Calculation of mutual information for nonlinear communication channel at large signal-to-noise ratio

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications - the backbone of the internet. At large signal-to-noise ratio we present the mutual information through the path-integral, which is convenient for the perturbative expansion in nonlinearity. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel.

Nuclear magnetic resonance spectroscopy and ultrasound

The work described in this thesis is directed to the examination of the hypothesis that ultrasound may be used to perturb molecular motion in the liquid phase. These changes can then be detected by nuclear magnetic resonance (NMR) in spin-lattice and spin-spin relaxation times. The objective being to develop a method capable of reducing the pulsed NMR acquisition times of slowly relaxing nuclei. The thesis describes the theoretical principles underlying both NMR spectroscopy and ultrasonics with particular attention being paid to factors that impinge on testing the above hypothesis. Apparatus has been constructed to enable ultrasound at frequencies between 1 and 10 mega-hertz with a variable power up to 100W/cm-2 to be introduced in the NMR sample. A broadband high frequency generator is used to drive PZT piezo-electric transducer via various transducer to liquid coupling arrangements. A commercial instrument of 20 kilo-hertz has also been employed to test the above hypothesis and also to demonstrate the usefulness of ultrasound in sonochemistry. The latter objective being, detection of radical formation in monomer and polymer ultrasonic degradation. The principle features of the results obtained are: Ultrasonic perturbation of T1 is far smaller for pure liquids than is for mixtures. The effects appear to be greater on protons (1H) than on carbon-13 nuclei (13C) relaxation times. The observed effect of ultrasonics is not due to temperature changes in the sample. As the power applied to the transducer is progressively increased T1 decreases to a minimum and then increases. The T1's of the same nuclei in different functional groups are influenced to different extents by ultrasound. Studies of the 14N resonances from an equimolar mixture of N, N-dimethylformamide and deuterated chloroform with ultrasonic frequencies at 1.115, 6, 6.42 and 10 MHz show that as the frequency is increased the NMR signal to noise ratio decreases to zero at the Larmor frequency of 6.42 MHz and then again rises. This reveals the surprising indication that an effect corresponding to nuclear acoustic saturation in the liquid may be observable. Ultrasonic irradiation of acidified ammonium chloride solution at and around 6.42 MHz appears to cause distinctive changes in the proton-nitrogen J coupling resonance at 89.56 MHz. Ultrasonic irradiation of N, N-dimethylacetamide at 2 KHz using the lowest stable power revealed the onset of coalescence in the proton spectrum. The corresponding effect achieved by direct heating required a temperature rise of approximately 30oC. The effects of low frequency (20 KHz) on relaxation times appear to be nil. Detection of radical formation proved difficult but is still regarded as the principle route for monomer and polymer degradation. The initial hypothesis is considered proven with the results showing significant changes in the mega-hertz region and none at 20 KHz.

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.

Detection of signals corrupted by the combination of Gaussian and Non-Gaussian noise

The detection of signals in the presence of noise is one of the most basic and important problems encountered by communication engineers. Although the literature abounds with analyses of communications in Gaussian noise, relatively little work has appeared dealing with communications in non-Gaussian noise. In this thesis several digital communication systems disturbed by non-Gaussian noise are analysed. The thesis is divided into two main parts. In the first part, a filtered-Poisson impulse noise model is utilized to calulate error probability characteristics of a linear receiver operating in additive impulsive noise. Firstly the effect that non-Gaussian interference has on the performance of a receiver that has been optimized for Gaussian noise is determined. The factors affecting the choice of modulation scheme so as to minimize the deterimental effects of non-Gaussian noise are then discussed. In the second part, a new theoretical model of impulsive noise that fits well with the observed statistics of noise in radio channels below 100 MHz has been developed. This empirical noise model is applied to the detection of known signals in the presence of noise to determine the optimal receiver structure. The performance of such a detector has been assessed and is found to depend on the signal shape, the time-bandwidth product, as well as the signal-to-noise ratio. The optimal signal to minimize the probability of error of; the detector is determined. Attention is then turned to the problem of threshold detection. Detector structure, large sample performance and robustness against errors in the detector parameters are examined. Finally, estimators of such parameters as. the occurrence of an impulse and the parameters in an empirical noise model are developed for the case of an adaptive system with slowly varying conditions.

Optical fibre limits:an approach using ASE channel estimation

In this talk we investigate the usage of spectrally shaped amplified spontaneous emission (ASE) in order to emulate highly dispersed wavelength division multiplexed (WDM) signals in an optical transmission system. Such a technique offers various simplifications to large scale WDM experiments. Not only does it offer a reduction in transmitter complexity, removing the need for multiple source lasers, it potentially reduces the test and measurement complexity by requiring only the centre channel of a WDM system to be measured in order to estimate WDM worst case performance. The use of ASE as a test and measurement tool is well established in optical communication systems and several measurement techniques will be discussed [1, 2]. One of the most prevalent uses of ASE is in the measurement of receiver sensitivity where ASE is introduced in order to degrade the optical signal to noise ratio (OSNR) and measure the resulting bit error rate (BER) at the receiver. From an analytical point of view noise has been used to emulate system performance, the Gaussian Noise model is used as an estimate of highly dispersed signals and has had consider- able interest [3]. The work to be presented here extends the use of ASE by using it as a metric to emulate highly dispersed WDM signals and in the process reduce WDM transmitter complexity and receiver measurement time in a lab environment. Results thus far have indicated [2] that such a transmitter configuration is consistent with an AWGN model for transmission, with modulation format complexity and nonlinearities playing a key role in estimating the performance of systems utilising the ASE channel emulation technique. We conclude this work by investigating techniques capable of characterising the nonlinear and damage limits of optical fibres and the resultant information capacity limits. REFERENCES McCarthy, M. E., N. Mac Suibhne, S. T. Le, P. Harper, and A. D. Ellis, “High spectral efficiency transmission emulation for non-linear transmission performance estimation for high order modulation formats," 2014 European Conference on IEEE Optical Communication (ECOC), 2014. 2. Ellis, A., N. Mac Suibhne, F. Gunning, and S. Sygletos, “Expressions for the nonlinear trans- mission performance of multi-mode optical fiber," Opt. Express, Vol. 21, 22834{22846, 2013. Vacondio, F., O. Rival, C. Simonneau, E. Grellier, A. Bononi, L. Lorcy, J. Antona, and S. Bigo, “On nonlinear distortions of highly dispersive optical coherent systems," Opt. Express, Vol. 20, 1022-1032, 2012.

Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems

In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dBSNR/dBPower suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error.

Analytical BER performance in differential n-PSK coherent transmission system influenced by equalization enhanced phase noise

Long-haul high speed optical transmission systems are significantly distorted by the interplay between the electronic chromatic dispersion (CD) equalization and the local oscillator (LO) laser phase noise, which leads to an effect of equalization enhanced phase noise (EEPN). The EEPN degrades the performance of optical communication systems severely with the increment of fiber dispersion, LO laser linewidth, symbol rate, and modulation format. In this paper, we present an analytical model for evaluating the performance of bit-error-rate (BER) versus signal-to-noise ratio (SNR) in the n-level phase shift keying (n-PSK) coherent transmission system employing differential carrier phase estimation (CPE), where the influence of EEPN is considered. Theoretical results based on this model have been investigated for the differential quadrature phase shift keying (DQPSK), the differential 8-PSK (D8PSK), and the differential 16-PSK (D16PSK) coherent transmission systems. The influence of EEPN on the BER performance in term of the fiber dispersion, the LO phase noise, the symbol rate, and the modulation format are analyzed in detail. The BER behaviors based on this analytical model achieve a good agreement with previously reported BER floors influenced by EEPN. Further simulations have also been carried out in the differential CPE considering EEPN. The results indicate that this analytical model can give an accurate prediction for the DQPSK system, and a leading-order approximation for the D8PSK and the D16PSK systems.

Fibre impairment compensation using artificial neural network equalizer for high-capacity coherent optical OFDM signals

We propose an artificial neural network (ANN) equalizer for transmission performance enhancement of coherent optical OFDM (C-OOFDM) signals. The ANN equalizer showed more efficiency in combating both chromatic dispersion (CD) and single-mode fibre (SMF)-induced non-linearities compared to the least mean square (LMS). The equalizer can offer a 1.5 dB improvement in optical signal-to-noise ratio (OSNR) compared to LMS algorithm for 40 Gbit/s C-OOFDM signals when considering only CD. It is also revealed that ANN can double the transmission distance up to 320 km of SMF compared to the case of LMS, providing a nonlinearity tolerance improvement of ∼0.7 dB OSNR.

NMR spectroscopy in the presence of ultrasound and other perturbations

The work described in this thesis has been concerned with exploring the potential uses of ultrasound in Nuclear Magnetic Resonance (NMR) spectroscopy, The NMR spectra of liquids provide detailed structural information that may be deduced from the chemical shifts and spin-spin coupling, that are evident in the narrow resonances, arising from some of the nuclear broadening interactions being reduced to zero. In the solid state, all of the nuclear broadening interactions are present and broad lines in the NMR spectrum are observed. Current techniques employed to reduce the line widths in solids are based on coherent averaging techniques such as MAS NMR1,2 which can remove first order interactions. Recently DOR3 and DAS4 have become available to remove higher order interactions. SINNMR (Sonically Induced Narrowing of the NMR spectra of solids) has been reported by Homer et al5 and developed by Homer and Howard6 to reduce the line widths of solids. The basis of their work is the proposal that a colloidal suspension of solid particles can be made to move like large molecules by using ultrasonic agitation. The advantage of the technique is that the particles move incoherently removing all of the nuclear interactions responsible for broad lines. This thesis describes work on the extension of SINNMR by showing that the line width of 27AI and 11B for the glass Na20/B203/AI203 can be reduced by placing solid particles in a colloidal suspension. Further line width reduction is possible by applying ultrasound, at 2 MHz, of sufficient intensity. It is proposed that a cavitation field is responsible for imparting sufficient rotational motion to the solid particles to partially average the nuclear interactions responsible for broad lines. Rapid stirring of the colloidal suspension generates turbulent flow, however, the motion is insufficient to narrow the line widths for 27AI in the glass. Investigations of sonochemical reactions for in situ rate measurements by NMR have been made. 8y using the Weissler reaction7, it has been shown that ultrasonic cavitation is possible up to 10MHz. Preliminary studies have been carried out into the rate of ultrasonic polymerisation of methylmethacrylate by NMR. Long range order in liquid crystals can imposed when they are aligned in the presence a magnetic field. The degree of alignment can be monitored by NMR using, for example a deuterated solute added to the liquid crystal8. Ultrasonic streaming can then be employed to deflect the directors of the liquid crystal from their equilibrium position, resulting in a change In the NMR spectrum. The angle of deflection has been found for the thermotropic liquid crystal (I35) to be ca, 35° and for the lyotropic (ZLI-1167) to be ca, 20°, Mechanical stirring can used to re- orientate the liquid crystal but was found to give a smaller deflection, In a separate study, that did not use ultrasound, it has been found that the signal to noise ratio of 13C NMR signals can be enhanced by rapidly stirring a Iiquid. Accelerating the diffusion of nuclei out of the coil region enables M0 to be re-established more rapidly than the normal relaxation process. This allows the pulse repetition rate to be reduced without saturating the spin system. The influence of varying the relaxation delay, acquisition time and inter-pulse delay have been studied and parameters optimised. By studying cholesterol the technique was found to be most effective for nuclei with long relaxation times, such as quaternary carbon sites. Key Worde: NMR, Ulf.rasciund, 1,.lqi.fi!:l cryllltalt!h SCll1C1otlemlstryl I!r1hano~d algnflllf

The visually evoked magnetic response (VEMR) to a pattern onset/offset stimulus

This study characterizes the visually evoked magnetic response (VEMR) to pattern onset/offset stimuli, using a single channel BTi magnetometer. The influence of stimulus parameters and recording protocols on the VEMR is studied with inferences drawn about the nature of cortical processing, its origins and optimal recording strategies. Fundamental characteristics are examined, such as the behaviour of successive averaged and unaveraged responses; the effects of environmental shielding; averaging; inter- and intrasubject variability and equipment specificity. The effects of varying check size, field size, contrast and refractive error on latency, amplitude and topographic distribution are also presented. Latency and amplitude trends are consistent with previous VEP findings and known anatomical properties of the visual system. Topographic results are consistent with the activity of sources organised according to the cruciform model of striate cortex. A striate origin for the VEMR is also suggested by the results to quarter, octant and annulus field stimuli. Similarities in the behaviour and origins of the sources contributing to the CIIm and CIIIm onset peaks are presented for a number of stimulus conditions. This would be consistent with differing processing event in the same, or similar neuronal populations. Focal field stimuli produce less predictable responses than full or half fields, attributable to a reduced signal to noise ratio and an increased sensitivity to variations in cortical morphology. Problems with waveform peak identification are encountered for full field stimuli that can only be resolved by the careful choice of stimulus parameters, comparisons with half field responses or with reference to the topographic distribution of each waveform peak. An anatomical study of occipital lobe morphology revealed large inter- and intrasubject variation in calcarine fissure shape and striate cortex distribution. An appreciation of such variability is important for VEMR interpretation, due to the technique's sensitivity to source depth and orientation, and it is used to explain the experimental results obtained.

Noise characterization and transmission evaluation of unrepeated Raman amplified DP-16QAM link

Impairments characterization and performance evaluation of Raman amplified unrepeated DP-16QAM transmissions are conducted. Experimental results indicate that small gain in forward direction enhance the system signal-to-noise ratio for longer reach without introducing noticeable penalty.

Symbol synchronization exploiting the symmetric property in optical fast OFDM

We propose a new simple method to achieve precise symbol synchronization using one start-of-frame (SOF) symbol in optical fast orthogonal frequency-division multiplexing (FOFDM) with subchannel spacing equal to half of the symbol rate per sub-carrier. The proposed method first identifies the SOF symbol, then exploits the evenly symmetric property of the discrete cosine transform in FOFDM, which is also valid in the presence of chromatic dispersion, to achieve precise symbol synchronization. We demonstrate its use in a 16.88-Gb/s phase-shifted-keying-based FOFDM system over a 124-km field-installed single-mode fiber link and show that this technique operates well in automatic precise symbol synchronization at an optical signal-to-noise ratio as low as 3 dB and after transmission.

Electronic dispersion compensation using full optical-field reconstruction in 10Gbit/s OOK based systems

We investigate the design of electronic dispersion compensation (EDC) using full optical-field reconstruction in 10Gbit/s on-off keyed transmission systems limited by optical signal-to-noise ratio (OSNR). By effectively suppressing the impairment due to low- frequency component amplification in phase reconstruction, properly designing the transmission system configuration to combat fiber nonlinearity, and successfully reducing the vulnerability to thermal noise, a 4.8dB OSNR margin can be achieved for 2160km single-mode fiber transmission without any optical dispersion compensation. We also investigate the performance sensitivity of the scheme to various system parameters, and propose a novel method to greatly enhance the tolerance to differential phase misalignment of the asymmetric Mach-Zehnder interferometer. This numerical study provides important design guidelines which will enable full optical-field EDC to become a cost-effective dispersion compensation solution for future transparent optical networks.

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.

Full-field electronic dispersion compensation of a 10 Gbit/s OOK signal over 4 x 124 km field-installed single-mode fibre

We experimentally demonstrate the use of full-field electronic dispersion compensation (EDC) to achieve a bit error rate of 5 x 10(-5) at 22.3 dB optical signal-to-noise ratio for single-channel 10 Gbit/s on-off keyed signal after transmission over 496 km field-installed single-mode fibre with an amplifier spacing of 124 km. This performance is achieved by designing the EDC so as to avoid electronic amplification of the noise content of the signal during full-field reconstruction. We also investigate the tolerance of the system to key signal processing parameters, and numerically demonstrate that single-channel 2160 km single mode fibre transmission without in-line optical dispersion compensation can be achieved using this technique with 80 km amplifier spacing and optimized system parameters.