Q parameter scaling in scalar and vector models with dominant signal-noise and noise-noise beating terms

The Q parameter scales differently with the noise power for the signal-noise and the noise-noise beating terms in scalar and vector models. Some procedures for including noise in the scalar model largely under-estimate the Q parameter.

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.

Numerical Q parameter estimates for scalar and vector models in optical communication system simulations

The Q parameter scales differently with the noise power for the signal-noise and the noise-noise beating terms in scalar and vector models. Some procedures for including noise in the scalar model largely under-estimate the Q parameter. We propose a simple method for including noise within a scalar model which will allow both the noise-noise dominated limit and the signal-noise dominated limit to be treated consistently. © 2005 Elsevier B.V. All rights reserved.

Broad direction bandwidths for complex motion mechanisms

Growing evidence from psychophysics and single-unit recordings suggests specialised mechanisms in the primate visual system for the detection of complex motion patterns such as expansion and rotation. Here we used a subthreshold summation technique to determine the direction tuning functions of the detecting mechanisms. We measured thresholds for discriminating noise and signal + noise for pairs of superimposed complex motion patterns (signal A and B) carried by random-dot stimuli in a circular 5° field. For expansion, rotation, deformation and translation we found broad tuning functions approximated by cos(d), where d is the difference in dot directions for signal A and B. These data were well described by models in which either: (a) cardinal mechanisms had direction bandwidths (half-widths) of around 60° or (b) the number of mechanisms was increased and their half-width was reduced to about 40°. When d = 180° we found summation to be greater than probability summation for expansion, rotation and translation, consistent with the idea that mechanisms for these stimuli are constructed from subunits responsive to relative motion. For deformation, however, we found sensitivity declined when d = 180°, suggesting antagonistic input from directional subunits in the deformation mechanism. This is a necessary property for a mechanism whose job is to extract the deformation component from the optic flow field. © 2001 Elsevier Science Ltd.

Raman fibre laser based amplification in coherent transmission systems

The thesis presents a detailed study of different Raman fibre laser (RFL) based amplification techniques and their applications in long-haul/unrepeatered coherent transmission systems. RFL based amplifications techniques were characterised from different aspects, including signal/noise power distributions, relative intensity noise (RIN), mode structures of induced Raman fibre lasers, and so on. It was found for the first time that RFL based amplification techniques could be divided into three categories in terms of the fibre laser regime, which were Fabry-Perot fibre laser with two FBGs, weak Fabry-Perot fibre laser with one FBG and very low reflection near the input, and random distributed feedback (DFB) fibre laser with one FBG. It was also found that lowering the reflection near the input could mitigate the RIN of the signal significantly, thanks to the reduced efficiency of the Stokes shift from the FW-propagated pump. In order to evaluate the transmission performance, different RFL based amplifiers were evaluated and optimised in long-haul coherent transmission systems. The results showed that Fabry-Perot fibre laser based amplifier with two FBGs gave >4.15 dB Q factor penalty using symmetrical bidirectional pumping, as the RIN of the signal was increased significantly. However, random distributed feedback fibre laser based amplifier with one FBG could mitigate the RIN of the signal, which enabled the use of bidirectional second order pumping and consequently give the best transmission performance up to 7915 km. Furthermore, using random DFB fibre laser based amplifier was proved to be effective to combat the nonlinear impairment, and the maximum reach was enhanced by >28% in mid-link single/dual band optical phase conjugator (OPC) transmission systems. In addition, unrepeatered transmission over >350 km fibre length using RFL based amplification technique were presented experimentally using DP-QPSK and DP-16QAM transmitter.

Perturbative discrete-time multivariate fiber channel model with finite memory

We introduce a discrete-time fibre channel model that provides an accurate analytical description of signal-signal and signal-noise interference with memory defined by the interplay of nonlinearity and dispersion. Also the conditional pdf of signal distortion, which captures non-circular complex multivariate symbol interactions, is derived providing the necessary platform for the analysis of channel statistics and capacity estimations in fibre optic links.

Enhanced information transmission with signal dependent noise in an array of LIF neurons

Sensory cells usually transmit information to afferent neurons via chemical synapses, in which the level of noise is dependent on an applied stimulus. Taking into account such dependence, we model a sensory system as an array of LIF neurons with a common signal. We show that information transmission is enhanced by a nonzero level of noise. Moreover, we demonstrate a phenomenon similar to suprathreshold stochastic resonance with additive noise. We remark that many properties of information transmission found for the LIF neurons was predicted by us before with simple binary units [Phys. Rev. E 75, 021121 (2007)]. This confirmation of our predictions allows us to point out identical roots of the phenomena found in the simple threshold systems and more complex LIF neurons.

Bit-error probability for direct detection of optical RZ signal degraded by ASE noise and timing jitter

We analyze theoretically the interplay between optical return-to-zero signal degradation due to timing jitter and additive amplified-spontaneous-emission noise. The impact of these two factors on the performance of a square-law direct detection receiver is also investigated. We derive an analytical expression for the bit-error probability and quantitatively determine the conditions when the contributions of the effects of timing jitter and additive noise to the bit error rate can be treated separately. The analysis of patterning effects is also presented. © 2007 IEEE.

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.

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.

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.

Contrast discrimination and pattern masking: contrast gain control with fixed additive noise

We studied the visual mechanisms that serve to encode spatial contrast at threshold and supra-threshold levels. In a 2AFC contrast-discrimination task, observers had to detect the presence of a vertical 1 cycle deg-1 test grating (of contrast dc) that was superimposed on a similar vertical 1 cycle deg-1 pedestal grating, whereas in pattern masking the test grating was accompanied by a very different masking grating (horizontal 1 cycle deg-1, or oblique 3 cycles deg-1). When expressed as threshold contrast (dc at 75% correct) versus mask contrast (c) our results confirm previous ones in showing a characteristic 'dipper function' for contrast discrimination but a smoothly increasing threshold for pattern masking. However, fresh insight is gained by analysing and modelling performance (p; percent correct) as a joint function of (c, dc) - the performance surface. In contrast discrimination, psychometric functions (p versus logdc) are markedly less steep when c is above threshold, but in pattern masking this reduction of slope did not occur. We explored a standard gain-control model with six free parameters. Three parameters control the contrast response of the detection mechanism and one parameter weights the mask contrast in the cross-channel suppression effect. We assume that signal-detection performance (d') is limited by additive noise of constant variance. Noise level and lapse rate are also fitted parameters of the model. We show that this model accounts very accurately for the whole performance surface in both types of masking, and thus explains the threshold functions and the pattern of variation in psychometric slopes. The cross-channel weight is about 0.20. The model shows that the mechanism response to contrast increment (dc) is linearised by the presence of pedestal contrasts but remains nonlinear in pattern masking.

Contrast masking in strabismic amblyopia: attenuation, noise, interocular suppression and binocular summation

To investigate amblyopic contrast vision at threshold and above we performed pedestal-masking (contrastdiscrimination) experiments with a group of eight strabismic amblyopes using horizontal sinusoidal gratings (mainly 3 c/deg) in monocular, binocular and dichoptic configurations balanced across eye (i.e. five conditions). With some exceptions in some observers, the four main results were as follows. (1) For the monocular and dichoptic conditions, sensitivity was less in the amblyopic eye than in the good eye at all mask contrasts. (2) Binocular and monocular dipper functions superimposed in the good eye. (3) Monocular masking functions had a normal dipper shape in the good eye, but facilitation was diminished in the amblyopic eye. (4) A less consistent result was normal facilitation in dichoptic masking when testing the good eye, but a loss of this when testing the amblyopic eye. This pattern of amblyopic results was replicated in a normal observer by placing a neutral density filter in front of one eye. The two-stage model of binocular contrast gain control [Meese, T.S., Georgeson, M.A. & Baker, D.H. (2006). Binocular contrast vision at and above threshold. Journal of Vision 6, 1224--1243.] was `lesioned' in several ways to assess the form of the amblyopic deficit. The most successful model involves attenuation of signal and an increase in noise in the amblyopic eye, and intact stages of interocular suppression and binocular summation. This implies a behavioural influence from monocular noise in the amblyopic visual system as well as in normal observers with an ND filter over one eye.

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.

Projection and interpolation based techniques for structured and impulsive noise filtering

In this chapter we present the relevant mathematical background to address two well defined signal and image processing problems. Namely, the problem of structured noise filtering and the problem of interpolation of missing data. The former is addressed by recourse to oblique projection based techniques whilst the latter, which can be considered equivalent to impulsive noise filtering, is tackled by appropriate interpolation methods.