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.

Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory

Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.

Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods

Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.

Simple eye-closure penalty estimate for amplitude noise-degraded signals

We present a simplified model for a simple estimation of the eye-closure penalty for amplitude noise-degraded signals. Using a typical 40-Gbit/s return-to-zero amplitude-shift-keying transmission, we demonstrate agreement between the model predictions and the results obtained from the conventional numerical estimation method over several thousand kilometers.

Simple eye-closure penalty estimate for amplitude noise-degraded signals

We present a simplified model for a simple estimation of the eye-closure penalty for amplitude noise-degraded signals. Using a typical 40-Gbit/s return-to-zero amplitude-shift-keying transmission, we demonstrate agreement between the model predictions and the results obtained from the conventional numerical estimation method over several thousand kilometers.

Seeing light vs dark lines: psychophysical performance is based on separate channels, limited by noise and uncertainty

Visual detection performance (d') is usually an accelerating function of stimulus contrast, which could imply a smooth, threshold-like nonlinearity in the sensory response. Alternatively, Pelli (1985 Journal of the Optical Society of America A 2 1508 - 1532) developed the 'uncertainty model' in which responses were linear with contrast, but the observer was uncertain about which of many noisy channels contained the signal. Such internal uncertainty effectively adds noise to weak signals, and predicts the nonlinear psychometric function. We re-examined these ideas by plotting psychometric functions (as z-scores) for two observers (SAW, PRM) with high precision. The task was to detect a single, vertical, blurred line at the fixation point, or identify its polarity (light vs dark). Detection of a known polarity was nearly linear for SAW but very nonlinear for PRM. Randomly interleaving light and dark trials reduced performance and rendered it non-linear for SAW, but had little effect for PRM. This occurred for both single-interval and 2AFC procedures. The whole pattern of results was well predicted by our Monte Carlo simulation of Pelli's model, with only two free parameters. SAW (highly practised) had very low uncertainty. PRM (with little prior practice) had much greater uncertainty, resulting in lower contrast sensitivity, nonlinear performance, and no effect of external (polarity) uncertainty. For SAW, identification was about v2 better than detection, implying statistically independent channels for stimuli of opposite polarity, rather than an opponent (light - dark) channel. These findings strongly suggest that noise and uncertainty, rather than sensory nonlinearity, limit visual detection.

Pulse compression applied to the detection of F.S.K. and P.S.K. signals

The matched filter detector is well known as the optimum detector for use in communication, as well as in radar systems for signals corrupted by Additive White Gaussian Noise (A.W.G.N.). Non-coherent F.S.K. and differentially coherent P.S.K. (D.P.S.K.) detection schemes, which employ a new approach in realizing the matched filter processor, are investigated. The new approach utilizes pulse compression techniques, well known in radar systems, to facilitate the implementation of the matched filter in the form of the Pulse Compressor Matched Filter (P.C.M.F.). Both detection schemes feature a mixer- P.C.M.F. Compound as their predetector processor. The Compound is utilized to convert F.S.K. modulation into pulse position modulation, and P.S.K. modulation into pulse polarity modulation. The mechanisms of both detection schemes are studied through examining the properties of the Autocorrelation function (A.C.F.) at the output of the P.C.M.F.. The effects produced by time delay, and carrier interference on the output A.C.F. are determined. Work related to the F.S.K. detection scheme is mostly confined to verifying its validity, whereas the D.P.S.K. detection scheme has not been reported before. Consequently, an experimental system was constructed, which utilized combined hardware and software, and operated under the supervision of a microprocessor system. The experimental system was used to develop error-rate models for both detection schemes under investigation. Performances of both F. S. K. and D.P. S. K. detection schemes were established in the presence of A. W. G. N. , practical imperfections, time delay, and carrier interference. The results highlight the candidacy of both detection schemes for use in the field of digital data communication and, in particular, the D.P.S.K. detection scheme, which performed very close to optimum in a background of A.W.G.N.

Subspace modelling for structured noise suppression

The problem of structured noise suppression is addressed by i)modelling the subspaces hosting the components of the signal conveying the information and ii)applying a nonlin- ear non-extensive technique for effecting the right separation. Although the approach is applicable to all situations satisfying the hypothesis of the proposed framework, this work is motivated by a particular scenario, namely, the cancellation of low frequency noise in broadband seismic signals.

Zero-dimensional noise:the best mask you never saw

The transmission of weak signals through the visual system is limited by internal noise. Its level can be estimated by adding external noise, which increases the variance within the detecting mechanism, causing masking. But experiments with white noise fail to meet three predictions: (a) noise has too small an influence on the slope of the psychometric function, (b) masking occurs even when the noise sample is identical in each two-alternative forced-choice (2AFC) interval, and (c) double-pass consistency is too low. We show that much of the energy of 2D white noise masks extends well beyond the pass-band of plausible detecting mechanisms and that this suppresses signal activity. These problems are avoided by restricting the external noise energy to the target mechanisms by introducing a pedestal with a mean contrast of 0% and independent contrast jitter in each 2AFC interval (termed zero-dimensional [0D] noise). We compared the jitter condition to masking from 2D white noise in double-pass masking and (novel) contrast matching experiments. Zero-dimensional noise produced the strongest masking, greatest double-pass consistency, and no suppression of perceived contrast, consistent with a noisy ideal observer. Deviations from this behavior for 2D white noise were explained by cross-channel suppression with no need to appeal to induced internal noise or uncertainty. We conclude that (a) results from previous experiments using white pixel noise should be re-evaluated and (b) 0D noise provides a cleaner method for investigating internal variability than pixel noise. Ironically then, the best external noise stimulus does not look noisy.

Effective electromagnetic noise cancellation with beamformers and synthetic gradiometry in shielded and partly shielded environments

The major challenge of MEG, the inverse problem, is to estimate the very weak primary neuronal currents from the measurements of extracranial magnetic fields. The non-uniqueness of this inverse solution is compounded by the fact that MEG signals contain large environmental and physiological noise that further complicates the problem. In this paper, we evaluate the effectiveness of magnetic noise cancellation by synthetic gradiometers and the beamformer analysis method of synthetic aperture magnetometry (SAM) for source localisation in the presence of large stimulus-generated noise. We demonstrate that activation of primary somatosensory cortex can be accurately identified using SAM despite the presence of significant stimulus-related magnetic interference. This interference was generated by a contact heat evoked potential stimulator (CHEPS), recently developed for thermal pain research, but which to date has not been used in a MEG environment. We also show that in a reduced shielding environment the use of higher order synthetic gradiometry is sufficient to obtain signal-to-noise ratios (SNRs) that allow for accurate localisation of cortical sensory function.

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.

Transparent heterogeneous terrestrial optical communication networks with phase modulated signals

This thesis presents a large scale numerical investigation of heterogeneous terrestrial optical communications systems and the upgrade of fourth generation terrestrial core to metro legacy interconnects to fifth generation transmission system technologies. Retrofitting (without changing infrastructure) is considered for commercial applications. ROADM are crucial enabling components for future core network developments however their re-routing ability means signals can be switched mid-link onto sub-optimally configured paths which raises new challenges in network management. System performance is determined by a trade-off between nonlinear impairments and noise, where the nonlinear signal distortions depend critically on deployed dispersion maps. This thesis presents a comprehensive numerical investigation into the implementation of phase modulated signals in transparent reconfigurable wavelength division multiplexed fibre optic communication terrestrial heterogeneous networks. A key issue during system upgrades is whether differential phase encoded modulation formats are compatible with the cost optimised dispersion schemes employed in current 10 Gb/s systems. We explore how robust transmission is to inevitable variations in the dispersion mapping and how large the margins are when suboptimal dispersion management is applied. We show that a DPSK transmission system is not drastically affected by reconfiguration from periodic dispersion management to lumped dispersion mapping. A novel DPSK dispersion map optimisation methodology which reduces drastically the optimisation parameter space and the many ways to deploy dispersion maps is also presented. This alleviates strenuous computing requirements in optimisation calculations. This thesis provides a very efficient and robust way to identify high performing lumped dispersion compensating schemes for use in heterogeneous RZ-DPSK terrestrial meshed networks with ROADMs. A modified search algorithm which further reduces this number of configuration combinations is also presented. The results of an investigation of the feasibility of detouring signals locally in multi-path heterogeneous ring networks is also presented.

Enhanced information transmission with signal-dependent noise in an array of nonlinear elements

We have investigated information transmission in an array of threshold units that have signal-dependent noise and a common input signal. We demonstrate a phenomenon similar to stochastic resonance and suprathreshold stochastic resonance with additive noise and show that information transmission can be enhanced by a nonzero level of noise. By comparing system performance to one with additive noise we also demonstrate that the information transmission of weak signals is significantly better with signal-dependent noise. Indeed, information rates are not compromised even for arbitrary small input signals. Furthermore, by an appropriate selection of parameters, we observe that the information can be made to be (almost) independent of the level of the noise, thus providing a robust method of transmitting information in the presence of noise. These result could imply that the ability of hair cells to code and transmit sensory information in biological sensory systems is not limited by the level of signal-dependent noise. © 2007 The American Physical Society.

The effect of Gaussian noise on the threshold, dynamic range, and loudness of analogue cochlear implant stimuli

The deliberate addition of Gaussian noise to cochlear implant signals has previously been proposed to enhance the time coding of signals by the cochlear nerve. Potentially, the addition of an inaudible level of noise could also have secondary benefits: it could lower the threshold to the information-bearing signal, and by desynchronization of nerve discharges, it could increase the level at which the information-bearing signal becomes uncomfortable. Both these effects would lead to an increased dynamic range, which might be expected to enhance speech comprehension and make the choice of cochlear implant compression parameters less critical (as with a wider dynamic range, small changes in the parameters would have less effect on loudness). The hypothesized secondary effects were investigated with eight users of the Clarion cochlear implant; the stimulation was analogue and monopolar. For presentations in noise, noise at 95% of the threshold level was applied simultaneously and independently to all the electrodes. The noise was found in two-alternative forced-choice (2AFC) experiments to decrease the threshold to sinusoidal stimuli (100 Hz, 1 kHz, 5 kHz) by about 2.0 dB and increase the dynamic range by 0.7 dB. Furthermore, in 2AFC loudness balance experiments, noise was found to decrease the loudness of moderate to intense stimuli. This suggests that loudness is partially coded by the degree of phase-locking of cochlear nerve fibers. The overall gain in dynamic range was modest, and more complex noise strategies, for example, using inhibition between the noise sources, may be required to get a clinically useful benefit. © 2006 Association for Research in Otolaryngology.