isophoric arrays massively thinned phased arrays with well controlled sidelobes traditional filled phased arrays have an element placed in every location of a uniform lattice with half wavelength spacing between the lattice points massively thinned arrays have fewer than half the elements of their filled counterparts such drastic thinning is normally accompanied by loss of sidelobe control this paper describes a class of massively thinned linear and planar arrays that show well behaved sidelobes in spite of the thinning the term isophoric is derived from greek roots to denote uniform weight in isophoric arrays element placement based on difference sets forces uniformly weighted spatial coverage this constraint forces the array power pattern to pass through v uniformly spaced equal and constant values that are less than 1 k times the main beam peak where v is the aperture size in half wavelengths and k is the number of elements in the array the net result is reduced peak sidelobes especially when compared to cut and try random placement approaches an isophoric array will exhibit this sidelobe control even when the array has been thinned to the extent that k is approximately the square root of v where more than one beam must be generated at a time isophoric array designs may be used to advantage even within a traditional filled array by interweaving two isophoric subarrays within a filled array and by appropriate cyclic shifting of the element assignments over time two independent antenna power patterns can be generated each with a sidelobe region that is approximately a constant value of 1 2k relative to the main beam where k is the number of elements in the subarray

reducing the number of elements in the synthesis of shaped beam patterns by the forward backward matrix pencil method the matrix pencil method mpm has been used to reduce the number of elements in the linear antenna array with a pencil beam pattern this work extends the mpm based synthesis method to the synthesis of shaped beam patterns by using the forward backward matrix pencil method fbmpm the fbmpm based synthesis method places a necessary restriction on the poles which correspond to element positions and consequently obtains more accurate synthesis results particularly for the synthesis of asymmetric patterns numerical examples show the effectiveness and advantages of the proposed method in the reduction of the number of elements for shaped beam patterns

exact closed form representations for the time domain surface impedances of a homogeneous lossy half space in this paper we derive exact closed form representations for the transverse electric and transverse magnetic time domain surface impedances associated with a plane wave that is obliquely incident on a homogeneous lossy half space the time domain surface impedances are expressed in terms of modified bessel functions and incomplete lipschitz hankel integrals the limitations on the validity of a previously published approximate expression are also discussed

optimization of sparse linear arrays using harmony search algorithms a sparse linear array composed of a uniformly spaced core subarray and an extended sparse subarray is synthesized using a harmony search hs and an exploratory harmony search ehs algorithms the optimal solution is searched by changing the amplitudes of all the elements and the positions of the extended elements under a set of practical constraints performance of the ehs the hs a genetic algorithm ga and a particle swarm optimization pso algorithm has also been compared in synthesizing these sparse linear arrays

a hybrid approach based on pso and hadamard difference sets for the synthesis of square thinned arrays a hybrid approach for the synthesis of planar thinned antenna arrays is presented the proposed solution exploits and combines the most attractive features of a particle swarm algorithm and those of a combinatorial method based on the noncyclic difference sets of hadamard type numerical experiments validate the proposed solution showing improvements with respect to previous results

sparse 2 d array placement for arbitrary pattern mask and with excitation constraints a simple deterministic approach we present a novel algorithm for the synthesis of planar 2 d arrays subject to arbitrary pattern masks and excitation constraints e g dynamic range the algorithm is simple and deterministic and considers the radiating element pattern the procedure starts with a conventional constrained fixed grid synthesis on a regular lattice yielding a goal radiated field next element locations are selected sequentially by maximizing projection on field difference to goal while excitation amplitudes are computed using fixed grid constrained synthesis for irregular lattices the final result is the sparse layout and constrained excitation coefficients the proposed method is validated against literature results application examples are given for circular flat top isoflux and triangular flat top shaped beam patterns with constraints on excitation coefficients dynamic range both for isotropic and patch type element patterns

the filter diagonalization method in antenna array optimization for pattern synthesis pattern synthesis of nonuniform antenna arrays has drawn significant attention because of its wide applications with the aim of reducing the number of elements in linear and planar arrays this paper introduces a novel non iterative method based on the filter diagonalization method fdm which was originally applied in the problem of identifying and quantifying chemical molecules with nuclear magnetic resonance nmr in quantum mechanical formalism the proposed method samples the data set from the desired discrete pattern and associates the sample data with a time autocorrelation function of a fictitious dynamical system which is described by an effective hamiltonian operator that contains the array element information the hamiltonian operator can be decomposed by a set of orthonormal eigenvectors therefore the original pattern synthesis is converted into solving the general eigenvalue decomposition with krylov bases the number of nonuniform array elements depends on the number of the krylov bases and the sample data the proposed method can obtain an optimized antenna array to reconstruct the desired radiation pattern with a high accuracy numerical examples show that proposed fdm pattern synthesis can use less prior knowledge to achieve the desired pattern with highly sparse antenna arrays

synthesis of modular contiguously clustered linear arrays through a sparseness regularized solver an innovative methodology for the design of modular and contiguously clustered linear arrays is proposed the approach formulates the subarraying problem as a pattern matching one in which elementary modules taken from a user defined dictionary are combined to synthesize the final antenna layout by recasting such a synthesis problem within the compressive sensing framework an efficient solver is used to determine the array architecture starting from the a priori specification of the features e g the length of the admissible subarrays a set of representative numerical experiments is discussed to assess the advantages and drawbacks of the proposed algorithm also in comparison with some state of the art methods

maximum likelihood direction of arrival estimation in unknown noise fields using sparse sensor arrays we address the problem of maximum likelihood ml direction of arrival doa estimation in unknown spatially correlated noise fields using sparse sensor arrays composed of multiple widely separated subarrays in such arrays intersubarray spacings are substantially larger than the signal wavelength and therefore sensor noises can be assumed to be uncorrelated between different subarrays this leads to a block diagonal structure of the noise covariance matrix which enables a substantial reduction of the number of nuisance noise parameters and ensures the identifiability of the underlying doa estimation problem a new deterministic ml doa estimator is derived for this class of sparse sensor arrays the proposed approach concentrates the ml estimation problem with respect to all nuisance parameters in contrast to the analytic concentration used in conventional ml techniques the implementation of the proposed estimator is based on an iterative procedure which includes a stepwise concentration of the log likelihood ll function the proposed algorithm is shown to have a straightforward extension to the case of uncalibrated arrays with unknown sensor gains and phases it is free of any further structural constraints or parametric model restrictions that are usually imposed on the noise covariance matrix and received signals in most existing ml based approaches to doa estimation in spatially correlated noise

hybrid ads based techniques for radio astronomy array design a set of techniques are presented that are based on the exploitation of low correlation sequences called almost difference sets adss to design correlator arrays for radio astronomy applications three approaches are discussed with different objectives and performances ads based analytical designs ga optimized arrangements and pso optimized arrays are presented and applied to the synthesis of open ended y and cross array configurations to maximize the u v coverage or to minimize the peak sidelobe level psl representative numerical results are illustrated to point out the features and performances of the proposed approaches and to assess their effectiveness in comparison with state of the art design methodologies as well the presented analysis indicates that the proposed approaches overcome existing pso based correlator arrays in terms of psl control e g 1 0 db reduction and tracking u v coverage e g up to 2 enhancement also improving the speed of convergence of the synthesis process

a stochastic mathematical framework for the analysis of spherically bound random arrays random arrays bound by a spherical volume are rigorously analyzed through a stochastic approach for uniform and gaussian element distributions the full mathematical derivation and process to determine the array characteristics are discussed and a key result is the form solution which describes both the sidelobe behavior and main beam characteristics it is also shown that the proposed approach shares many conceptual similarities to the probabilistic approach applied to circular random arrays and comparisons are made the 3 db beamwidth directivity grating lobes and sidelobe level are examined analytically and in numerical simulation for a conceptual system of isotropic wide band radiators with a 100 1 bandwidth

optimal far field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions a new approach providing new theoretical results to the optimal far field focusing of uniformly spaced arrays subject to a completely arbitrary mask for sidelobe bounds is presented and discussed in both cases of linear or planar arrays with rectangular boundaries it is first shown that the problem can be formulated without any loss to performances on the maximum as a linear programming one guaranteeing a globally optimal solution second a sufficient uniqueness criterion for the solution of the overall problem is also developed which shows how the solution may not be unique as is actually the case when planar arrays are considered in addition further globally effective optimization procedures are proposed for the latter case in order to optimize directivity smoothness of excitations or other performance parameters in the set of equivalent solutions last an extension to planar arrays with a nonrectangular boundary is also given a thorough numerical analysis confirms the effectiveness of the approach proposed and of the solution codes developed

synthesis of two dimensional antenna array using independent compression regions the synthesis of two dimensional antenna arrays that allows to optimize the number of its elements is of great interest for long term evolution lte advanced wireless systems in this communication we present a novel synthesis approach which focuses on reducing the number of antenna elements using independent compression regions icr we base our approach on the non iterative matrix pencil method mpm and the iterative bayesian compressive sampling bcs method both of these techniques have been previously used for the compression of linear arrays and now we apply them in the context of two dimensional arrays our compression method is based on the idea of segmenting the array in independent regions a set of numerical experiments small and large 2d arrays shaped beam antenna patterns are presented to assess the performance and potentialities of icr design approach

generalized analytical technique for the synthesis of unequally spaced arrays with linear planar cylindrical or spherical geometry an effective method for optimizing the performance of a fixed current distribution uniformly spaced antenna array has been to adjust its element positions to provide performance improvement in comparison with the default uniform structure this approach yields performance improvements such as smaller sidelobe levels or beamwidth values additionally it provides practical advantages such as reductions in size weight and number of antenna elements the objective of this paper is to describe a unified mathematical approach to nonlinear optimization of multidimensional array geometries the approach utilizes a class of limiting properties of sinusoidal bessel or legendre functions that are dictated by the array geometry addressed the efficacy of the method is demonstrated by its generalized application to synthesis of rectangular cylindrical and spherical arrays the unified mathematical approach presented below is a synthesis technique founded on the mathematical transformation of the desired field pattern followed by the application of limiting forms of the transformation and resulting in the development of a closed form expression for the element positions the method offers the following advantages over previous techniques such as direct nonlinear optimization or genetic algorithms first it is not an iterative searching algorithm and provides element spacing values directly in a single run of the algorithm thereby saving valuable cpu time and memory storage second it permits the array designer to place practical constraints on the array geometry e g the minimum maximum spacing between adjacent elements

rectangular thinned arrays based on mcfarland difference sets a new class of analytical rectangular thinned arrays with low peak sidelobe level psl is introduced the proposed synthesis technique exploits binary sequences derived from mcfarland difference sets to design thinned layouts on a lattice of p p p 2 positions for any prime p the pattern features of the arising massively thinned arrangements characterized by only p p 1 active elements are discussed and the results of an extensive numerical analysis are presented to assess advantages and limitations of the mcfarland based arrays

sparse array beampattern synthesis via alternating direction method of multipliers in this paper we devise beampattern synthesis algorithms for sparse arrays using the alternating direction method of multipliers admm unlike the usual weighted l 1 norm we utilize the l p norm of the array weight vector where 0 as the objective function to enhance its sparsity for arbitrary array configurations to solve the resultant nonconvex and nonlinear optimization problem we introduce auxiliary variables to decouple the array weight vector in the objective function from the complicated constraints on main lobes and sidelobes and then the array weight vector and auxiliary variables are updated alternately via admm to determine the array weight vector with the l p norm we analyze the convexity or concavity of the subfunction related to each weight element using its derivatives on the other hand we divide the objective function of auxiliary variables into multiple nonlinear subfunctions each of which is only dependent of the magnitude of the corresponding auxiliary variable and is calculated in parallel via analyzing simplified two sided constraints furthermore we extend our methodology to the symmetric excitation case with symmetric array configurations numerical examples show that the proposed methods can obtain satisfactory radiation pattern with fewer antennas than the existing techniques and are applicable for arbitrary or symmetric array configurations

reducing the number of elements in a linear antenna array by the matrix pencil method the synthesis of a nonuniform antenna array with as few elements as possible has considerable practical applications this paper introduces a new non iterative method for linear array synthesis based on the matrix pencil method mpm the method can synthesize a nonuniform linear array with a reduced number of elements and can be also used to reduce the number of elements for linear arrays designed by other synthesis techniques in the proposed method the desired radiation pattern is first sampled to form a discrete pattern data set then we organize the discrete data set in a form of hankel matrix and perform the singular value decomposition svd of the matrix by discarding the non principal singular values we obtain an optimal lower rank approximation of the hankel matrix the lower rank matrix actually corresponds to fewer antenna elements the matrix pencil method is then utilized to reconstruct the excitation and location distributions from the approximated matrix numerical examples show the effectiveness and advantages of the proposed synthesis method

linear array thinning exploiting almost difference sets this paper describes a class of linear thinned arrays with predictable and well behaved sidelobes the element placement is based on almost difference sets and the array power pattern is forced to pass through n uniformly spaced values that although neither equal nor constant as for difference sets are a priori known from the knowledge of the aperture size the number of active array elements k and the features of the correlation function such a property allows one to predict the bounds of the confidence range of the peak sidelobe of the admissible arrays obtainable through simple shift operations on a binary sequence the expected peak sidelobe performances turn out to be comparable with those from difference sets even though obtainable in a wider set of array configurations and improved in comparison with cut and try random placements

aperiodic array layout optimization by the constraint relaxation approach an optimization procedure for the layout assessment of electrically large but finite planar arrays is presented the synthesis takes into account the desired directivity pattern that is prescribed employing bound constraints moreover the size of the radiators is taken into account which results in a hard nonoverlapping between the elements constraint the latter should not be violated if we want the attained solution not only to obey the far field mask but also to be physically realizable as stated the optimization problem is twofold an antenna design is associated with a packing problem in order to take the constraints on the layout into account and solve the whole problem we propose the constraint relaxation approach which is equipped with a packing algorithm our study is applied to various initial geometries and the resulting arrays appear to comply with the desired pattern and the nonoverlapping constraint several examples for different cases including symmetric arrays and a study on maximally sparse arrays are presented which show the applicability and merit of the method

fluctuations of finite time stability exponents in the standard map and the detection of small islands some statistical properties of finite time stability exponents in the standard map can be estimated analytically the mean exponent averaged over the entire phase space behaves quite differently from all the other cumulants whereas the mean carries information about the strength of the interaction and only indirect information about dynamical correlations the higher cumulants carry information about dynamical correlations and essentially no information about the interaction strength in particular the variance and higher cumulants of the exponent are very sensitive to dynamical correlations and easily detect the presence of very small islands of regular motion via their anomalous time scalings the average of the stability matrix inverse trace is even more sensitive to the presence of small islands and has a seemingly fractal behavior in the standard map parameter the usual accelerator modes and the small islands created through double saddle node bifurcations which come halfway between the positions in interaction strength of the usual accelerator modes are clearly visible in the variance whose time scaling is capable of detecting the presence of islands as small as 0 01 of the phase space we study these quantities with a local approximation to the trace of the stability matrix which significantly simplifies the numerical calculations as well as allows for generalization of these methods to higher dimensions we also discuss the nature of this local approximation in some detail

wavelet based compressive imaging of sparse targets the application of the compressive sensing cs paradigm to retrieve non single pixels contrast profiles is discussed by exploiting a wavelet representation to model complex scatterer distributions with sparse vectors of coefficients an efficient bayesian cs bcs strategy is adopted to solve the arising inverse scattering problem a set of representative numerical examples is presented to illustrate the advantages and the limitations of the proposed approach also with respect to comparable state of the art inversion methods

higher order impedance and absorbing boundary conditions traditionally generalized impedance boundary conditions gibcs have been used to model dielectrics and coated surfaces and absorbing boundary conditions abcs have been used to simulate nonreflecting surfaces the two types have the same mathematical form and in most instances a higher order condition involving higher order field derivatives has a better accuracy we demonstrate that there is a close connection between the two and this enables us to use a systematic method which is available for generating gibcs of any desired order to derive new two and three dimensional abcs the method is applicable to curvilinear doubly curved surfaces and examples are given finally curves are presented that quantify the accuracy of two dimensional abcs up to the fourth order and show how higher order abcs can improve the efficiency of large scale partial differential equation pde solutions

anomalous convergence of lyapunov exponent estimates numerical experiments reveal that estimates of the lyapunov exponent for the logistic map ital x sub ital t 1 ital f ital x sub ital t 4 ital x sub ital t 1 minus ital x sub ital t are anomalously precise they are distributed with a standard deviation that scales as 1 ital n where ital n is the length of the trajectory not as 1 radical ital n the scaling expected from an informal interpretation of the central limit theorem we show that this anomalous convergence follows from the fact that the logistic map is conjugate to a constant slope map the lyapunov estimator is just one example of a chaotic walk we show that whether or not a general chaotic walk exhibits anomalously small variance depends only on the autocorrelation of the chaotic process

bayesian compressive sampling for pattern synthesis with maximally sparse non uniform linear arrays a numerically efficient technique based on the bayesian compressive sampling bcs for the design of maximally sparse linear arrays is introduced the method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine rvm for the problem solution the proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non uniformly spaced active elements the numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state of the art techniques for the design of sparse arrays

minimum sidelobe levels for linear arrays a method of finding the optimum sidelobe minimizing weights for an arbitrary linear array is derived that holds for any scan direction beamwidth and type of antenna element used optimum linear array positions are then determined via the particle swarm optimization method hence the two together can give a global bound on antenna array performance with regards to sidelobe minimization results are presented for linear arrays of 2 6 elements for different scan angles beamwidths and antenna elements

synthesis of sparse arrays with focused or shaped beampattern via sequential convex optimizations an iterative procedure for the synthesis of sparse arrays radiating focused or shaped beampattern is presented the algorithm consists in solving a sequence of weighted l1 convex optimization problems the method can thus be readily implemented and efficiently solved in the optimization procedure the objective is the minimization of the number of radiating elements and the constraints correspond to the pattern requirements the method can be applied to synthesize either focused or shaped beampattern and there is no restriction regarding the array geometry and individual element patterns numerical comparisons with standard benchmark problems assess the efficiency of the proposed approach whose computation time is several orders of magnitude below those of so called global optimization algorithms

ads based guidelines for thinned planar arrays we propose an analytical technique based on almost difference sets adss for thinning planar arrays with well controlled sidelobes the method allows one to synthesize bidimensional arrangements with peak sidelobe levels psls predictable and deducible from the knowledge of the array aperture the filling factor and the autocorrelation function of the ads at hand the numerical validation concerned with both small and very large apertures points out that the expected psl values are significantly below those of random arrays and comparable with those from different sets dss although obtainable in a wider range of configurations

characteristic distributions of finite time lyapunov exponents we study the probability densities of finite time or local lyapunov exponents in low dimensional chaotic systems while the multifractal formalism describes how these densities behave in the asymptotic or long time limit there are significant finite size corrections which are coordinate dependent depending on the nature of the dynamical state the distribution of local lyapunov exponents has a characteristic shape for intermittent dynamics and at crises dynamical correlations lead to distributions with stretched exponential tails while for fully developed chaos the probability density has a cusp exact results are presented for the logistic map stackrel ensuremath rightarrow x 4x 1 ensuremath x at intermittency the density is markedly asymmetric while for typical chaos it is known that the central limit theorem obtains and a gaussian density results local analysis provides information on the variation of predictability on dynamical attractors these densities which are used to characterize the nonuniform spatial organization on chaotic attractors are robust to noise and can therefore be measured from experimental data

a global local synthesis approach for large non regular arrays a method is proposed for the synthesis of large planar non regular arrays assuming constant magnitude for the excitation of the elements the approach which combines global and local optimization is based on distinguishing aperture type and non coherent parts of the array factor the following constraints are considered minimal separation of the antennas maximum size of the array and fixed mainbeam width the level of the sidelobes is reduced via the minimization of a new type of flexible averaging cost function based on an lp norm possible applications of this model lie in the field of radio astronomy satellite communications and radar systems the proposed optimization strategy consists of three successive steps designed to be independent of each other starting with an equivalent continuous aperture the first two steps act as global transformations of the radial and azimuthal positions of the elements in the initial array while the third step performs a local optimization of individual elements of the array this last step heavily relies on computations of the gradient of the cost function which can be done quickly using an fft based procedure the method is illustrated for several large scale examples by considering as inputs four different types of non regular arrays

square array antennas based on hadamard difference sets a regular method for synthesizing a planar aperiodic thinned array antenna aa with a low peak sidelobe level is suggested it is based on using specific combinatorial constructions noncyclic difference sets dss the method uses the fact that when the elements of an equiamplitude aa are arranged according to a ds law its power pattern takes constant value in the net of uniformly located space points in the sidelobe region and this value is less than where is the element number in distinction to the method using cyclic dss see leeper 1999 which enables one to build planar aas only on rectangular grids with co prime sidelengths the represented method omits such a constraint the most important class of the noncyclic 2 d dss is represented by the sets of hadamard type sets based on such sets rectangular and square aperiodic roughly half filled aas can be built here the numerical results obtained for the square aas with the element number in the array up to 300 are presented

element positioning for linear arrays using generalized gaussian quadrature we present a novel approach for designing small narrowband linear arrays with unequally spaced elements our approach involves discretising a line source with a desirable beam pattern and relies on the fact that beam patterns are bandlimited we show that given a nonnegative weighting function for a line source one can design a linear array of elements whose beam pattern approximates that of the line source to any desired degree of accuracy we make use of the prolate spheroidal wave functions to analyze line source beam patterns since they are eigenfunctions of the finite fourier transform these functions form a tchebycheff system which allows us to calculate exactly integrals involving these functions via a generalized gaussian quadrature rule this quadrature rule then gives the appropriate set of element positions and weights we give results for several weighting functions and we consider both broadside and electronically scanned linear arrays as an example we show how a broadside array with half wavelength spacing and dolph tchebycheff weights may be improved upon using the method described

surface impedance boundary conditions in time domain for guided structures of arbitrary cross section with lossy dielectric walls this paper presents a procedure to implement the concept of surface impedance boundary condition sibc for lossy dielectrics in time domain the sibc formulation validation and results are obtained with a time domain numerical method namely the transmission line matrix tlm the formulation of surface impedance in frequency domain is converted to the time domain using a rational approximation followed by a bilinear transform with a canonical representation in the state space this surface impedance formulation has been implemented in tlm simulations show that the proposed model is valid for interfaces between air and a lossy dielectric and arbitrary conductivity sigma an application that concerns mode propagation in a rectangular tunnel with lossy dielectric walls is shown a comparison with an approximate method proposed by marcatilli is presented it confirms that the propagation in electrically large guided structures such as tunnels with lossy dielectric walls can be efficiently modeled by this approach

hybrid bcs deterministic approach for sparse concentric ring isophoric arrays an innovative methodology for the synthesis of sparse concentric ring isophoric arrays matching a user defined reference pattern is proposed the synthesis problem is recast as a two step approach firstly aimed at a determining the sparsest auxiliary layout of concentric current rings matching the reference pattern through a bayesian compressive sensing method and successively b yielding the concentric ring isophoric array by means of a density tapering technique a selected set of numerical experiments is presented to provide some insights about the effectiveness the numerical efficiency and the flexibility of the proposed hybrid method

numerical computation of the incomplete lipschitz hankel integral je o a z abstract two factorial neumann series expansions are derived for the incomplete lipschitz hankel integral je 0 a z these expansions are used together with the neumann series expansion given by agrest in an algorithm which efficiently computes je 0 a z to a user defined number of significant digits other expansions for je 0 a z which are found in the literature are also discussed but these expansions are found to offer no significant computational advantages when compared with the expansions used in the algorithm

statistics of finite time lyapunov exponents in the ulam map the statistical properties of finite time lyapunov exponents at the ulam point of the logistic map are investigated the exact analytical expression for the autocorrelation function of one step lyapunov exponents is obtained allowing the calculation of the variance of exponents computed over time intervals of length n the variance anomalously decays as 1 n 2 the probability density of finite time exponents noticeably deviates from the gaussian shape decaying with exponential tails and presenting 2 n 1 spikes that narrow and accumulate close to the mean value with increasing n the asymptotic expression for this probability distribution function is derived it provides an adequate smooth approximation to describe numerical histograms built for not too small n where the finiteness of bin size trims the sharp peaks

on the design of maximally sparse beamforming arrays the problem of designing nonuniformly spaced arrays is formulated as one of constrained optimization in which the cost function is chosen to select the array with the minimum number of elements the response of the array is controlled by a set of inequality point response constraints it is shown that a suitable cost function for this problem is the l sub p quasi norm for 0

autocorrelation driven synthesis of antenna arrays the case of ds based planar isophoric thinned arrays a new methodology for the design of isophoric thinned arrays with a priori controlled pattern features is introduced a fully analytical and general i e valid for any lattice and set of weights relationship between the autocorrelation of the array excitations and the power pattern samples is first derived binary 2 d sequences with known autocorrelation properties namely the difference sets ds s are then chosen as a representative benchmark to prove that it is possible to deduce closed form synthesis formulas that a priori guarantee to fit requirements on the sidelobe level sll the directivity the half power beamwidth and the power pattern in user defined directions the selected results from a wide numerical assessment which also includes full wave simulations with realistic radiators are illustrated to validate the reliability and the accuracy of the proposed design equations and the associated performance bounds

peak sidelobe level reduction with a hybrid approach based on gas and difference sets this paper presents an approach for the optimization of the beam pattern produced by massively thinned arrays the method which combines the most attractive features of a genetic algorithm and those of a combinatorial technique namely the difference sets method is aimed at synthesizing massively thinned antenna arrays in order to suitably reduce the peak sidelobe level selected numerical results are presented in order to assess the effectiveness and reliability of the proposed approach

on the robustness to element failures of linear ads thinned arrays the robustness of the analytical thinning based on almost difference sets adss is analyzed when faulty elements are present in linear arrays peak sidelobe level psl statistics of the damaged layouts are numerically inferred from representative simulations dealing with different aperture sizes and element failure rates

synchronization threshold in coupled logistic map lattices abstract we consider regular lattices of coupled chaotic maps whose local dynamics is ruled by the logistic map x 4 x 1 x a usual paradigm of chaotic systems through finite time exponents we scrutinize the lattice dynamics in the vicinity of the threshold of complete synchronization we connect dynamical features such as relaxation to the coherent state and intermittency with the statistics of finite time exponents focusing on the implications of the particular statistics related to the logistic map although numerical examples are given for lattice couplings decaying with distance as a power law our results are expected to be valid for a wider class of schemes coupling logistic maps

reducing the number of elements in multiple pattern linear arrays by the extended matrix pencil methods previously the matrix pencil method mpm and the forward backward mpm fbmpm were used to effectively reduce the number of antenna elements in the single pattern linear arrays this work extends the mpm and fbmpm based synthesis methods to the synthesis of multiple pattern linear arrays with a smaller number of elements the extended mpm resp the extended fbmpm method organizes all the multiple pattern data into a composite hankel resp composite hankel toeplitz matrix from which the minimum number of elements and the common poles corresponding to element positions can be obtained with similar processing used in the original mpm or fbmpm synthesis method in particular the extended fbmpm inherits the advantage of the original fbmpm that a useful restriction is put on the distribution of poles which makes the element positions obtained much more accurate and robust numerical experiments are conducted to validate the effectiveness and robustness of the proposed methods for the tested cases the element saving is about 20 25 for reconfigurable shaped patterns and can be even more for electrically large linear arrays with scanned pencil beams

the use of surface impedance concepts in the finite difference time domain method surface impedance concepts are introduced into the finite difference time domain fdtd method lossy conductors are replaced by surface impedance boundary conditions sibc reducing the solution space and producing significant computational savings specifically a sibc is developed to replace a lossy dielectric half space an efficient implementation of this fdtd sibc based on the recursive properties of convolution with exponentials is presented finally three problems are studied to illustrate the accuracy of the fdtd sibc formulation a plane wave incident on a lossy dielectric half space a line current over a lossy dielectric half space and wave propagation in a parallel plate waveguide with lossy walls

an accurate and efficient analysis for transient plane waves obliquely incident on a conductive half space te case we develop a method for the analytical evaluation of the inverse laplace transform representations for transient transverse magnetic tm plane wave obliquely incident on a conductive half space we assume that the permittivity and conductivity of the dispersive half space are independent of frequency the time domain expressions for the reflected and transmitted waves are first represented as inverse laplace transforms the transient fields are then shown to consist of two canonical integrals the canonical integrals in turn are solved analytically thereby yielding close form solutions involving incomplete lipschitz hankel integrals ilhis the ilhis are computed numerically using efficient convergent and asymptotic series expansions thus enabling the efficient computation of the transient fields the exact closed form expressions are verified by comparing with previously published results and with results obtained using standard numerical integration and fast fourier transform fft algorithms an asymptotic series representation for the ilhis is also employed to obtain a relatively simple late time approximation for the transient fields this approximate late time expression is shown to accurately model the fields over a large portion of its time history

lyapunov spectrum and synchronization of piecewise linear map lattices with power law coupling we study the synchronization properties of a lattice of chaotic piecewise linear maps the coupling strength decreases with the lattice distance in a power law fashion we obtain the lyapunov spectrum of the coupled map lattice and investigate the relation between spatiotemporal chaos and synchronization of amplitudes and phases using suitable numerical diagnostics

local predictability and nonhyperbolicity through finite lyapunov exponent distributions in two degrees of freedom hamiltonian systems received 13 september 2007 revised manuscript received 5 november 2008 published 4 december 2008by using nite lyapunov exponent distributions we get insight into both the local and global properties ofa dynamical ow including its nonhyperbolic behavior several distributions of nite lyapunov exponentshave been computed in two prototypical four dimensional phase space hamiltonian systems they have beencomputed calculating the growth rates of a set of orthogonal axes arbitrarily pointed at given intervals weanalyze how such distributions serve or not for tracing the orbit nature and local ow properties such as theunstable dimension variability as the axes are allowed or not to tend to the largest stretching direction therelationship between the largest and closest to zero exponent distribution is analyzed it shows a linear depen dency at short intervals related to the number of degrees of freedom of the system finally the hyperbolicityindexes associated to the shadowing times are calculated they provide interesting information at very localscales even when there are no gaussian distributions and the values cannot be regarded as random variables doi 10 1103 physreve 78 066204 pacs number s 05 45 a

near field radar imaging via compressive sensing a novel two dimensional 2 d compressive sensing cs based method is presented for near field radar imaging first an accurate near field approximation is proposed based on which the circular wavefront curvature of spherical waves can be compensated by mapping the images to a rectified new grid more importantly the near field approximation makes the two dimensions of the scattered data separable for the range and cross range directions which makes it possible to solve the 2 d reflectivity matrix for the image reconstruction directly then a 2 d proximal subgradient algorithm for near field radar imaging based on a fast iterative shrinkage thresholding algorithm fista is introduced to resolve the memory usage and computation time issues simulation and experimental results are provided to demonstrate the performance of the proposed method with comparisons to the traditional fourier based method and to the conjugate gradient cg based method which proves that the proposed method is an effective way to solve the near field radar imaging problem

robust beamforming with magnitude response constraints using iterative second order cone programming the problem of robust beamforming for antenna arrays with arbitrary geometry and magnitude response constraints is one of considerable importance due to the presence of the non convex magnitude response constraints conventional convex optimization techniques cannot be applied directly a new approach based on iteratively linearizing the non convex constraints is then proposed to reformulate the non convex problem to a series of convex subproblems each of which can be optimally solved using second order cone programming socp moreover in order to obtain a more robust beamformer against array imperfections the proposed method is further extended by optimizing its worst case performance using again socp different from some conventional methods which are restricted to linear arrays the proposed method is applicable to arbitrary array geometries since the weight vector rather than its autocorrelation sequence is used as the variable simulation results show that the performance of the proposed method is comparable to the optimal solution previously proposed for uniform linear arrays and it also gives satisfactory results under different array specifications and geometries tested

synthesis of linear and planar arrays with minimum element selection a new method for the synthesis of linear and planar arrays having prescribed beamwidth and sidelobe levels and a minimum number of elements is proposed in the method the number of elements in an array is minimized while constraining the amplitude response error in the mainlobe region the attenuation in the sidelobe region and the array dimensions an iterative constrained optimization method is used where the amplituderesponse error is linearly approximated at each iteration while concurrently minimizing a re weighted l1 norm of the array coefficients to ensure robustness of the array we constrain a sensitivity parameter namely the white noise gain to be above a prescribed level furthermore the method also provides the additional flexibility of controlling the array dimensions symmetry properties and element positions of the array two variants have been developed in the first variant both the array coefficients and the positions of the elements are optimized in the second variant only the array coefficients are optimized while the elements are fixed at predefined positions experimental comparisons with several state of the art competing methods show that the proposed method provides greater flexibility of controlling the robustness beampattern response error array dimensions and element positions while at the same time the number of elements is less than or equal to that of the competing methods

analytical results for coupled map lattices with long range interactions we obtain exact analytical results for lattices of maps with couplings that decay with distance as r ensuremath ensuremath alpha we analyze the effect of the coupling range on the system dynamics through the lyapunov spectrum for lattices whose elements are piecewise linear maps we get an algebraic expression for the lyapunov spectrum when the local dynamics is given by a nonlinear map the lyapunov spectrum for a completely synchronized state is analytically obtained the critical line characterizing the synchronization transition is determined from the expression for the largest transversal lyapunov exponent in particular it is shown that in the thermodynamical limit such transition is only possible for sufficiently long range interactions namely for ensuremath alpha l ensuremath alpha c d where d is the lattice dimension

complex weight sparse linear array synthesis by bayesian compressive sampling an innovative method for the synthesis of maximally sparse linear arrays matching arbitrary reference patterns is proposed in the framework of sparseness constrained optimization the approach exploits the multi task mt bayesian compressive sensing bcs theory to enable the design of complex non hermitian layouts with arbitrary radiation and geometrical constraints by casting the pattern matching problem into a probabilistic formulation a relevance vector machine rvm technique is used as solution tool the numerical assessment points out the advances of the proposed implementation over the extension to complex patterns of and it gives some indications about the reliability flexibility and numerical efficiency of the mt bcs approach also in comparison with state of the art sparse arrays synthesis methods