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

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

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

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

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

the topological structure of fuzzy sets with endograph metric for a non degenerate convex subset y of the n dimensional euclidean space r n let k y be the family of all fuzzy sets of r n which are upper semicontinuous fuzzy convex and normal with compact supports contained in y we show that the space k y with the topology of endograph metric is homeomorphic to the hilbert cube q 1 1 w iff y is compact and the space k y is homeomorphic to x n q sup x n 1 iff y is non compact and locally compact

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

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

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

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

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

distribution of first passage times to specific targets on compactly explored fractal structures the distribution of the first passage times fpt of a one dimensional random walker to a target site follows a power law f t t ensuremath 3 2 we generalize this result to another situation pertinent to compact exploration and consider the fpt of a random walker with specific source and target points on an infinite fractal structure with spectral dimension d s l2 we show that the probability density of the first return to the origin has the form f t t d s 2 ensuremath 2 and the fpt to a specific target at distance r follows the law f mathbf r t r d w ensuremath d f t d s 2 ensuremath 2 where d w and d f are the walk dimension and the fractal dimension of the structure respectively the distance dependence of f mathbf r t reproduces the one of the mean fpt of a random walk in a confined domain

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

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

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

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

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

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