From cardinal spline wavelet bases to highly coherent dictionaries

Wavelet families arise by scaling and translations of a prototype function, called the mother wavelet. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis scheme. Thus, the usual way of increasing the dimension of the multi-resolution subspaces is by augmenting the scaling factor. We show here that, when working on a compact interval, the identical effect can be achieved without changing the wavelet scale but reducing the translation parameter. By such a procedure we generate a redundant frame, called a dictionary, spanning the same spaces as a wavelet basis but with wavelets of broader support. We characterize the correlation of the dictionary elements by measuring their 'coherence' and produce examples illustrating the relevance of highly coherent dictionaries to problems of sparse signal representation.

Unrepeatered field transmission of 2 Tbit/s multi-banded coherent WDM over 124 km of installed SMF

In this paper we report field transmission of a 2Tbit/s multi-banded Coherent WDM signal over BT Ireland's installed SMF, using EDFA amplification only, with mixed Ethernet (with FEC) and PRBS payloads. To the best of our knowledge, the results obtained represent the highest total capacity transmitted over installed SMF with orthogonal subcarriers. BERs below 10(-5) and no frame-loss were recorded for all 49 subcarriers. Extended BER measurements over several hours showed fluctuations that can be attributed to PMD and to dynamic effects associated with clock instabilities.

PMD tolerance of 288 Gbit/s Coherent WDM and transmission over unrepeatered 124 km of field-installed single mode optical fiber

Low-cost, high-capacity optical transmission systems are required for metropolitan area networks. Direct-detected multi-carrier systems are attractive candidates, but polarization mode dispersion (PMD) is one of the major impairments that limits their performance. In this paper, we report the first experimental analysis of the PMD tolerance of a 288Gbit/s NRZ-OOK Coherent Wavelength Division Multiplexing system. The results show that this impairment is determined primarily by the subcarrier baud rate. We confirm the robustness of the system to PMD by demonstrating error-free performance over an unrepeatered 124km field-installed single-mode fiber with a negligible penalty of 0.3dB compared to the back-to-back measurements. (C) 2010 Optical Society of America

MAP detection for impairment compensation in coherent WDM systems

We propose a novel recursive-algorithm based maximum a posteriori probability (MAP) detector in spectrally-efficient coherent wavelength division multiplexing (CoWDM) systems, and investigate its performance in a 1-bit/s/Hz on-off keyed (OOK) system limited by optical-signal-to-noise ratio. The proposed method decodes each sub-channel using the signal levels not only of the particular sub-channel but also of its adjacent sub-channels, and therefore can effectively compensate deterministic inter-sub-channel crosstalk as well as inter-symbol interference arising from narrow-band filtering and chromatic dispersion (CD). Numerical simulation of a five-channel OOK-based CoWDM system with 10Gbit/s per channel using either direct or coherent detection shows that the MAP decoder can eliminate the need for phase control of each optical carrier (which is necessarily required in a conventional CoWDM system), and greatly relaxes the spectral design of the demultiplexing filter at the receiver. It also significantly improves back-to-back sensitivity and CD tolerance of the system.

Experimental comparison of coherent polarization-switched QPSK to polarization-multiplexed QPSK for 10 x 100 km WDM transmission

Polarization-switched quadrature phase-shift keying has been demonstrated experimentally at 40.5Gb/s with a coherent receiver and digital signal processing. Compared to polarization-multiplexed QPSK at the same bit rate, its back-to-back sensitivity at 10-3 bit-error-ratio shows 0.9dB improvement, and it tolerates about 1.6dB higher launch power for 10 × 100km, 50GHz-spaced WDM transmission allowing 1dB penalty in required optical-signal-to-noise ratio relative to back-to-back.

Impact of longitudinal power budget in coherent transmission systems employing digital back-propagation

We report the impact of longitudinal signal power profile on the transmission performance of coherently-detected 112 Gb/s m-ary polarization multiplexed quadrature amplitude modulation system after compensation of deterministic nonlinear fibre impairments. Performance improvements up to 0.6 dB (Q(eff)) are reported for a non-uniform transmission link power profile. Further investigation reveals that the evolution of the transmission performance with power profile management is fully consistent with the parametric amplification of the amplified spontaneous emission by the signal through four-wave mixing. In particular, for a non-dispersion managed system, a single-step increment of 4 dB in the amplifier gain, with respect to a uniform gain profile, at similar to 2/3(rd) of the total reach considerably improves the transmission performance for all the formats studied. In contrary a negative-step profile, emulating a failure (gain decrease or loss increase), significantly degrades the bit-error rate.

Offset-QAM based coherent WDM for spectral efficiency enhancement

Optically multiplexed multi-carrier systems with channel spacing reduced to the symbol rate per carrier are highly susceptible to inter-channel crosstalk, which places stringent requirements for the specifications of system components and hinders the use of high-level formats. In this paper, we investigate the performance benefits of using offset 4-, 16-, and 64-quadrature amplitude modulation (QAM) in coherent wavelength division multiplexing (CoWDM). We compare this system with recently reported Nyquist WDM and no-guard-interval optical coherent orthogonal frequency division multiplexing, and show that the presented system greatly relaxes the requirements for device specifications and enhances the spectral efficiency by enabling the use of high-level QAM. The achieved performance can approach the theoretical limits using practical components.

Novel real-time homodyne coherent receiver using a feed-forward based carrier extraction scheme for phase modulated signals

We report a novel real-time homodyne coherent receiver based on a DPSK optical-electrical-optical (OEO) regenerator used to extract a carrier from carrier-less phase modulated signals based on feed-forward based modulation stripping. The performance of this non-DSP based coherent receiver was evaluated for 10.66Gbit/s BPSK signals. Self-homodyne coherent detection and homodyne detection with an injection-locked local oscillator laser was demonstrated. The performance was evaluated by measuring the electrical signal-to-noise (SNR) and recording the eye diagrams. Using injection-locking for the LO improves the performance and enables homodyne detection with optical injection-locking to operate with carrier-less BPSK signals without the need for polarization multiplexed pilot-tones.

Impact of Raman amplification on a 2 Tb/s coherent WDM system

The impact of hybrid erbium-doped fiber amplifier (EDFA)/Raman amplification on a spectrally efficient coherent-wavelength-division-multiplexed (CoWDM) optical communication system is experimentally studied and modeled. Simulations suggested that 23-dB Raman gain over an unrepeatered span of 124 km single-mode fiber would allow a decrease of the mean input power of ~6 dB for a fixed bit-error rate (BER). Experimentally we demonstrated 1.2-dB Q-factor improvement for a 2-Tb/s seven-band CoWDM with backward Raman amplification. The system delivered an optical signal-to-noise ratio of 35 dB at the output of the receiver preamplifier providing a worst-case BER of 2 × 10 -6 over 49 subcarriers at 42.8 Gbaud, leaving a system margin (in terms of Q -factor) of ~4 dB from the forward-error correction threshold.

Towards a practical implementation of coherent WDM:analytical, numerical, and experimental studies

Future optical networks will require the implementation of very high capacity (and therefore spectral efficient) technologies. Multi-carrier systems, such as Orthogonal Frequency Division Multiplexing (OFDM) and Coherent WDM (CoWDM), are promising candidates. In this paper, we present analytical, numerical, and experimental investigations of the impact of the relative phases between optical subcarriers of CoWDM systems, as well as the effect that the number of independently modulated subcarriers can have on the performance. We numerically demonstrate a five-subcarrier and three-subcarrier 10-GBd CoWDM system with direct detected amplitude shift keying (ASK) and differentially/coherently detected (D) phase shift keying (PSK). The simulation results are compared with experimental measurements of a 32-Gbit/s DPSK CoWDM system in two configurations. The first configuration was a practical 3-modulator array where all three subcarriers were independently modulated, the second configuration being a traditional 2-modulator odd/even configuration, where only odd and even subcarriers were independently modulated. Simulation and experimental results both indicate that the independent modulation implementation has a greater dependency on the relative phases between subcarriers, with a stronger penalty for the center subcarrier than the odd/even modulation scheme.

Compensation of nonlinear fibre impairments in coherent systems employing spectrally efficient modulation formats

We investigate electronic mitigation of linear and non-linear fibre impairments and compare various digital signal processing techniques, including electronic dispersion compensation (EDC), single-channel back-propagation (SC-BP) and back-propagation with multiple channel processing (MC-BP) in a nine-channel 112 Gb/s PM-mQAM (m=4,16) WDM system, for reaches up to 6,320 km. We show that, for a sufficiently high local dispersion, SC-BP is sufficient to provide a significant performance enhancement when compared to EDC, and is adequate to achieve BER below FEC threshold. For these conditions we report that a sampling rate of two samples per symbol is sufficient for practical SC-BP, without significant penalties.

Stabilization of self-coherent OFDM with injection locked laser

With the rebirth of coherent detection, various algorithms have come forth to alleviate phase noise, one of the main impairments for coherent receivers. These algorithms provide stable compensation, however they limit the DSP. With this key issue in mind, Fabry Perot filter based self coherent optical OFDM was analyzed which does not require phase noise compensation reducing the complexity in DSP at low OSNR. However, the performance of such a receiver is limited due to ASE noise at the carrier wavelength, especially since an optical amplifier is typically employed with the filter to ensure sufficient carrier power. Subsequently, the use of an injection-locked laser (ILL) to retrieve the frequency and phase information from the extracted carrier without the use of an amplifier was recently proposed. In ILL based system, an optical carrier is sent along with the OFDM signal in the transmitter. At the receiver, the carrier is extracted from the OFDM signal using a Fabry-Perot tunable filter and an ILL is used to significantly amplify the carrier and reduce intensity and phase noise. In contrast to CO-OFDM, such a system supports low-cost broad linewidth lasers and benefits with lower complexity in the DSP as no carrier frequency estimation and correction along with phase noise compensation is required.

Pre-attentive auditory sensory processing in autistic spectrum disorder:are electromagnetic measurements telling us a coherent story?

Sensory processing is a crucial underpinning of the development of social cognition, a function which is compromised in variable degree in patients with pervasive developmental disorders (PDD). In this manuscript, we review some of the most recent and relevant contributions, which have looked at auditory sensory processing derangement in PDD. The variability in the clinical characteristics of the samples studied so far, in terms of severity of the associated cognitive deficits and associated limited compliance, underlying aetiology and demographic features makes a univocal interpretation arduous. We hypothesise that, in patients with severe mental deficits, the presence of impaired auditory sensory memory as expressed by the mismatch negativity could be a non-specific indicator of more diffuse cortical deficits rather than causally related to the clinical symptomatology. More consistent findings seem to emerge from studies on less severely impaired patients, in whom increased pitch perception has been interpreted as an indicator of increased local processing, probably as compensatory mechanism for the lack of global processing (central coherence). This latter hypothesis seems extremely attractive and future trials in larger cohorts of patients, possibly standardising the characteristics of the stimuli are a much-needed development. Finally, specificity of the role of the auditory derangement as opposed to other sensory channels needs to be assessed more systematically using multimodal stimuli in the same patient group. (c) 2006 Elsevier B.V. All rights reserved.

Pilot tone design for dispersion estimation in coherent optical fast OFDM systems

We show that inserting pilot tones with frequency intervals inversely proportional to the subcarrier index exhibits greatly improved dispersion estimation performance when compared to the equal spacing design in optical fast orthogonal frequency division multiplexing (F-OFDM). With the proposed design, a 20-Gbit/s four amplitude shift keying optical F-OFDM system with 840-km transmission without optical dispersion compensation is experimentally demonstrated. It is shown that a single F-OFDM symbol with six pilot tones can achieve near-optimal estimation performance for the 840-km dispersion. This is in contrast to the minimum of ten pilot tones using an equal spacing design with either cubic or Fourier-transform-based interpolation. © 2013 Elsevier B.V. All rights reserved.