Experimental demonstration of low-complexity fiber chromatic dispersion mitigation for reduced guard-interval OFDM coherent optical communication systems based on digital spectrum sub-band multiplexing.

We experimentally demonstrate a novel digital signal processing (DSP) structure for reduced guard-interval (RGI) OFDM coherent optical systems. The proposed concept is based on digitally slicing optical channel bandwidth into multiple spectrally disjoint sub-bands which are then processed in parallel. Each low bandwidth sub-band has a smaller delay-spread compared to a full-band signal. This enables compensation of both chromatic dispersion (CD) and polarization mode dispersion using a simple timing and one-tap-per-symbol frequency domain equalizer with a small cyclic prefix overhead. In terms of the DSP architecture, this allows for a highly efficient parallelization of DSP tasks performed over the received signal samples by deploying multiple processors running at a lower clock rate. It should be noted that this parallelization is performed in the frequency domain and it allows for flexible optical transceiver schemes. In addition, the resulting optical receiver is simplified due to the removal of the CD compensation equalizer compared to conventional RGI-OFDM systems. In this paper we experimentally demonstrate digital sub-banding of optical bandwidth. We test the system performance for different modulation formats (QPSK, 16QAM and 32QAM) over various transmission distances and optical launch powers using a 1.5% CP overhead in all scenarios. We also compare the proposed RGI-OFDM architecture performance against common single carrier modulation formats. At the same total data rate and signal bandwidth both systems have similar performance and transmission reach whereas the proposed method allows for a significant reduction of computational complexity due to removal of CD pre/post compensation equalizer.

Nonlinear Digital Back Propagation compensator for coherent optical OFDM based on factorizing the Volterra Series Transfer Function.

We introduce an efficient and accurate nonlinear compensator (NLC) for digital back-propagation (DBP) of coherent optical OFDM receivers, based on a factorization procedure for the Volterra Series Transfer Function (VSTF) with 3N degrees of freedom for N frequency samples. The O(N2) nonlinear compensation complexity of generic Volterra evaluation (normalized per-subcarrier) is reduced to 28 + 6logN. Our analysis and simulations indicate that this NLC system outperforms previous VSTF-based non-linear compensation methods. Compared to a most recent VSTF-based method, the new method incurs 52% extra computational complexity in return for improved nonlinear tolerance of ~2 dB for the particular analyzed link.

Doubling direct-detection data rate by polarization multiplexing of 16-QAM without active polarization control.

We introduce and simulate a technique enabling to utilize the polarization dimension in direct-detection optical transmission, supporting polarization multiplexing (POL-MUX) over direct-detection (DD) methods previously demonstrated for a single polarization such as direct-detection OFDM. POL-MUX is currently precluded in self-coherent DD with remotely transmitted pilot, as signal x pilot components may randomly fade out. We propose POL-MUX transmission of advanced modulation formats, such as 16-QAM and higher, by means of a novel low-complexity photonic integrated optical front-end and adaptive 3x2 MIMO DSP. The principle of operation is as follows: an additional X x Y cross-polarizations signal is generated, providing three projections onto an over-complete frame of three dependent vectors. This enables to resiliently reconstruct the received state of polarization even when the remotely transmitted pilot fades along one of the received polarization axes.

Estimating the Volterra Series Transfer Function over coherent optical OFDM for efficient monitoring of the fiber channel nonlinearity.

We present an efficient method for system identification (nonlinear channel estimation) of third order nonlinear Volterra Series Transfer Function (VSTF) characterizing the four-wave-mixing nonlinear process over a coherent OFDM fiber link. Despite the seemingly large number of degrees of freedom in the VSTF (cubic in the number of frequency points) we identified a compressed VSTF representation which does not entail loss of information. Additional slightly lossy compression may be obtained by discarding very low power VSTF coefficients associated with regions of destructive interference in the FWM phased array effect. Based on this two-staged VSTF compressed representation, we develop a robust and efficient algorithm of nonlinear system identification (optical performance monitoring) estimating the VSTF by transmission of an extended training sequence over the OFDM link, performing just a matrix-vector multiplication at the receiver by a pseudo-inverse matrix which is pre-evaluated offline. For 512 (1024) frequency samples per channel, the VSTF measurement takes less than 1 (10) msec to complete with computational complexity of one real-valued multiply-add operation per time sample. Relative to a naïve exhaustive three-tone-test, our algorithm is far more tolerant of ASE additive noise and its acquisition time is orders of magnitude faster.

An analytical study of the improved nonlinear tolerance of DFT-spread OFDM and its unitary-spread OFDM generalization.

DFT-spread (DFT-S) coherent optical OFDM was numerically and experimentally shown to provide improved nonlinear tolerance over an optically amplified dispersion uncompensated fiber link, relative to both conventional coherent OFDM and single-carrier transmission. Here we provide an analytic model rigorously accounting for this numerical result and precisely predicting the optimal bandwidth per DFT-S sub-band (or equivalently the optimal number of sub-bands per optical channel) required in order to maximize the link non-linear tolerance (NLT). The NLT advantage of DFT-S OFDM is traced to the particular statistical dependency introduced among the OFDM sub-carriers by means of the DFT spreading operation. We further extend DFT-S to a unitary-spread generalized modulation format which includes as special cases the DFT-S scheme as well as a new format which we refer to as wavelet-spread (WAV-S) OFDM, replacing the spreading DFTs by Hadamard matrices which have elements +/-1 hence are multiplier-free. The extra complexity incurred in the spreading operation is almost negligible, however the performance improvement with WAV-S relative to plain OFDM is more modest than that achieved by DFT-S, which remains the preferred format for nonlinear tolerance improvement, outperforming both plain OFDM and single-carrier schemes.

A self-coherent receiver for detection of PolMUX coherent signals.

A self-coherent receiver capable of demultiplexing PolMUX-signals without an external polarization controller is presented. Training sequences are introduced to estimate the polarization rotation, and a decision feedback recursive algorithm mitigates the random walk of the recovered field. The concept is tested for a PolMUX-DQPSK modulation format where one polarization carries a normal DQPSK signal while the other polarization is encoded as a progressive phase-shift DQPSK signal. An experimental demonstration of the scheme for a 112 Gbit/s PolMUX-DQPSK signal is presented.

Self-coherent complex field reconstruction with in-phase and quadrature delay detection without a direct-detection branch.

Self-coherent detection with interferometric field reconstruction aims at retrieving the complex-valued optical field (amplitude and phase) by digitally processing delay interferometer (DI) measurements, in order to realize a differential direct detection receiver with capabilities akin to that of a fully coherent receiver with polarization multiplexing, albeit without requiring a local oscillator laser in the receiver. Here we introduce a novel digital recursive algorithm capable of accurately reconstructing the optical complex field (both amplitude and phase) solely from the quadrature DI outputs, eliminating the AM photo-detector branch. We analyze a key impairment namely the accumulation of errors and fluctuations in the reconstructed amplitude and phase due to ADC quantization noise, recirculating in the recursion. We introduce signal processing measures to effectively mitigate this noise impairment leading to a potentially practical self-coherent receiver, demonstrated in this paper for a single polarization. We also investigate the range of applicability of self-coherent detection concluding that it is most suitable to relatively low baud-rate systems such as passive optical networks, for which application the self-coherent receiver outperforms the coherent homodyne receiver due to its improved laser noise tolerance, obtained due to the removal of the optical local oscillator.

Joint phase noise and frequency offset estimation and mitigation for optically coherent QAM based on adaptive multi-symbol delay detection (MSDD).

This paper extends our prior coherent MSDD Carrier Recovery system from QPSK to QAM operation and also characterizes for the first time the Carrier Frequency Offset (CFO) mitigation capabilities of the novel MSDD for QAM systems. We introduce and numerically investigate the performance of an improved MSDD carrier recovery system (differing from the one disclosed in our MSDD for QPSK prior paper), automatically adapting to the channel statistics for optimal phase-noise mitigation. Remarkably, we do not require a separate structure to estimate and mitigate CFO, but the same adaptive structure originally intended for phase noise mitigation is shown to also automatically provide frequency offset estimation and recovery functionality. The CFO capture range of our system is in principle infinite, whereas prior CFO mitigation systems have CFO capture ranges limited to a small a fraction of the baud-rate. When used for 16-QAM with coherent-grade lasers of 100 KHz linewidth, our MSDD system attains the best tradeoffs between performance and complexity, relative to other carrier recovery systems combining blind-phase-search with maximum likelihood detection. We also present additional MSDD phase-noise recovery system variants whereby substantially reduced complexity is traded off for slightly degraded performance. Our MSDD system is able to switch "on-the-fly" to various m-QAM constellation sizes, e.g. seamlessly transition between 16-QAM and QPSK, which may be useful for dynamically adaptive optical networks.

Spatially distributed successive approximation register (SDSAR) photonic ADCs based on phase-domain quantization.

We explore photonic ADC architectures based on encoding voltage-under-test into phase. The first step is to identify two basic optical building blocks: the optical phase comparator (1-bit ADC), based on interferometric comparison of phases in the well-known balanced photo-detection configuration, and the optical 1-bit DAC, namely electro-optic modulation with a bipolar electrical pulse. Equipped with these fundamental building blocks, we proceed to systematically port and adapt known ADC quantization architectures to photonic ADC, conceiving a hybrid between the Successive Approximation Register (SAR) and the Pipeline classic ADC architectures, referred to here as Spatially Distributed SAR (SDSAR). This novel photonic ADC, constructed out of B 1-bit ADCs and B-2 1-bit DACs, with B the number of bits, is not equivalent to any of the previous photonic ADCs in the literature, but appears superior to prior schemes in both optical power efficiency and electro-optic modulation complexity. We derive upper bounds on resolution, Effective Number of Bits (ENOB) performance as a function of average optical power for the new SDSAR device, developing analytic and numeric Monte-Carlo statistical models, comprising quantization, shot, thermal and DAC voltage noise sources. Our findings indicate that SDSAR is limited to ~11.5 ENOBs, assuming state-of-the-art mode-locked-lasers providing ~250 mW of average power (assuming ~7 dB excess losses). However, this upper bound is not tight, due to various physical impairments. In particular, the mode locked laser jitter is shown to have negligible impact on overall performance for RMS jitter < 20 fsec.

Carrier phase estimation for optically coherent QPSK based on Wiener-optimal and adaptive Multi-Symbol Delay Detection (MSDD).

The MSDD carrier phase estimation technique is derived here for optically coherent QPSK transmission, introducing the principle of operation while providing intuitive insight in terms of a multi-symbol extension of naïve delay-detection. We derive here for the first time Wiener-optimized and LMS-adapted versions of MSDD, introduce simplified hardware realizations, and evaluate complexity and numerical performance tradeoffs of this highly robust and low-complexity carrier phase recovery method. A multiplier-free carrier phase recovery version of the MSDD provides nearly optimal performance for linewidths up to ~0.5 MHz, whereas for wider linewidths, the Wiener or LMS versions provide optimal performance at about 9 taps, using 1 or 2 complex multipliers per tap.

Filter-bank based efficient transmission of reduced-guard-interval OFDM.

We propose a new way to structure the digital signal processing for reduced guard-interval (RGI) OFDM optical receivers. The idea is to digitally parallelize the processing over multiple parallel virtual sub-channels, occupying disjoint spectral sub-bands. This concept is well known in the optical or analog sub-carrier domains, but it turns out that it can also be performed efficiently in the digital domain. Here we apply critically sampled uniform analysis and synthesis DFT filter bank signal processing techniques in order to realize a novel hardware efficient variant of RGI OFDM, referred to as Multi-Sub-Band OFDM (MSB-OFDM), reducing by 10% receiver computational complexity, relative to a single-polarization version of the CD pre-equalizer. In addition to being more computationally efficient than a conventional RGI OFDM system, the signal flow architecture of our scheme is amenable to being more readily realized over multiple FPGAs, for experimental demonstrations or flexible prototyping.

Cascadable and reconfigurable photonic logic gates based on linear lightwave interference and non-linear phase erasure.

Feasibility of cascading and reconfiguring a pair of linear-nonlinear all-optical logic gate structures is experimentally demonstrated using RF photonics. Progress in highly integrated O/E/O repeaters over Si/InP hybrid platforms enables large-scale reconfigurable gate arrays.

All-optical linear reconfigurable logic with nonlinear phase erasure.

We introduce a novel all-optical logic architecture whereby the gates may be readily reconfigured to reprogram their logic to implement (N)AND/(N)OR/X(N)OR. A single gate structure may be used throughout the logic circuit to implement multiple truth tables. The reconfiguration is effected by an optical reference signal. The reference may also be adapted to an arbitrary Boolean complex alphabet at the gate logic inputs and calibrated to correct gate imperfections. The all-optical gate structure is partitioned into a linear interferometric front end and a nonlinear back end. In the linear section, two optical logic inputs, along with a reference signal, linearly interfere. The nonlinear back end realizes a phase-erasure (or phase-reset) function. The reconfiguration and recalibration capabilities, along with the functional decoupling between the linear and nonlinear sections of each gate, facilitate the potential aggregation of large gate counts into logic arrays. A fundamental lower bound for the expended energy per gate is derived as 3hnu+kT ln2 Joules per bit.

Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links.

We develop an analytic model of Coherent Optical Orthogonal Frequency Division Multiplexing (OFDM) propagation and detection over multi-span long-haul fiber links, comprehensively and rigorously analyzing the impairments due the combined effects of FWM, Dispersion and ASE noise. Consistent with prior work of Innoe and Schadt in the WDM context, our new closed-form expressions for the total FWM received power fluctuations in the wake of dispersive phase mismatch in OFDM transmission, indicate that the FWM contributions of the multitude of spans build-up on a phased-array basis. For particular ultra-long haul link designs, the effectiveness of dispersion in reducing FWM is far greater than previously assumed in OFDM system analysis. The key is having the dominant FWM intermodulation products due to the multiple spans, destructively interfere, mutually cancelling their FWM intermodulation products, analogous to operating at the null of a phased-array antenna system. By applying the new analysis tools, this mode of effectively mitigating the FWM impairment, is shown under specific dispersion and spectral management conditions, to substantially suppress the FWM power fluctuations. Accounting for the phased-array concept and applying the compact OFDM design formulas developed here, we analyzed system performance of a 40 Gbps coherent OFDM system, over standard G.652 fiber, with cyclic prefix based electronic dispersion compensation but no optical compensation along the link. The transmission range for 10-3 target BER is almost tripled from 2560 km to 6960 km, relative to a reference system performing optical dispersion compensation in every span (ideally accounting for FWM and ASE noise and the cyclic prefix overhead, but excluding additional impairments).

Efficient hierarchical list decoder for massive optical MIMO transmission.

We propose a novel MIMO scheme over multimode fiber, acting as a distributed random code generator fed by spatial codes, using silicon photonics in the transmitter and efficient list-based hierarchical submaximum-likelihood electronic detection in the receiver, providing an alternative to CWDM for implementation of ultra-high speed parallel transmission over short-range optical interconnects.

Chromatic dispersion tolerance in optimized NRZ-, RZ- and CSRZ-DPSK demodulation.

We present the results of a comprehensive analysis optimizing the performance of DPSK systems with increased FSR and narrow optical filtering, establishing improved chromatic dispersion tolerance of NRZ-DPSK by 20%, RZ-DPSK by 71% and CSRZ-DPSK by 74% approximately. Transmitting a 40Gb/s signals on a spectrally efficient 50GHz DWDM grid still exhibit improvements of 7% for NRZ-DPSK, 37% for RZ-DPSK and 22% for CSRZ-DPSK, relative to a typical DPSK receiver. The optimized delay and optical filtering scale with the amount of chromatic dispersion. We also demonstrate the impact of limited transmitter bandwidth on optimal optical filtering and bit delay parameters.

Combination of optical and electronic logic gates for error correction in multipath differential demodulation.

We present an optical multipath error correction technique for differentially encoded modulation formats such as differential-phase-shift-keying (DPSK) and differential polarization shift keying (DPolSK) for fiber-based and free-space communication. This multipath error correction method combines optical and electronic logic gates. The scheme can easily be implemented using commercially available interferometers and high speed logic gates and does not require any data overhead therefore does not affect the effective bandwidth of the transmitted data. It is not merely compatible but also complementary to error correction codes commonly used in optical transmission systems such as forward-error-correction (FEC). The technique consists of separating the demodulation at the receiver in multiple paths. Each path consists of a Mach-Zehnder interferometer with a different integer bit delay used in each path. Some basic logic operations follow and the three paths are compared using a simple majority vote algorithm. Experimental results show that the scheme improves receiver sensitivity by 1.5 dB at BER of 10(-3),in back-to-back configuration. Numerical results indicate a 1.6 dB improvement in the presence of Chromatic Dispersion for a 25% increase in tolerance for a 3dB penalty from +/-1220 ps/nm to +/-1520 ps/nm. and a 0.35 dB improvement for back-to-back operation.

Broadcast MIMO over multimode optical interconnects by modal beamforming.

We introduce broadcast MIMO communication systems over multimode optical fibers or waveguides. Based on BeamForming (BF) at the transmitter, decoupled virtual subchannels are provided to multiple uncoordinated conventional direct detection receivers. This optical technique, extending Zero-Forcing BF wireless MIMO techniques to quadratic detection, is applicable to photonic interconnects, e.g. short-reach point-to-(multi)point transmission over MMF, up to rates of 100 Gb/s for distances up to 100 m.

Generalized Stokes parameters shift keying approach to multichip differential phase encoded optical modulation formats.

Conventional and advanced modulation formats that simultaneously modulate two or more of the optical attributes of phase, amplitude, and polarization and/or utilize observation intervals longer than two chips (time slots) are designed by using a unified interpretation as signaling by means of generalized Stokes parameters. In particular, the new paradigm is applied to the recently introduced multichip extension of optical differential phase shift keying.

Quantum key distribution over a fiber-optic channel by means of pulse position modulation.

New methods are proposed for extending the range of fiber-optic one-way quantum key distribution (QKD), inspired by classical optical communication formats. A new time-domain technique based on pulse position modulation (PPM) is combined with differential phase-shift keying to optically implement a six-state protocol. Finally, some recently proposed PPM schemes are critically reviewed and applied to synthesize a new QKD asymmetric optical realization, applicable to local or metropolitan area networks.