The Gaussian assumption in second-order estimation problems in digital communications

This paper deals with the goodness of the Gaussian assumption when designing second-order blind estimationmethods in the context of digital communications. The low- andhigh-signal-to-noise ratio (SNR) asymptotic performance of the maximum likelihood estimator—derived assuming Gaussiantransmitted symbols—is compared with the performance of the optimal second-order estimator, which exploits the actualdistribution of the discrete constellation. The asymptotic study concludes that the Gaussian assumption leads to the optimalsecond-order solution if the SNR is very low or if the symbols belong to a multilevel constellation such as quadrature-amplitudemodulation (QAM) or amplitude-phase-shift keying (APSK). On the other hand, the Gaussian assumption can yield importantlosses at high SNR if the transmitted symbols are drawn from a constant modulus constellation such as phase-shift keying (PSK)or continuous-phase modulations (CPM). These conclusions are illustrated for the problem of direction-of-arrival (DOA) estimation of multiple digitally-modulated signals.

Second-order parameter estimation

This work provides a general framework for the design of second-order blind estimators without adopting anyapproximation about the observation statistics or the a prioridistribution of the parameters. The proposed solution is obtainedminimizing the estimator variance subject to some constraints onthe estimator bias. The resulting optimal estimator is found todepend on the observation fourth-order moments that can be calculatedanalytically from the known signal model. Unfortunately,in most cases, the performance of this estimator is severely limitedby the residual bias inherent to nonlinear estimation problems.To overcome this limitation, the second-order minimum varianceunbiased estimator is deduced from the general solution by assumingaccurate prior information on the vector of parameters.This small-error approximation is adopted to design iterativeestimators or trackers. It is shown that the associated varianceconstitutes the lower bound for the variance of any unbiasedestimator based on the sample covariance matrix.The paper formulation is then applied to track the angle-of-arrival(AoA) of multiple digitally-modulated sources by means ofa uniform linear array. The optimal second-order tracker is comparedwith the classical maximum likelihood (ML) blind methodsthat are shown to be quadratic in the observed data as well. Simulationshave confirmed that the discrete nature of the transmittedsymbols can be exploited to improve considerably the discriminationof near sources in medium-to-high SNR scenarios.

Determining rotational direction of rotation structures using prolate shaped grains within till

Micromorphology is used to analyze a wide range of sediments. Many microstructures have, as yet, not been analyzed. Rotation structures are the least understood of microstructures: their origin and development forms the basis of this thesis. Direction of rotational movement helps understand formative deformational and depositional processes. Twenty-eight rotation structures were analyzed through two methods of data extraction: (a) angle of grain rotation measured from Nikon NIS software, and (b) visual analyses of grain orientation, neighbouring grainstacks, lineations, and obstructions. Data indicates antithetic rotation is promoted by lubrication, accounting for 79% of counter-clockwise rotation structures while 21 % had clockwise rotation. Rotation structures are formed due to velocity gradients in sediment. Subglacial sediments are sheared due to overlying ice mass stresses. The grains in the sediment are differentially deformed. Research suggests rotation structures are formed under ductile conditions under low shear, low water content, and grain numbers inducing grain-to-grain interaction.

Acoustic radiation and scattering from cylindrical bodies and analysis of transducer arrays

New mathematical methods to analytically investigate linear acoustic radiation and scattering from cylindrical bodies and transducer arrays are presented. Three problems of interest involving cylinders in an infinite fluid are studied. In all the three problems, the Helmholtz equation is used to model propagation through the fluid and the beam patterns of arrays of transducers are studied. In the first problem, a method is presented to determine the omni-directional and directional far-field pressures radiated by a cylindrical transducer array in an infinite rigid cylindrical baffle. The solution to the Helmholtz equation and the displacement continuity condition at the interface between the array and the surrounding water are used to determine the pressure. The displacement of the surface of each transducer is in the direction of the normal to the array and is assumed to be uniform. Expressions are derived for the pressure radiated by a sector of the array vibrating in-phase, the entire array vibrating in-phase, and a sector of the array phase-shaded to simulate radiation from a rectangular piston. It is shown that the uniform displacement required for generating a source level of 220 dB ref. μPa @ 1m that is omni directional in the azimuthal plane is in the order of 1 micron for typical arrays. Numerical results are presented to show that there is only a small difference between the on-axis pressures radiated by phased cylindrical arrays and planar arrays. The problem is of interest because cylindrical arrays of projectors are often used to search for underwater objects. In the second problem, the errors, when using data-independent, classical, energy and split beam correlation methods, in finding the direction of arrival (DOA) of a plane acoustic wave, caused by the presence of a solid circular elastic cylindrical stiffener near a linear array of hydrophones, are investigated. Scattering from the effectively infinite cylinder is modeled using the exact axisymmetric equations of motion and the total pressures at the hydrophone locations are computed. The effect of the radius of the cylinder, a, the distance between the cylinder and the array, b, the number of hydrophones in the array, 2H, and the angle of incidence of the wave, α, on the error in finding the DOA are illustrated using numerical results. For an array that is about 30 times the wavelength and for small angles of incidence (α<10), the error in finding the DOA using the energy method is less than that using the split beam correlation method with beam steered to α; and in some cases, the error increases when b increases; and the errors in finding the DOA using the energy method and the split beam correlation method with beam steered to α vary approximately as a7 / 4 . The problem is of interest because elastic stiffeners – in nearly acoustically transparent sonar domes that are used to protect arrays of transducers – scatter waves that are incident on it and cause an error in the estimated direction of arrival of the wave. In the third problem, a high-frequency ray-acoustics method is presented and used to determine the interior pressure field when a plane wave is normally incident on a fluid cylinder embedded in another infinite fluid. The pressure field is determined by using geometrical and physical acoustics. The interior pressure is expressed as the sum of the pressures due to all rays that pass through a point. Numerical results are presented for ka = 20 to 100 where k is the acoustic wavenumber of the exterior fluid and a is the radius of the cylinder. The results are in good agreement with those obtained using field theory. The directional responses, to the plane wave, of sectors of a circular array of uniformly distributed hydrophones in the embedded cylinder are then computed. The sectors are used to simulate linear arrays with uniformly distributed normals by using delays. The directional responses are compared with the output from an array in an infinite homogenous fluid. These outputs are of interest as they are used to determine the direction of arrival of the plane wave. Numerical results are presented for a circular array with 32 hydrophones and 12 hydrophones in each sector. The problem is of interest because arrays of hydrophones are housed inside sonar domes and acoustic plane waves from distant sources are scattered by the dome filled with fresh water and cause deterioration in the performance of the array.

Changing direction on direction of fit

In this paper, I show that we should understand the direction of fit of beliefs and desires in normative terms. After rehearsing a standard objection to Michael Smith’s analysis of direction of fit, I raise a similar problem for Lloyd Humberstone’s analysis. I go on to offer my own account, according to which the difference between beliefs and desires is determined by the normative relations such states stand in. I argue that beliefs are states which we have reason to change in light of the world, whereas desires are states that give us reason to change the world. After doing this, I show how the view avoids various objections, including two from David Sobel and David Copp. The paper ends by briefly discussing the relevance of the view to the Humean theory of motivation.

Verbs in space: axis and direction of motion norms for 299 English verbs

A strong body of work has explored the interaction between visual perception and language comprehension; for example, recent studies exploring predictions from embodied cognition have focused particularly on the common representation of sensory—motor and semantic information. Motivated by this background, we provide a set of norms for the axis and direction of motion implied in 299 English verbs, collected from approximately 100 native speakers of British English. Until now, there have been no freely available norms of this kind for a large set of verbs that can be used in any area of language research investigating the semantic representation of motion. We have used these norms to investigate the interaction between language comprehension and low-level visual processes involved in motion perception, validating the norming procedure’s ability to capture the motion content of individual verbs. Supplemental materials for this study may be downloaded from brm.psychonomic-journals.org/content/supplemental.

A faraway quasar in the direction of the highest energy Auger event

The highest energy cosmic ray event reported by the Auger Observatory has an energy of 148 EeV. It does not correlate with any nearby (z<0.024) object capable of originating such a high energy event. Intrigued by the fact that the highest energy event ever recorded (by the Fly`s Eye collaboration) points to a faraway quasar with very high radio luminosity and large Faraday rotation measurement, we have searched for a similar source for the Auger event. We find that the Auger highest energy event points to a quasar with similar characteristics to the one correlated to the Fly`s Eye event. We also find the same kind of correlation for one of the highest energy AGASA events. We conclude that so far these types of quasars are the best source candidates for both Auger and Fly`s Eye highest energy events. We discuss a few exotic candidates that could reach us from gigaparsec distances.

LARGE-SCALE DISTRIBUTION OF ARRIVAL DIRECTIONS OF COSMIC RAYS DETECTED ABOVE 10(18) eV AT THE PIERRE AUGER OBSERVATORY

A thorough search for large-scale anisotropies in the distribution of arrival directions of cosmic rays detected above 10(18) eV at the Pierre Auger Observatory is presented. This search is performed as a function of both declination and right ascension in several energy ranges above 10(18) eV, and reported in terms of dipolar and quadrupolar coefficients. Within the systematic uncertainties, no significant deviation from isotropy is revealed. Assuming that any cosmic-ray anisotropy is dominated by dipole and quadrupole moments in this energy range, upper limits on their amplitudes are derived. These upper limits allow us to test the origin of cosmic rays above 10(18) eV from stationary Galactic sources densely distributed in the Galactic disk and predominantly emitting light particles in all directions.

"Experimental and computational approaches to historical masonry structures: A study in the direction of filling the gap"

The assessment of historical structures is a significant need for the next generations, as historical monuments represent the community’s identity and have an important cultural value to society. Most of historical structures built by using masonry which is one of the oldest and most common construction materials used in the building sector since the ancient time. Also it is considered a complex material, as it is a composition of brick units and mortar, which affects the structural performance of the building by having different mechanical behaviour with respect to different geometry and qualities given by the components.