direction finding in partly calibrated sensor arrays composed of multiple subarrays we consider the direction finding problem in partly calibrated arrays composed of several calibrated and identically oriented but possibly nonidentical subarrays that are displaced by unknown and possibly time varying vector translations a new search free eigenstructure based direction finding approach is proposed for such class of sensor arrays it is referred to as the rank reduction rare estimator and enjoys simple implementation that entails computing the eigendecomposition of the sample array covariance matrix and polynomial rooting closed form expressions for the deterministic cramer rao bounds crbs on direction of arrival doa estimation for the considered class of sensor arrays are derived comparison of these expressions with simulation results show that the finite sample performance of rare algorithms in both time invariant and time varying array cases is close to the corresponding bounds moreover comparisons of the derived crbs with the well known bounds for the fully calibrated time invariant array case help to discover several interesting properties of doa estimation in partly calibrated and time varying arrays

on the geometry of isotropic arrays we consider array geometries whose direction of arrival doa estimation performance is isotropic an isotropic array is one whose cramer rao bound crb on the doa of a single source is uniform for all angles for both planar arrays and volume arrays we derive necessary and sufficient conditions on array element locations so that the array is isotropic we also present several designs of isotropic planar and volume arrays the results apply to both narrowband and wideband scenarios we analyze the special case where a planar array is used to estimate the doa of three dimensional 3 d source finally we compare isotropic array performance to the best possible array performance

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

investigative study of planar array ambiguities based on hyperhelical parameterization in this paper a novel approach is proposed for the calculation of ambiguous generator sets of directions for planar arrays this approach is based on the concept of hyperhelical curves and their equivalent linear arrays which provide a vehicle for investigating planar array ambiguities by adopting and extending techniques proposed for linear arrays thus ambiguous generator sets of directions of constant azimuth and different elevation are initially calculated and the concept of ambiguous generator lines is introduced then by using cone angle parametrization ambiguities associated with directions of different azimuth and different elevation are investigated

manifold studies of nonlinear antenna array geometries the manifold of a general two or three dimensional 2 d or 3 d array of sensors is studied using differential geometry by considering the azimuth and elevation angles as the parameters of interest a manifold surface is formed embedded in a multidimensional complex space initially this surface is investigated by establishing a number of differential geometry parameters associated with the array manifold then the concept of development is proposed for mapping manifold surfaces embedded in a multidimensional complex space on the real 2 d parameter plane the proposed mapping preserves certain differential geometry characteristics of the manifold surface and provides a simplified representation for the analysis the potential benefits of this mapping as well as of the proposed parameters are demonstrated in the analysis of 3 d and planar arrays of omnidirectional sensors and in a number of potential applications varying from array design to handling the array ambiguity problem

sparse array design for azimuthal direction of arrival estimation we propose a novel approach to the design of array geometries for azimuthal direction of arrival doa estimation the proposed array design is related to that of minimum redundancy arrays but the array sensors are not required to lie on a uniform grid based on the proposed array geometry design we develop a subspace based doa estimation technique which allows to estimate the doas of more sources than sensors using only second order statistics of the received data this doa estimation technique is related to the covariance augmentation technique but in contrast to the latter technique it provides nonambiguous doa estimates for the full 360 azimuth field of view

extended array manifolds functions of array manifolds the response of an array processing system has been widely modelled using the concept of the array manifold the conventional array manifold is a function of the geometry of the array the carrier frequency and the directions of arrival doas of the sources only however the emergence of more sophisticated array systems for instance antenna array communication systems dictates the extension of this array manifold into various new types of manifolds that incorporate additional system and channel parameters such as the code division multiple access cdma spreading and scrambling codes the lack of synchronization doppler effects polarization parameters subcarriers etc this paper is concerned with the definition and geometric investigation of a generic model for these new manifolds that can be expressed as functions of the conventional array manifolds and hence are defined herein as extended array manifolds thus initially the concept of the extended array manifold is introduced and is shown to accommodate both existing and newly defined extensions of the widely employed in the literature conventional or spatial array manifold next the geometric properties and parameters of the extended array manifold are studied and linked with the properties of the associated spatial array manifold in an attempt to facilitate the geometric study of the former by taking advantage of the well understood study of the latter

positive galois coverings of self injective algebras abstract in the article we study the structure of galois coverings of self injective artin algebras with infinite cyclic galois groups in particular we characterize all basic connected self injective artin algebras having galois coverings by the repetitive algebras of basic connected artin algebras and with the galois groups generated by positive automorphisms of the repetitive algebras

tristability of thin orthotropic shells with uniform initial curvature composite shells show a rich multistable behaviour of interest for the design of shape changing morphing structures previous studies have investigated how the initial shape determines the shell

a polynomial rooting approach to super resolution array design this paper is concerned with the design of super resolution direction finding df arrays that satisfy prespecified performance levels such as detection resolution thresholds and cramer rao bounds on error variance the sensor placement problem is formulated in the framework of subspace based df techniques and a novel polynomial rooting approach to the design problem based on the new concept of the sensor locator polynomial slp is proposed this polynomial is constructed using the prespecified performance levels and its roots yield the sensor locations of the desired array the distinguishing feature of the proposed technique is that it hinges on the properties of the array manifold which plays a central role in all subspace based df algorithms

a bayesian approach to array geometry design in this paper we consider the design of planar arrays that optimize direction of arrival doa estimation performance we assume that the single source doa is a random variable with a known prior probability distribution and the sensors of the array are constrained to lie in a region with an arbitrary boundary the crame spl acute r rao bound crb and the fisher information matrix fim for single source doa constitute the basis of the optimality criteria we relate the design criteria to a bayesian crb criterion and to array beamwidth we also derive closed form expressions for the design criteria when the doa prior is uniform on a sector of angles we show that optimal arrays have elements on the constraint boundary thus providing a reduced dimension iterative solution procedure finally we present example designs

selfinjective algebras having a generalized standard family of quasi tubes maximally saturated by simple and projective modules abstract we give a complete description of finite dimensional selfinjective algebras over an algebraically closed field whose auslander reiten quiver admits a generalized standard family of quasi tubes maximally saturated by simple and projective modules in particular we show that these algebras are selfinjective algebras of strictly canonical type

discrete approximations of the foppl von karman shell model from coarse to more refined models abstract the problem of deducing from the foppl von karman energy functional a sequence of reduced discrete models having few degrees of freedom is analyzed similar discrete models have been recently intensively studied to analyze the multistable behavior of shallow shells the bifurcations of composite laminates under temperature loads or the wrinkling in soft tissues in particular three relevant examples are discussed and compared among them where the curvature is assumed uniform linearly and quadratically varying through the shell while the uniform curvature assumption dates back to mansfield 1962 linear variations of the shell curvatures can describe smooth transitions between everted configurations while quadratic variations can account for the usually disregarded bending boundary conditions for their deduction we revisit the maxwell mohr method accordingly a sequence of auxiliary elliptic problems of plane elasticity is solved to determine the statically unknown membranal stresses this is a key ingredient for the presented models to compare extremely well with finite element approximations or with literature models with far more degrees of freedom

multilinear array manifold interpolation two algorithmic solutions for interpolating between array manifold grid points are presented the algorithms are for sensor arrays in vector or in scalar wavefields the algorithms make successful use of the condition that the reciprocal doa direction of arrival spectrum is a multilinear function in the small i e over the region of adjacent grid points since polarization is a linear parameter subspace a doa spectrum can be computed without recourse to the unknown polarizations then vector interpolation is replaced by bivector interpolation to address the radio wavefield case the approach distinguishes between sensor arrays in scalar wavefields e g acoustic and those in vector wavefields e g electromagnetic since both storage and computational load vary with the reciprocal of the grid spacing or its square the design relationship between desired accuracy and the required array manifold grid spacing is given

modeling and estimation of ambiguities in linear arrays the problem of ambiguities inherent in the manifold of any linear array structure is investigated ambiguities which can be classified into trivial and nontrivial depending on the ease of their identification arise when an array cannot distinguish between two different sets of directional sources initially the new concept of an ambiguous generator set is introduced it represents generates an infinite number of ambiguous sets of directions then by uniformly nonuniformly partitioning the array manifold curve of a linear array different ambiguous generator sets ran be calculated and as a direct result a sufficient condition for the presence of ambiguities is obtained the theoretical aspects of the investigation are followed by the proposal of an innovative approach that calculates not only all such ambiguities existing in a linear array of arbitrary geometry but the rank of ambiguity in each case as well the main results presented in the paper are supported by a number of representative examples

a candecomp parafac perspective on uniqueness of doa estimation using a vector sensor array we address the uniqueness problem in estimating the directions of arrival doas of multiple narrowband and fully polarized signals impinging on a passive sensor array composed of identical vector sensors the data recorded on such an array present the so called multiple invariances which can be linked to the candecomp parafac cp model cp refers to a family of low rank decompositions of three way or higher way mutidimensional data arrays where each dimension is termed as a mode a sufficient condition is derived for uniqueness of the cp decomposition of a three way three mode array in the particular case where one of the three loading matrices each associated to one mode involved in the decomposition has full column rank based on this upper bounds on the maximal number of identifiable doas are deduced for the two typical cases i e the general case of uncorrelated or partially correlated sources and the case where the sources are coherent

effects of boundary conditions on bistable behaviour in axisymmetrical shallow shells multistable shells are thin walled structures that have more than one stable state of self stress we consider isotropic axisymmetrical shallow shells of arbitrary polynomial shapes using a foppl von karman analytical model by employing a rayleigh ritz approach we identify stable shapes from local minima in the strain energy formulation and we formally characterize the level of influence of the boundary conditions on the critical geometry for achieving bistable inversion an effect not directly answered in the literature systematic insight is afforded by connecting the boundary to ground through sets of extensional and rotational linear springs for typical cap like shells it is shown that bistability is generally enhanced when the extensional spring stiffness increases and when the rotational spring stiffness decreases i e when boundary movements in plane are resisted but when their rotations are not however for certain other shapes and large in plane stiffness values bistability can be enhanced by resisting but not entirely preventing edge rotations our predictions are furnished as detailed regime maps of the critical geometry which are accurately correlated against finite element analysis furthermore the suitabilities of single degree of freedom models for which solutions are achieved in closed form are evaluated and compared to our more accurate predictions

the impact of sensor positioning on the array manifold a framework is presented in this study which analyzes the importance of each sensor in an antenna array based on its location in the overall geometry moving away from the conventional methods of measuring sensor importance by means of application specific criteria a new approach based on the array manifold and its differential geometry is used to measure the significance of each sensor s position in an array by considering two dimensional manifolds function of azimuth and elevation angles of planar arrays of isotropic sensors and by using previously established results on the differential geometry of such manifolds a sensitivity analysis is performed which leads to characterization and quantification of sensor location importance in an array geometry based on this framework a criterion is developed for assessing an overall geometry this criterion may be used as a figure of merit for comparing diverse array geometries

antenna geometry conditions for mimo radar with uncoupled direction estimation we mainly focus on the role played by the antenna geometry in the direction estimation performance for a direction finding df bistatic multiple input multiple output mimo radar first we introduce the signal and the noise models which satisfy the space time separability conditions then we derive an expression of the cramer rao lower bound crlb on target parameters with the antenna locations for a single point target in the far field scenario we show that under the space time separability conditions the temporal dimension parameters range and range rate and spatial dimension parameters direction of departure dod and the direction of arrival doa are uncoupled we also show that dod and doa are uncoupled because of their spatial independence in addition we derive a set of the necessary and sufficient geometrical constraints for the uncoupled direction estimation which is based on the diagonal fisher information matrix fim we present that when both the transmit and the receive antenna location parameters have equivalent auto moment of inertia tensors of x and y axes and zero cross moment of inertia tensors of x y and z axes the bistatic mimo radar system with uncoupled direction estimation can be obtained the corresponding conditions are extended to monostatic mimo radar case for their commonness of the colocated antenna geometry in numerical example section we show several representative antenna geometries to illustrate the antenna geometry conditions derived in this paper