS
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Table 1.
Nominal Fiber Parameters, Single Mode at 1550 nm
Parameter
SMF
Loss, α dB∕km Core effective area, Aeff μm2 Dispersion, D ps∕nm km Nonlinear coeff, γ×10−3 m−1 W−1
MDF
0.19 80 17.0 1.16
0.21 55 7.3 1.91
LAF 0.18 130 20 .717
principal of ICA source separation is the central limit theorem: the mixture of non-Gaussian signals tends to Gaussian. Therefore, ICA attempts to maximize the “non-Gaussianity” (entropy) of the signal. The advantage to this approach is that an ICA equalizer can separate any two signal sources regardless of modulation format provided that they are each, in general, not Gaussian-distributed [22]. The ICA equalizer is configured in an identical fashion to the butterfly structure of the CMA-based equalizer, Fig. 2. The tap update rule, however, is based on the natural gradient method that possesses the equivariance property; it converges asymptotically based on the stochastic properties of the source signals and regardless of the channel (or mixing) description [22]. A step-by-step analysis of the ICAbased polarization demultiplexor is available in [23]. For optical systems where the two convolved signals are the orthogonal polarization modes, the polarization demultiplexing equalizer is also required to compensate for polarization mode dispersion (PMD). While a single-tap ICA equalizer can asynchronously separate sampled data, to compensate for PMD the equalizer needs enough (more than one) taps to cover the time walk-off of the polarization modes. Thus timing recovery must be performed prior to the polarization mode separation via ICA. The carrier phase recovery algorithm used for 16 QAM transmission is derived from the “stop-andgo” decision-directed algorithm described in [24] and in [25]. Also called a “phase integrator,” the algorithm employs a decision-directed recovery loop to estimate the carrier phase with the rule θk1 θk − μθ Imfzk ek g;
(9)
where θk is the phase estimate, zk are the message symbols, μθ is the step size parameter, and ek zk − ak is the error signal.
The LMS equalizer is a classical adaptive filter that can also be considered a stochastic gradient algorithm; its derivation is covered thoroughly in the literature [26,27]. No further cross-polarization interference cancellation is attempted (i.e., this filter is not arranged in a “butterfly” structure). The purpose of this filter is to remove any residual CD and ISI that the channel imposes, and to output a single sample per symbol for detection. We note that although the basic DSP functions have been implemented in other systems for many years, the data rate and the impairments of optical channels present many new implementation challenges [28]. D.
Georgia Tech Terabit Optical Network Testbed
A wide variety of fibers have been made available by OFS for link transmission tests within the consortium, among them standard SMF, large area fiber (LAF), and medium dispersion fiber (MDF), Table 1. Each span is comprised of fiber with 80–90 km lengths. Two different link configurations are available: point-to-point (PtP) link and recirculating loop, Fig. 3. In the PtP link, Fig. 3(a), each span is comprised of one EDFA with midstage access for optional dispersion compensation modules (DCM). Multiple spans of fiber and EDFAs are used to simulate long-haul transmission systems with total reach of ∼1000 km. Longer reach systems are simulated using a recirculating loop, Fig. 3(b), which allows the optical signal to pass through the loop multiple times. The recirculating loop includes three spans of fiber and corresponding EDFAs for loss compensation, a booster EDFA, and a gain equalization filter (implemented with a wavelength selective switch). These network elements have been provided by ADVA Optical Networks. Two high-speed acousto-optic switches are used to control the load in and out of optical signals. In the data load-in stage, the loadin switch (SW1) is on and loop switch (SW2) is off. The incoming optical signals pass through SW1 and are split into two parts by a 2 × 2 fiber-optic directional coupler. One part is loaded into the transmission system and the other is sent to the receiver. In the loop stage, SW1 is off and SW2 is set to on so that the optical signals can circulate through the loop. Finally, a time-gating pulse enables the receiver
Fig. 3. Experimental setup for various single-mode network configurations and fiber types (nominal operating wavelength: 1550 nm). 5828
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Fig. 4. Georgia Tech Terabit Consortium Testbed.
to detect only the optical signals that passes through the transmission system for a predetermined number of circulations. The number of circulations is limited by the EDFA-induced ASE noise limit and any enhanced nonlinear effects. Extensive transmission results are available in [13,14,27]. In addition to the SMF testbed, Fig. 4, the Georgia Tech Terabit Optical Networking Consortium, also includes an extensive MMF (also provided by OFS) for a separate short-reach testbed. MMF is utilized in a variety of applications including data centers and high performance computing which involve short reach links where the deployed technologies are more cost sensitive. Hence, these links are required to minimize complexity and coherent systems are unlikely for the foreseeable future. Typically such links use direct modulation of VCSELs with various types of MMF, Table 2. For example, the emerging 100GBASE-SR4 standard uses 25G VCSELs over four lanes (distinct fibers) of MMF at a data rate of 25.78125 Gb∕s to allow forward error correction. Figure 5 shows the schematic of the experimental testbed with state-of-the-art 25 G multimode oxide-aperture VCSEL die, a MMF channel, and custom designed 30 G optical receivers created at Georgia Tech. The optical receiver consists of an InGaAs PIN 20 μm diameter photodiode with responsivity ∼0.36 A∕W at 850 nm and TIA on a laser-etched board with a net effective bandwidth ∼28 GHz. The 30 Gbit∕s capable SHF 12124A outputs high-quality electrical PRBS patterns with a built-in 4-tap, T-spaced FIR pre-emphasis filter that compensates bandwidth limitations in the link. 3. Gaussian Noise Model of Nonlinear Link Noise
Fiber-optic transmission is fundamentally limited by nonlinear refraction [11], a phenomena whereby the phase of the propagating signal is changed proportionally to its intensity. This effect limits the total available optical signal-to-noise ratio (OSNR); the launch power (which is the primary method of controlling the OSNR) can only be increased to a certain point, beyond which the performance of the signal begins to degrade. The fiber nonlinearities create both intra- and inter-channel mixing products via the Table 2.
Fig. 5. Georgia Tech MMF experimental network with custom receiver and high-speed VCSELs.
four-wave mixing (FWM) process that interferes with the desired signals and increases with increasing launch power. Generally, the total fiber-optic network performance is determined by including all copropagating signals in the fiber (data channels, ASE noise, etc.) and numerically simulating the propagation with FWM and other nonlinear impairments over the entire link, which may have a varying number of WDM channels a be comprised of spans of different fiber type and distance. This is typically accomplished by numerically solving the nonlinear Schrödinger wave equation via step-by-step methods that require both time domain computations for nonlinearities and frequency domain computations to handle CD; simulations are a slow, time-consuming process. However, it has been shown that systems without inline dispersion compensation offer performance advantages over dispersion-managed systems [29]. This arises from the fact that [29–33] uncompensated dispersion renders the four signal components—X, Y, I, and Q—statistically independent, noise-like, and Gaussian-distributed at reception. This Gaussian characteristic is also maintained throughout the DSP chain. In addition to performance benefits, many uncompensated systems are dramatically easier to assess in the nonlinear regime where many deployed systems operate. Perturbative models of nonlinear propagation which did not work well for dispersionmanaged systems can now accurately predict systems for uncompensated transmission [34]. Specifically, it allows the mixing products to be treated as noise. Thus, the definition of signal-to-noise ratio (SNR) can be recast by adding the variance of the nonlinear noise directly to the variance of the ASE
Nominal Fiber Parameters, Multimode
Parameter Dispersion, D ps∕nm km EMBc (MHz-km) Dispersion, D ps∕nm km EMBc (MHz-km)
λ0
OM3
OM4
850 nm
108 2800 44 2400
108 5700 44 1000 km distances. Software-defined coherent optical transceivers may be the next logical step in the evolution of transport networks. The SDOT relies on a hybrid analog/ digital hardware implementation, DSP techniques, and flexible electro-optical hardware; it provides unparalleled flexibility for traffic management and system diagnosis. MMF links meet the critical short-reach (
Georgia Tech Research Institute, Electronic Systems Laboratory, 400 10th St. NW, Atlanta, Georgia 30332, USA
2
Georgia Institute of Technology, Department of Electrical and Computer Engineering, Atlanta, Georgia 30332, USA 3
ADVA Optical Networking, Norcross, Georgia 30092, USA 4 5
OFS Optics, Norcross, Georgia 30071, USA
Harris Corporation, Melbourne, Florida 32904, USA
*Corresponding author: [email protected] Received 23 May 2014; accepted 11 June 2014; posted 15 July 2014 (Doc. ID 212725); published 29 August 2014
We summarize the most recent research of the Georgia Tech Terabit Optical Networking Consortium and the state-of-the-art in fiber telecommunications. These results comprise high-capacity single-mode fiber systems with digital coherent receivers and shorter-reach multimode fiber links with vertical cavity surface emitting lasers. We strongly emphasize the capabilities that sophisticated digital signal processing and electronics add to these fiber-based data transport links. © 2014 Optical Society of America OCIS codes: (060.4510) Optical communications; (060.4080) Modulation; (060.4250) Networks. http://dx.doi.org/10.1364/AO.53.005824
1. Introduction
The communications infrastructure of the world has changed dramatically over the past decades in response to the staggering increase in traffic demands. Global IP traffic has increased by two orders of magnitude over the last two decades [1]. These high traffic demands have been supported by commensurate increases in both the short and long reach optical fiber link capacities. For example, wavelength division multiplexed (WDM) systems with single channel capacity of 200 Gb∕s and total capacity of 20 Tb∕s are commercially available for long reach applications [2]. The performance capabilities have 1559-128X/14/255824-17$15.00/0 © 2014 Optical Society of America 5824
APPLIED OPTICS / Vol. 53, No. 25 / 1 September 2014
been achieved through a careful combination of optical, electronic, and signal processing technologies. Optical link functionality has been dramatically enhanced by exploiting high-speed silicon CMOS circuits and algorithms. Optimized transport solutions invariably require maximizing the capacity of the optical components. Specifically, maximizing the bits/s/km per source and receiver unit. Historically, this is the trend observed in the telecom market as optical systems grew from OC48 (2.5 Gb∕s) to OC192 (10 Gb∕s) employing a single laser source and single receiver. Similarly, short reach systems using 850 nm technologies with directly modulated lasers have evolved from sub Gb/s to 10 Gb∕s thus maximizing the capacity of each source and receiver. Until recently these higher data rates were achieved by increases in the symbol rate
and receiver bandwidth while strictly employing On–Off keying (OOK) modulation. Most systems are deployed with digital signal processing (DSP) in the form of forward error correction (FEC) [3]. These economics continue today with longer reach (>10 km) systems being deployed at 100 Gb∕s per each C-band (∼1550 nm) laser wavelength [4] achieved using higher modulation formats and digital coherent receiver (DCR) technology. DCRs incorporate a stable but unlocked optical local oscillator (LO) at the receiver together with significant DSP within a Si-CMOS ASIC to recover the timing and symbol phase, to correct for chromatic dispersion (CD), to perform polarization alignment, and to mitigate other channel impairments [5]. Similar to the deployment of the EDFA and DWDM technology, DCRs have revolutionized modern high-capacity fiber links, now enabling capacity close to the Shannon limit. One hundred gigabit-per-second dual-polarization quadrature phase shift keying (100G PDM-QPSK) transceivers with DCR technology have been available for more than 5 years [6]. Separately, the 40G/100G fiber-optic cables Ethernet standard is nearing completion. Within this IEEE 802.3 bm standard effort are goals to define 100 Gb∕s operation over at least 100 m of multimode fiber (MMF) [7] utilizing 4 lanes of 25 Gb∕s on OM4 fiber (100GBASE-SR4). These systems will be deployed within data centers to interconnect thousands of servers. Existing 850 nm vertical cavity surface emitting laser (VCSEL) technology is limited to ∼20 GHz bandwidth (over the required temperature range) which yields maximum single channel OOK rates to ∼25 Gb∕s [8]. Importantly, these rates are achieved using limited FEC and both transmitter and receiver equalization filters to provide gain boost at higher frequencies. Four hundred gigabit-per-second standards efforts have begun within the IEEE 802.3 400 Gb∕s study group. These efforts will exploit 100 G technologies and aim to support 400G over 100 m of MMF and potentially implementing higher modulation formats. In this paper we review the work performed within the Georgia Institute of Technology Terabit Optical Networking Consortium—formerly the 100G Consortium—which was founded in 2008 by ADVA Optical Networking, OFS, Verizon, and Ciena and hosted at Georgia Tech to investigate solutions and challenges for 100 Gb∕s transport (100g.gatech.edu). Since its inception, the Consortium has been joined by Harris Corp, Avago, Oclaro, Optametra, Picometrix, Nistica, Agilent, and RSoft. Over the past 6 years the consortium has evolved beyond 100 G and has begun to addresses the challenges for 400 Gb∕s and 1 Tb∕s data rates in signal processing, hardware, and simulations. We highlight the most recent efforts in high-capacity single-mode fiber (SMF) systems employing DCRs emphasizing the capabilities added by the use of DSP. We also describe shorter reach VCSEL-based MMF link technologies that support 25 Gb∕s and
greater serial data rates again emphasizing the impact of signal processing and the eventual transition to higher level modulation. 2. Electronic-Optical Interface: Waveform Generation and Detection A. Transmitters and Modulation
Optical quadrature modulation is typically achieved with an integrated structure consisting of two independent Mach–Zehnder interferometers (MZI) nested within an outer third MZI, Fig. 1. The outer MZI ensures a π∕2 phase difference between the two arms. Each polarization requires one of these nested MZI structures. The single-polarization quadrature amplitude modulation (QAM) signal can be described as s ∞ 2Es X st a cos2πf c t T s m−∞ I;m − aQ;m sin2πf c tgt − mT s :
(1)
The complex symbol am aI;m jaQ;m takes values defined by the order of the QAM format and gt is the pulse shape (which may span more than one symbol). In optical systems, the pulse shape is primarily determined by the low-pass transfer function of the external modulator structure, the drive electronics, and by the optional use of return-to-zero (RZ) pulse carving. Additionally, optical channel filters and wavelength switches affect the pulse shape; the cascaded behavior of these components is an area of active research [9–12]. For a detailed description of the exact transmitter see [13]. For the work reported here (Section 3), no special signal processing was utilized to craft specific pulse shapes at the transmitter. An RZ carver was selectively utilized for different experiments; the RZ carver is comprised of a MZM driven with a sinusoidal clock synchronous to the data stream. RZ carving offers better transmission performance in certain link configurations [14]. Waveform generation for long-haul transport has evolved beyond NRZ/RZ to support “per wavelength”
Fig. 1. I∕Q modulator constructed from three nested MZIs. To achieve the required carrier coherence along the waveguide paths, this structure is general integrated in a single package. Return-tozero carving (dashed box) can be optionally achieved with an external (or integrated) MZI driven by the symbol clock signal. 1 September 2014 / Vol. 53, No. 25 / APPLIED OPTICS
5825
data rates greater than 1 Tb∕s. Strategies are typically separated into two main approaches: Nyquist-WDM and coherent orthogonal frequency division multiplexing (Co-OFDM). Both NyquistWDM and Co-OFDM seek to stack spectral content as tight as possible while minimizing inter-channel interference (ICI) and inter-symbol interference (ISI), necessary conditions to approach the Shannon limit. For Nyquist-WDM, the ideal spectral shape for each subchannel is rectangular with the channel spacing (Δf ) equal to the baud rate. That is, the pulse gt within each channel is a sinc shape in the time domain. In contrast, Co-OFDM produces a sincshaped carrier in the frequency domain (rectangular pulse in the time domain). In practical systems, the transmitter cannot produce gt to perfectly eliminate ISI and ICI; efforts to reduce the impact of ISI and ICI are areas of active research [15]. B.
Optical Coherent Receivers
Optical coherent receivers are directly analogous to wireless or wire-line radios: a LO is mixed with the received signal to down convert the waveform to (or near) baseband for demodulation. In the ideal homodyne case, a coherent receiver linearly translates the channel of interest into a complex electrical baseband waveform. The general structure of a polarization-diverse coherent optical receiver is depicted in Fig. 2. The complex envelope of the received optical signal field Es t plus noise Nt and LO ELO are first split into X and Y polarization. Next, the X and Y components of the received signal and LO are independently combined via a 90° optical hybrid. The optical hybrid allows the subsequent mixing to extract both the in-phase and the quadrature components of the X or Y polarization of Es t. The fouroutput 90° optical hybrid, Fig. 2, is described by the transfer matrix
2 p 1 − ϵI expfjϕI g 6 p 6E 7 6 ϵI 6 27 6 6 7 6 p 4 E3 5 6 1 − ϵQ expfjϕQ g 4 p E4 ϵQ Es N ; × ELO 2
E1
3
p ϵI p 1 − ϵI expfjϕI g p j ϵQ p j 1 − ϵQ expfjϕQ g
3 7 7 7 7 7 5
(2)
where ϵ1 and ϵ2 are the power transfer coefficients, and ϕI and ϕQ are the phase misalignments of the two paths of the optical combiner. After the squarelaw photodetectors with responsivity Rk, the electrical signals Sk t Rk jEk tj2 are of the form S1 R1 1 − ϵI jEs j2 jNj2 2 RefEs N g ϵI jELO j2 p 2 expfjϕI g ϵI 1 − ϵI RefEs ELO NELO g: (3) If the photodiodes are perfectly balanced (Rk R) and the optical combiners perfectly matched ϵI ϵQ 0.5; ϕI ϕQ 0 the receiver rejects all common-mode direct-detection photocurrents, yielding SI t 2R RefEs tELO NtELO g;
(4)
SQ t 2R ImfEs tELO NtELO g:
(5)
In an ideal homodyne receiver, ELO is both temporally static and a perfect phase reference to the incoming optical field. That is, ELO is phase-locked to Es t and the term ELO is a constant scalar, enabling the photocurrents SI and SQ to vary proportionally to the real (I, in-phase) and imaginary (Q, quadrature) parts of the received signal. The coherent receiver is therefore capable of detecting the complex envelope of the in-phase and quadrature components of two
Fig. 2. Polarization-diverse optical coherent receiver. The stages of the receiver are coherent detection, digitization, and DSP. The performance of the receiver is determined by the combined performance of each optical and electronic component as well as the signal processing algorithms. 5826
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linear polarization modes (albeit at an arbitrary orientation [16,17]). Frequency locking of the LO with the incoming signal carrier had been the conventional approach for coherent optical receivers. Today, modern high-speed DSP capabilities allow the equivalent functionality in the digital domain after high-speed sampling of the electrical signals. The first term inside the Ref•g and Imf•g parts of Eqs. (4) and (5) is the desired signal term. The second term is the LO-noise beat term (the only beat term of relevance—both the signal–noise and noise–noise beat terms are eliminated in ideal balanced detection). Because a coherent receiver operates as a linear transformation the statistics of the both the signal and noise optical fields are preserved in the conversion to an electrical waveform. In contrast, direct-detection receivers with one or more delay interferometers yield non-Gaussian noise statistics. The advantages of coherent detection compared to direct detection can be summarized in three points. a. The coherent receiver offers received signal gain proportional to the LO power, improving receiver sensitivity. b. The output electrical photocurrent is a linear transformation of the optical signal field (containing full phase and amplitude information). c. The coherent receiver enables DSP in the electronics domain. DSP techniques have advanced at a breathtaking pace in the past decade and have largely driven the exponential proliferation of wireless and mobile electronics. With the introduction of optical coherent receivers, DSP algorithms can fully compensate or mitigate nearly all channel impairments of a fiberoptic system in the purely electronic domain. C.
Signal Processing for Digital Transmission
For optical fiber channels, there are four primary processing steps that the signal processing engine must perform regardless of the signal modulation format, Fig. 2. In general order these steps are CD compensation, symbol timing recovery, polarization demultiplexing, and carrier phase recovery. We also perform sampling skew removal immediately after digitization and before CD equalization and leastmean square (LMS) equalization before symbol detection. This first step removes any subsample-rate offset between the four sampled channels using a high-precision fractionally spaced filter, determined by a careful measurement and calibration of the sampling behavior of the digital oscilloscope used as the sampler. After digitization and sampling skew removal the DSP must first compensate for the accumulated CD [18]. The transfer function H CD ω expfjλ20 DLω2 ∕4πcg
(6)
describes the dominant quadratic phase dependence of second-order dispersion. The value DL s∕m
represents the total accumulated dispersion that the filter compensates and is as large as 20; 000 ps∕nm or greater for long-haul systems. Since the single channel signal bandwidths are ∼30 GHz (0.27 nm) the transfer function is typically implemented in the frequency domain since the temporal delays can be 5000 ps (5000∕32.5 153.8 bit-periods at 32 Gbaud). Optimum CD compensation can be determined by maximizing the variance of the received signal. Dispersion compensation was managed using compensating fiber until the deployment of DCRs. To recover the symbol timing phase we implement the nondata-aided (NDA) feed-forward digital filter and square method [19]. This block of the DSP estimates the symbol time on each polarization independently by first squaring the symbols and then centering on the maximum eye opening. That is, the timing estimate returns 1 τˆ − arg 2π
LN−1 X m0
jxm1
j2
j2πm ; exp − N
(7)
which is the normalized phase between −1∕2 and 1∕2. In Eq. (7), xm are the message symbols, L is the number of symbols per frame, and N is the number of samples per symbol. The magnitude square operation is proportional to the instantaneous power and maximum at the maximum eye opening since the QPSK waveform will, with high probability, pass through regions of low power. Polarization demultiplexing in SMF links is a 2 × 2 MIMO process governed by the Jones matrix that describes the fiber and the alignments of the transmitter and receiver linearly polarized E-fields. For dual-polarization fiber transmission, the MIMO equalizer is arranged in a “butterfly” structure, Fig. 2, and adapts four sets of complex coefficients, bridging each of the possible paths from X and Y input to X and Y output, to jointly minimize the resulting error in the output [error, would be determined by the choice of updating rule—the constant modulus algorithm (CMA) is a common choice]. Convergence is assured to avoid false recovery at both X and Y outputs when constrained by the relationship ¯ hxx h¯ yx
h¯ xy u¯ −¯v h¯ yy
v¯ ; u¯
(8)
where u and v are complex-valued vectors with one element per equalizer tap. The complex conjugate operation also implies a time reversal of the vectors. The CMA is the classical choice for QPSK-based fiber transmission [20,21] for optimizing the polarization demux. However, CMA does not adapt optimally for modulation formats that are not constrained to a constant envelope. An alternate method of separating polarization uses independent component analysis (ICA). ICA is based on the observation that the two orthogonally polarized waveforms are statistically independent and uncorrelated. The 1 September 2014 / Vol. 53, No. 25 / APPLIED OPTICS
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Table 1.
Nominal Fiber Parameters, Single Mode at 1550 nm
Parameter
SMF
Loss, α dB∕km Core effective area, Aeff μm2 Dispersion, D ps∕nm km Nonlinear coeff, γ×10−3 m−1 W−1
MDF
0.19 80 17.0 1.16
0.21 55 7.3 1.91
LAF 0.18 130 20 .717
principal of ICA source separation is the central limit theorem: the mixture of non-Gaussian signals tends to Gaussian. Therefore, ICA attempts to maximize the “non-Gaussianity” (entropy) of the signal. The advantage to this approach is that an ICA equalizer can separate any two signal sources regardless of modulation format provided that they are each, in general, not Gaussian-distributed [22]. The ICA equalizer is configured in an identical fashion to the butterfly structure of the CMA-based equalizer, Fig. 2. The tap update rule, however, is based on the natural gradient method that possesses the equivariance property; it converges asymptotically based on the stochastic properties of the source signals and regardless of the channel (or mixing) description [22]. A step-by-step analysis of the ICAbased polarization demultiplexor is available in [23]. For optical systems where the two convolved signals are the orthogonal polarization modes, the polarization demultiplexing equalizer is also required to compensate for polarization mode dispersion (PMD). While a single-tap ICA equalizer can asynchronously separate sampled data, to compensate for PMD the equalizer needs enough (more than one) taps to cover the time walk-off of the polarization modes. Thus timing recovery must be performed prior to the polarization mode separation via ICA. The carrier phase recovery algorithm used for 16 QAM transmission is derived from the “stop-andgo” decision-directed algorithm described in [24] and in [25]. Also called a “phase integrator,” the algorithm employs a decision-directed recovery loop to estimate the carrier phase with the rule θk1 θk − μθ Imfzk ek g;
(9)
where θk is the phase estimate, zk are the message symbols, μθ is the step size parameter, and ek zk − ak is the error signal.
The LMS equalizer is a classical adaptive filter that can also be considered a stochastic gradient algorithm; its derivation is covered thoroughly in the literature [26,27]. No further cross-polarization interference cancellation is attempted (i.e., this filter is not arranged in a “butterfly” structure). The purpose of this filter is to remove any residual CD and ISI that the channel imposes, and to output a single sample per symbol for detection. We note that although the basic DSP functions have been implemented in other systems for many years, the data rate and the impairments of optical channels present many new implementation challenges [28]. D.
Georgia Tech Terabit Optical Network Testbed
A wide variety of fibers have been made available by OFS for link transmission tests within the consortium, among them standard SMF, large area fiber (LAF), and medium dispersion fiber (MDF), Table 1. Each span is comprised of fiber with 80–90 km lengths. Two different link configurations are available: point-to-point (PtP) link and recirculating loop, Fig. 3. In the PtP link, Fig. 3(a), each span is comprised of one EDFA with midstage access for optional dispersion compensation modules (DCM). Multiple spans of fiber and EDFAs are used to simulate long-haul transmission systems with total reach of ∼1000 km. Longer reach systems are simulated using a recirculating loop, Fig. 3(b), which allows the optical signal to pass through the loop multiple times. The recirculating loop includes three spans of fiber and corresponding EDFAs for loss compensation, a booster EDFA, and a gain equalization filter (implemented with a wavelength selective switch). These network elements have been provided by ADVA Optical Networks. Two high-speed acousto-optic switches are used to control the load in and out of optical signals. In the data load-in stage, the loadin switch (SW1) is on and loop switch (SW2) is off. The incoming optical signals pass through SW1 and are split into two parts by a 2 × 2 fiber-optic directional coupler. One part is loaded into the transmission system and the other is sent to the receiver. In the loop stage, SW1 is off and SW2 is set to on so that the optical signals can circulate through the loop. Finally, a time-gating pulse enables the receiver
Fig. 3. Experimental setup for various single-mode network configurations and fiber types (nominal operating wavelength: 1550 nm). 5828
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Fig. 4. Georgia Tech Terabit Consortium Testbed.
to detect only the optical signals that passes through the transmission system for a predetermined number of circulations. The number of circulations is limited by the EDFA-induced ASE noise limit and any enhanced nonlinear effects. Extensive transmission results are available in [13,14,27]. In addition to the SMF testbed, Fig. 4, the Georgia Tech Terabit Optical Networking Consortium, also includes an extensive MMF (also provided by OFS) for a separate short-reach testbed. MMF is utilized in a variety of applications including data centers and high performance computing which involve short reach links where the deployed technologies are more cost sensitive. Hence, these links are required to minimize complexity and coherent systems are unlikely for the foreseeable future. Typically such links use direct modulation of VCSELs with various types of MMF, Table 2. For example, the emerging 100GBASE-SR4 standard uses 25G VCSELs over four lanes (distinct fibers) of MMF at a data rate of 25.78125 Gb∕s to allow forward error correction. Figure 5 shows the schematic of the experimental testbed with state-of-the-art 25 G multimode oxide-aperture VCSEL die, a MMF channel, and custom designed 30 G optical receivers created at Georgia Tech. The optical receiver consists of an InGaAs PIN 20 μm diameter photodiode with responsivity ∼0.36 A∕W at 850 nm and TIA on a laser-etched board with a net effective bandwidth ∼28 GHz. The 30 Gbit∕s capable SHF 12124A outputs high-quality electrical PRBS patterns with a built-in 4-tap, T-spaced FIR pre-emphasis filter that compensates bandwidth limitations in the link. 3. Gaussian Noise Model of Nonlinear Link Noise
Fiber-optic transmission is fundamentally limited by nonlinear refraction [11], a phenomena whereby the phase of the propagating signal is changed proportionally to its intensity. This effect limits the total available optical signal-to-noise ratio (OSNR); the launch power (which is the primary method of controlling the OSNR) can only be increased to a certain point, beyond which the performance of the signal begins to degrade. The fiber nonlinearities create both intra- and inter-channel mixing products via the Table 2.
Fig. 5. Georgia Tech MMF experimental network with custom receiver and high-speed VCSELs.
four-wave mixing (FWM) process that interferes with the desired signals and increases with increasing launch power. Generally, the total fiber-optic network performance is determined by including all copropagating signals in the fiber (data channels, ASE noise, etc.) and numerically simulating the propagation with FWM and other nonlinear impairments over the entire link, which may have a varying number of WDM channels a be comprised of spans of different fiber type and distance. This is typically accomplished by numerically solving the nonlinear Schrödinger wave equation via step-by-step methods that require both time domain computations for nonlinearities and frequency domain computations to handle CD; simulations are a slow, time-consuming process. However, it has been shown that systems without inline dispersion compensation offer performance advantages over dispersion-managed systems [29]. This arises from the fact that [29–33] uncompensated dispersion renders the four signal components—X, Y, I, and Q—statistically independent, noise-like, and Gaussian-distributed at reception. This Gaussian characteristic is also maintained throughout the DSP chain. In addition to performance benefits, many uncompensated systems are dramatically easier to assess in the nonlinear regime where many deployed systems operate. Perturbative models of nonlinear propagation which did not work well for dispersionmanaged systems can now accurately predict systems for uncompensated transmission [34]. Specifically, it allows the mixing products to be treated as noise. Thus, the definition of signal-to-noise ratio (SNR) can be recast by adding the variance of the nonlinear noise directly to the variance of the ASE
Nominal Fiber Parameters, Multimode
Parameter Dispersion, D ps∕nm km EMBc (MHz-km) Dispersion, D ps∕nm km EMBc (MHz-km)
λ0
OM3
OM4
850 nm
108 2800 44 2400
108 5700 44 1000 km distances. Software-defined coherent optical transceivers may be the next logical step in the evolution of transport networks. The SDOT relies on a hybrid analog/ digital hardware implementation, DSP techniques, and flexible electro-optical hardware; it provides unparalleled flexibility for traffic management and system diagnosis. MMF links meet the critical short-reach (
