improvement and comparison of heuristics for solving the uncapacitated multisource weber problem the multisource weber problem is to locate simultaneouslym facilities in the euclidean plane to minimize the total transportation cost for satisfying the demand ofn fixed users each supplied from its closest facility many heuristics have been proposed for this problem as well as a few exact algorithms heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms we compare various heuristics i e alternative location allocation cooper 1964 projection bongartz et al 1994 tabu search brimberg and mladenovic 1996a p median plus weber hansen et al 1996 genetic search and several versions of variable neighbourhood search based on empirical tests that are reported it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that variable neighbourhood search gives consistently best results on average in moderate computing time

antenna array pattern synthesis via convex optimization we show that a variety of antenna array pattern synthesis problems can be expressed as convex optimization problems which can be numerically solved with great efficiency by recently developed interior point methods the synthesis problems involve arrays with arbitrary geometry and element directivity constraints on far and near field patterns over narrow or broad frequency bandwidth and some important robustness constraints we show several numerical simulations for the particular problem of constraining the beampattern level of a simple array for adaptive and broadband arrays

broadband doa estimation using frequency invariant beamforming a new method of direction of arrival doa estimation for multiple broadband farfield signals is presented the technique uses a beamspace preprocessing structure based on frequency invariant beamforming specifically a set of beam shaping filters focus the received array data in the time domain thereby avoiding the need for frequency decomposition hence the proposed method is conceptually different from most other broadband doa estimators which require frequency decomposition numerical results are presented to demonstrate the use of the new method and compare it with conventional coherent signal subspace methods

an efficient newton barrier method for minimizing a sum of euclidean norms a new newton barrier method is proposed for minimizing a sum of euclidean norms msn f x sum i 1 k a i t x b i 2 msn is a nonsmooth problem because f is not differentiable at any point x where any of the norms is zero the method used is based on approximating f with a smooth function which in the limit has the same optimal value as f msn is shown to have a dual problem with properties very similar to duality theory in linear programming this is used in the development of the method and to give a proof of when an optimal solution for the smooth approximation is epsilon optimal measured in the duality gap for the original problem an implementation of the algorithm is described for large sparse problems and numerical results are presented for problems with more than 270 000 nonlinear variables these problems arise from plastic collapse analysis

design of frequency invariant beamformer without temporal filtering a novel method for the design of frequency invariant beamformers for uniformly spaced three dimensional 3 d arrays is proposed unlike the traditional method which is based on the use of temporal filtering the proposed design can achieve a frequency invariant response without employing any temporal filtering process and the resultant beamformer does not suffer from the beam broadening effect at high off boresight steering angles a design example is provided to show the effectiveness of the proposed method

unicast multi antenna relay beamforming with per antenna power control optimization and duality we consider amplify and forward multi antenna relaying between a single pair of source and destination under relay per antenna power constraints we design the optimal relay processing matrix to minimize the maximum per antenna power budget for a received snr target with given transmit and receive beamformers at the source and destination respectively we first focus on the equivalent system with single antenna source and destination although non convex we show that the optimization satisfies strong lagrange duality and can be solved in the lagrangian dual domain we reveal a prominent structure of this problem by establishing its duality with direct simo beamforming system with an uncertain noise this enables us to derive a semi closed form expression for the optimal relay processing matrix that depends on a set of dual variables which can be determined through numerical optimization with a significantly reduced problem space we further show that the dual problem has a semi definite programming form which enables efficient numerical optimization methods to determine the dual variables with polynomial complexity using this result the reverse problem of snr maximization under a set of relay per antenna power constraints is then addressed we then consider the maximum relay beamforming achievable rate under different combinations of antenna setups at source and destination in particular we generalize the duality to mimo relay beamforming vs direct mimo beamforming and establish the dual relation of the two systems for different multi antenna setups at source and destination

on the integral representations for the confluent hypergeometric function in this paper we derive a new contour integral representation for the confluent hypergeometric function as well as for its various special cases consequently we derive expansions of the confluent hypergeometric function in terms of functions of the same kind furthermore we obtain a new identity involving integrals and sums of confluent hypergeometric functions our results generalized several well known results in the literature

regularization using monte carlo simulation to make optimal beamformers robust to system perturbations design of optimal beamformers that withstand system perturbations such as channel mismatch sensor position error and pointing error has been a key issue in real world applications of arrays this paper aims to characterize the array performance in relation to the random perturbations from a statistical perspective in the synthesis stage directivity index and front to back ratio are employed as the performance measures for beamformer optimization filter coefficients of the arrays are determined using the least squares and convex optimization approaches using the preceding performance measures next monte carlo sampling are conducted to simulate the stochastic system perturbations following either uniform distribution or normal distribution statistics including the sample mean maximum minimum and the maximum likelihood ml of the preceding performance measures are calculated three regularization criteria based on max mean max min and max ml of performance measures are proposed for choosing regularization parameters used in beamformer optimization the max mean criterion was found most useful to determine either a simple constant or a frequency dependent regularization parameter to validate the proposed methods experiments of beam patterns and automatic speech recognition test were conducted for directional and diffuse noise suppression problems where optimal beamformers designed with the regularization parameter selected by the preceding procedures were utilized

a note on treating a second order cone program as a special case of a semidefinite program it is well known that a vector is in a second order cone if and only if its arrow matrix is positive semidefinite but much less well known is about the relation between a second order cone program socp and its corresponding semidefinite program sdp the correspondence between the dual problem of socp and sdp is quite direct and the correspondence between the primal problems is much more complicated given a sdp primal optimal solution which is not necessarily arrow shaped we can construct a socp primal optimal solution the mapping from the primal optimal solution of sdp to the primal optimal solution of socp can be shown to be unique conversely given a socp primal optimal solution we can construct a sdp primal optimal solution which is not an arrow matrix indeed in general no primal optimal solutions of the socp related sdp can be an arrow matrix

second order conic approximation for disassembly line design with joint probabilistic constraints a problem of profit oriented disassembly line design and balancing with possible partial disassembly and presence of hazardous parts is studied the objective is to design a production line providing a maximal revenue with balanced workload task times are assumed to be random variables with known normal probability distributions the cycle time constraints are to be jointly satisfied with at least a predetermined probability level an and or graph is used to model the precedence relationships among tasks several lower and upper bounding schemes are developed using second order cone programming and convex piecewise linear approximation to show the relevance and applicability of the proposed approach a set of instances from the literature are solved to optimality

a algorithm for convex minimization for convex minimization we introduce an algorithm based on space decomposition the method uses a bundle subroutine to generate a sequence of approximate proximal points when a primal dual track leading to a solution and zero subgradient pair exists these points approximate the primal track points and give the algorithm s or corrector steps the subroutine also approximates dual track points that are gradients needed for the method s newton predictor steps with the inclusion of a simple line search the resulting algorithm is proved to be globally convergent the convergence is superlinear if the primal dual track points and the objective s hessian are approximated well enough

on the use of hadamard expansions in hyperasymptotic evaluation differential equations of hypergeometric type we describe how a modication of a common technique for developing asymptotic expansions of solutions of linear di erential equations can be used to derive hadamard expansions of solutions of di erential equations hadamard expansions are convergent series that share some of the features of hyperasymptotic expansions particularly that of having exponentially small remainders when truncated and as a consequence provide a useful computational tool for evaluating special functions the methods we discuss can be applied to linear di erential equations of hypergeometric type and may have wider applicability

neighborhood search heuristics for the uncapacitated facility location problem abstract the uncapacitated facility location problem is one of choosing sites among a set of candidates in which facilities can be located so that the demands of a given set of clients are satisfied at minimum costs applications of neighborhood search methods to this problem have not been reported in the literature in this paper we first describe and compare several neighborhood structures used by local search to solve this problem we then describe neighborhood search heuristics based on tabu search and complete local search with memory to solve large instances of the uncapacitated facility location problem our computational experiments show that on medium sized problem instances both these heuristics return solutions with costs within 0 075 of the optimal with execution times that are often several orders of magnitude less than those required by exact algorithms on large sized instances the heuristics generate low cost solutions quite fast and terminate with solutions whose costs are within 0 0345 of each other

extension of karmarkar s algorithm onto convex quadratically constrained quadratic problems convex quadratically constrained quadratic problems are considered it is shown that such problems can be transformed to aconic form the feasible set of the conic form is the intersection of a direct product of standard quadratic cones intersected with a hyperplane the analogue of a simplex and a linear subspace for a problem of such form the analogue of karmarkar s projective transformation and logarithmic barrier function are built this allows us to extend word by word the method of karmarkar for lp to qcqp and allows us to obtain a similar polynomial worst case bound for the number of iterations

a nonlinear primal dual method for total variation based image restoration we present a new method for solving total variation tv minimization problems in image restoration the main idea is to remove some of the singularity caused by the nondifferentiability of the quantity nabla u in the definition of the tv norm before we apply a linearization technique such as newton s method this is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function which can be interpreted as the normal vector to the level sets of the image u our method can be viewed as a primal dual method as proposed by conn and overton a primal dual interior point method for minimizing a sum of euclidean norms preprint 1994 and andersen ph d thesis odense university denmark 1995 for the minimization of a sum of euclidean norms in addition to possessing local quadratic convergence experimental results show that the new method seems to be globally convergent

a new method for optimal truss topology design truss topology optimization formulated in terms of displacements and bar volumes results in a large nonconvex optimization problem for the case of maximization of stiffness for a prescribed volume this paper presents a new equivalent an unconstrained and convex minimization problem in displacements only where the function to be minimized is the sum of terms each of which is the maximum of two convex quadratic functions existence of solutions is proved as is the convergence of a nonsmooth steepest descent type algorithm for solving the topology optimization problem the algorithm is computationally attractive and has been tested on a large number of examples some of which are presented

theory and design of broadband sensor arrays with frequency invariant far field beam patterns the theory and design of a broadband array of sensors with a frequency invariant far field beam pattern over an arbitrarily wide design bandwidth is presented the frequency invariant beam pattern property is defined in terms of a continuously distributed sensor and the problem of designing a practical sensor array is then treated as an approximation to this continuous sensor using a discrete set of filtered broadband omnidirectional array elements the design methodology is suitable for one two and three dimensional sensor arrays it imposes no restrictions on the desired aperture distribution beam shape and can cope with arbitrarily wide bandwidths an important consequence of the results is that the frequency response of the filter applied to the output of each sensor can be factored into two components one component is related to a slice of the desired aperture distribution and the other is sensor independent the results also indicate that the locations of the sensors are not a crucial design consideration although it is shown that nonuniform spacings simultaneously avoid spatial aliasing and minimize the number of sensors an example design which covers a 10 1 frequency range which is suitable for speech acquisition using a microphone array illustrates the utility of the method finally the theory is generalized to cover a parameterized class of arrays in which the frequency dependence of the beam pattern can be controlled in a continuous manner from a classical single frequency design to a frequency invariant design

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

fir filter design by convex optimization using directed iterative rank refinement algorithm the advances in convex optimization techniques have offered new formulations of design with improved control over the performance of fir filters by using lifting techniques the design of a length l fir filter can be formulated as a convex semidefinite program sdp in terms of an l times l matrix that must be rank 1 although this formulation provides means for introducing highly flexible design constraints on the magnitude and phase responses of the filter convex solvers implementing interior point methods almost never provide a rank 1 solution matrix to obtain a rank 1 solution we propose a novel directed iterative rank refinement dirr algorithm where at each iteration a matrix is obtained by solving a convex optimization problem the semidefinite cost function of that convex optimization problem favors a solution matrix whose dominant singular vector is on a direction determined in the previous iterations analytically it is shown that the dirr iterations provide monotonic improvement and the global optimum is a fixed point of the iterations over a set of design examples it is illustrated that the dirr requires only a few iterations to converge to an approximately rank 1 solution matrix the effectiveness of the proposed method and its flexibility are also demonstrated for the cases where in addition to the magnitude constraints the constraints on the phase and group delay of filter are placed on the designed filter

improving beampatterns of two dimensional random arrays using convex optimization sensors are becoming ubiquitous and can be combined in arrays for source localization purposes if classical conventional beamforming is used then random arrays have poor beampatterns by pre computing sensor weights these beampatterns can be improved significantly the problem is formulated in the frequency domain as a desired look direction a frequency independent transition region and the power minimized in a rejection region using this formulation the frequency dependent sensor weights can be obtained using convex optimization since the weights are data independent they can be pre computed the beamforming has similar computational complexity as conventional beamforming the approach is demonstrated for real 2d arrays

an efficient primal dual interior point method for minimizing a sum of euclidean norms the problem of minimizing a sum of euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature this nonsmooth optimization problem arises in many different kinds of modern scientific applications we derive a primal dual interior point algorithm for the problem by applying newton s method directly to a system of nonlinear equations characterizing primal and dual feasibility and a perturbed complementarity condition the main work at each step consists of solving a system of linear equations the schur complement equations this schur complement matrix is not symmetric unlike in linear programming we incorporate a mehrotra type predictor corrector scheme and present some experimental results comparing several variations of the algorithm including as one option explicit symmetrization of the schur complement with a skew corrector term we also present results obtained from a code implemented to solve large sparse problems using a symmetrized schur complement this has been applied to problems arising in plastic collapse analysis with hundreds of thousands of variables and millions of nonzeros in the constraint matrix the algorithm typically finds accurate solutions in less than 50 iterations and determines physically meaningful solutions previously unobtainable

a logarithmic barrier function algorithm for quadratically constrained convex quadratic programming an interior point method for quadratically constrained convex quadratic programming is presented that is based on a logarithmic barrier function approach and terminates at a required accuracy of an approximate solution in polynomial time this approach generates a sequence of unconstrained optimization problems each of which is approximately solved by taking a single step in a newton direction

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

asymptotically perfect wideband focusing of multiring circular arrays the concept of coherent focusing of sensor arrays introduced by wang and kaveh led to the development of high performance and computationally efficient algorithms for wideband direction finding and beamforming nonetheless the quality of focusing depends on the understanding and the proper exploitation of specific array manifold properties circular arrays exhibit uniform isotropic performance over the entire azimuthal range and allow the use of fast algorithms originally developed for uniform linear arrays by decomposing the manifold into circular harmonics coherent wideband focusing of circular arrays suffers from ambiguities noise warping and numerical ill conditioning in this work it is shown that a fast orthonormal beamspace transformation combining the responses of two concentric rings can perfectly focus wideband sources at all azimuth angles in the circular harmonic domain in the limit of infinite number of sensors the information loss after focusing is minimized through an analytical approach the proposed focusing scheme is computationally very efficient and can be directly extended to multiring circular arrays that are arranged into a set of nested two ring subarrays to cover very large bandwidths

spatially varying spectral filtering of signals on the unit sphere this paper presents a general framework for spatially varying spectral filtering of signals defined on the unit sphere as an analogy to joint time frequency filtering for this purpose we first map spherical signals from spatial domain into joint spatio spectral domain where a spatio spectral signal transformation or modification is introduced for mapping spatial signals into joint spatio spectral domain we use the spatially localized spherical harmonic transform slsht from the literature we then propose a suitable scheme to transform the modified signal from the spatio spectral domain back to an admissible signal in the spatial domain using the least squares approach we also show that the overall action of the slsht and spatio spectral signal modification can be described through a single transformation matrix which is useful in practice finally we discuss two specific and useful instances of spatially varying spectral filtering defined through multiplicative and convolutive modification of the slsht distribution and show through numerical examples their effectiveness in selective spectral filtering of different spatial regions of the signal

robust solutions to uncertain semidefinite programs in this paper we consider semidefinite programs sdps whose data depend on some unknown but bounded perturbation parameters we seek robust solutions to such programs that is solutions which minimize the worst case objective while satisfying the constraints for every possible value of parameters within the given bounds assuming the data matrices are rational functions of the perturbation parameters we show how to formulate sufficient conditions for a robust solution to exist as sdps when the perturbation is full our conditions are necessary and sufficient in this case we provide sufficient conditions which guarantee that the robust solution is unique and continuous holder stable with respect to the unperturbed problem s data the approach can thus be used to regularize ill conditioned sdps we illustrate our results with examples taken from linear programming maximum norm minimization polynomial interpolation and integer programming

second order cone programming formulations for feature selection this paper addresses the issue of feature selection for linear classifiers given the moments of the class conditional densities the problem is posed as finding a minimal set of features such that the resulting classifier has a low misclassification error using a bound on the misclassification error involving the mean and covariance of class conditional densities and minimizing an l1 norm as an approximate criterion for feature selection a second order programming formulation is derived to handle errors in estimation of mean and covariances a tractable robust formulation is also discussed in a slightly different setting the fisher discriminant is derived feature selection for fisher discriminant is also discussed experimental results on synthetic data sets and on real life microarray data show that the proposed formulations are competitive with the state of the art linear programming formulation

the p q active uncapacitated facility location problem investigation of the solution space and an lp fitting heuristic abstract the p q active uncapacitated facility location problem is the problem of locating p facilities on n possible sites each serving at least q of the m clients at the minimum cost the problem is an extension of the uncapacitated facility location problem ufl where constraints on the number of facilities and their minimum activity have been added a use of this formulation could be the opening of p new schools where each must have at least q pupils p q active is np hard like the ufl in this paper we present a thorough investigation of the p q active ufl and propose a heuristic solution method different geometric and random cost problem instances are considered experiments show that 60 of the problems can be solved to optimality just by solving the corresponding lp relaxation using a simple local search heuristic the remaining geometric problems are solved with an average gap of 0 1 to a lower bound found by lp relaxation an effort is put into isolating problem types that are hard to solve problems with low p p q close to m combined with clustered clients or a low variation in the facility opening cost are most likely to give results worse than average gaps up to 8 are observed in the worst cases

an efficient tabu search procedure for the p median problem abstract in this paper we present a new solution heuristic for the p median problem the algorithm is based on tabu search principles and uses short term and long term memory as well as strategic oscillation and random tabu list sizes our proposed procedure is compared with two other move heuristics a well known interchange heuristic and a recent hybrid heuristic in computational tests on networks ranging in size up to 500 nodes the new heuristic is found to be superior with respect to the quality of solutions produced

synthesis of sparse arrays with frequency invariant focused beam patterns under accurate sidelobe control by iterative second order cone programming it is shown in this communication that the problem of synthesizing a frequency invariant fi beam pattern with as few elements as possible can be transformed into a sequence of weighted ell 1 optimizations under multiple convex constraints the objective of the weighted ell 1 optimization is to minimize the number of radiating elements for the filter and sum beamforming structure this is equivalent to minimizing the number of filters each with a set of optimized coefficients the multiple constraints are adopted to individually control the mainlobe and sidelobe pattern characteristics so as to preserve the fi property in the mainlobe region while satisfying a given upper bound in the sidelobe region the wng constraint can also be incorporated into the proposed method to enhance the synthesis robustness this method can be easily implemented by iterative second order cone programming socp and only few iterations are required to reach the convergence a set of examples for the synthesis of fi patterns with uniform sidelobe level sll or multiple nulls scannable fi patterns and the synthesis of fi pattern for an arc array with directive elements is presented to validate the effectiveness and advantages of the proposed method the element saving is about 23 3 50 for the test cases

fast directional spatially localized spherical harmonic transform we propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio spectral domain when used in conjunction with an asymmetric window function we call this transform the directional spatially localized spherical harmonic transform directional slsht which extends the slsht from the literature whose usefulness is limited to symmetric windows we present an inversion relation to synthesize the original signal from its directional slsht distribution for an arbitrary window function as an example of an asymmetric window the most concentrated band limited eigenfunction in an elliptical region on the sphere is proposed for directional spatio spectral analysis and its effectiveness is illustrated on the synthetic and mars topographic data sets finally since such typical data sets on the sphere are of considerable size and the directional slsht is intrinsically computationally demanding depending on the band limits of the signal and window a fast algorithm for the efficient computation of the transform is developed the floating point precision numerical accuracy of the fast algorithm is demonstrated and a full numerical complexity analysis is presented

an efficient algorithm for minimizing a sum of euclidean norms with applications in recent years rich theories on polynomial time interior point algorithms have been developed these theories and algorithms can be applied to many nonlinear optimization problems to yield better complexity results for various applications in this paper the problem of minimizing a sum of euclidean norms is studied this problem is convex but not everywhere differentiable by transforming the problem into a standard convex programming problem in conic form we show that an epsilon optimal solution can be computed efficiently using interior point algorithms as applications to this problem polynomial time algorithms are derived for the euclidean single facility location problem the euclidean multifacility location problem and the shortest network under a given tree topology in particular by solving the newton equation in linear time using em gaussian elimination on leaves of a tree we present an algorithm which computes an epsilon optimal solution to the shortest network under a given full steiner topology interconnecting n regular points in o n sqrt n log bar c epsilon log n arithmetic operations where bar c is the largest pairwise distance among the given points the previous best known result on this problem is a graphical algorithm which requires o n2 arithmetic operations under certain conditions

l infinity norm design of linear phase robust broadband beamformers using constrained optimization a new method for the design of linear phase robust far field broadband beamformers using constrained optimization is proposed in the method the maximum passband ripple and minimum stopband attenuation are ensured to be within prescribed levels while at the same time maintaining a good linear phase characteristic at a prescribed group delay in the passband since the beamformer is intended primarily for small sized microphone arrays where the microphone spacing is small relative to the wavelength at low frequencies the beamformer can become highly sensitive to spatial white noise and array imperfections if a direct minimization of the error is performed therefore to limit the sensitivity of the beamformer the optimization is carried out by constraining a sensitivity parameter namely the white noise gain wng to be above prescribed levels across the frequency band two novel design variants have been developed the first variant is formulated as a convex optimization problem where the maximum error in the passband is minimized while the second variant is formulated as an iterative optimization problem and has the advantage of significantly improving the linear phase characteristics of the beamformer under any prescribed group delay or linear array configuration in the second variant the passband group delay deviation is minimized while ensuring that the maximum passband ripple and stopband attenuation are within prescribed levels to reduce the computational effort in carrying out the optimization a nonuniform variable sampling approach over the frequency and angular dimensions is used to compute the required parameters experiment results show that beamformers designed using the proposed methods have much smaller passband group delay deviation for similar passband ripple and stopband attenuation than a modified version of an existing method

steerable frequency invariant beamforming for arbitrary arrays frequency invariant beamforming aims to parameterize array filter coefficients such that the spectral and spatial response profiles of the array can be adjusted independently solutions to this problem have been presented for specific sensor configurations often requiring a larger number of sensors however in practical applications the number and location of sensors are often restricted this paper proposes to find an optimal linear basis transformation that decouples the frequency response from the spatial response a least squares optimal basis transform can be computed numerically for arbitrary sensor configurations for which typically no exact analytical solutions are available this transform can be further combined with a spherical harmonics basis resulting in readily steerable broadband beams this solution to broadband beamforming effectively decouples the array geometry from the steering geometry furthermore for frequency invariant beams this approach results in a significant reduction in the number of beam design parameters here the method is demonstrated for an optimal design of far field response for an irregular linear array with as few as three sensors

computing the confluent hypergeometric function m a b x the confluent hypergeometric function m a b x arises naturally in both statistics and physics although analytically well behaved extreme but practically useful combinations of parameters create extreme computational difficulties a brief review of known analytic and computational results highlights some difficult regions including b a 0 with x much larger than b existing power series and integral representations may fail to converge numerically while asymptotic series representations may diverge before achieving the accuracy desired continued fraction representations help somewhat variable precision can circumvent the problem but with reductions in speed and convenience in some cases known analytic properties allow transforming a difficult computation into an easier one the combination of existing computational forms and transformations still leaves gaps for b a 0 two new power series in terms of gamma and beta cumulative distribution functions respectively help in some cases numerical evaluations highlight the abilities and limitations of existing and new methods overall a rational approximation due to luke and the new gamma based series provide the best performance

transmitter optimization for per antenna power constrained multi antenna downlinks an slnr maximization methodology in this paper we consider signal to leakage plus noise ratio slnr maximized precoding for multi antenna downlinks under per antenna power constraints papcs in contrast to the conventional sum power constraint the per antenna power constrained slnr precoder design problem no longer admits a simple closed form solution and achieving its optimal solution turns out to be much more challenging to conquer the difficulty we first propose to perform the charnes cooper transformation on the problem of interest which yields a solvable simpler second order cone program socp moving beyond this approach we are then able to obtain a semi closed form solution to the optimal slnr precoder the power allocation among users is also optimized for further performance enhancement for which we devise two numerical methods based on gradient projection and a low complexity approximation finally focusing on the imperfect channel state information csi scenario we develop a robust slnr based precoder to combat the performance degradation caused by random csi errors the superiority of all proposed precoder designs in this work is confirmed by numerical simulations

an ol n 3 potential reduction algorithm for linear programming we describe a primal dual potential function for linear programming phi x s rho ln x t s sum limits j 1 n ln x j s j where n x is the primal variable ands is the dual slack variable as a result we develop an interior point algorithm seeking reductions in the potential function with rho n sqrt n neither tracing the central path nor using the projective transformation the algorithm converges to the optimal solution set in o sqrt n l iterations and uses o n3l total arithmetic operations we also suggest a practical approach to implementing the algorithm

uniform concentric circular arrays with frequency invariant characteristics theory design adaptive beamforming and doa estimation this paper proposes a new digital beamformer for uniform concentric circular arrays uccas having nearly frequency invariant fi characteristics the basic principle is to transform the received signals to the phase mode and remove the frequency dependency of the individual phase mode through the use of a digital beamforming or compensation network as a result the far field pattern of the array which is governed by a set of variable beamformer weights is electronically steerable and it is approximately invariant over a wider range of frequencies than conventional uniform circular arrays ucas this also makes it possible to design the compensation network and the beamformer weights separately the design of the compensation network is formulated as a second order cone programming socp problem and is solved optimally for minimax criterion by employing the beamspace approach using the outputs of a set of fixed ucca frequency invariant beamformers fibs a new beamspace music algorithm is proposed for estimating the direction of arrivals doas of broadband sources since the beampatterns of the ucca fib is approximately invariant with frequency and is governed by a small set of weights a very efficient adaptive beamformer using the minimum variance beamforming mvb approach can be developed simulation results using broadband gaussian and multisinusoidal inputs show that the proposed adaptive ucca fib is numerically better conditioned than the conventional broadband tapped delay line based adaptive beamformers due to the fi property and significantly fewer numbers of adaptive parameters consequently a higher output signal to inference plus noise ratio over the conventional tapped delay line approach is observed the usefulness of the proposed ucca fib in broadband doa estimation is also verified by computer simulation

3 d array pattern synthesis with frequency invariant property for concentric ring array this correspondence proposes a method for array pattern synthesis of a concentric ring array that yields invariant array pattern over a certain frequency band for beamforming in three dimensions the proposed method uses the fourier bessel series to determine the weights from different rings to form the overall array pattern simulation examples are given to illustrate the proposed method

remarks on some series expansions associated with certain products of the incomplete gamma functions abstract in several recent works some interesting generalizations of the first order volterra type integro differential equation governing the unsaturated behavior of the free electron laser fel were introduced and investigated by making use of fractional calculus that is calculus of integrals and derivatives of an arbitrary real or complex order among other things it is observed here that an expansion formula for the confluent hypergeometric function in a series of the product of two entire integral incomplete gamma functions does not hold true as asserted and applied in these earlier works some necessary corrections and possible remedies are also pointed out

efficient computation of slepian functions for arbitrary regions on the sphere in this paper we develop a new method for the fast and memory efficient computation of slepian functions on the sphere slepian functions which arise as the solution of the slepian concentration problem on the sphere have desirable properties for applications where measurements are only available within a spatially limited region on the sphere and or a function is required to be analyzed over the spatially limited region slepian functions are currently not easily computed for large band limits for an arbitrary spatial region due to high computational and large memory storage requirements for the special case of a polar cap the symmetry of the region enables the decomposition of the slepian concentration problem into smaller subproblems and consequently the efficient computation of slepian functions for large band limits by exploiting the efficient computation of slepian functions for the polar cap region on the sphere we develop a formulation supported by a fast algorithm for the approximate computation of slepian functions for an arbitrary spatial region to enable the analysis of modern datasets that support large band limits for the proposed algorithm we carry out accuracy analysis of the approximation computational complexity analysis and review of memory storage requirements we illustrate through numerical experiments that the proposed method enables faster computation and has smaller storage requirements while allowing for sufficiently accurate computation of the slepian functions

complete characterizations of stable farkas lemma and cone convex programming duality we establish necessary and sufficient conditions for a stable farkas lemma we then derive necessary and sufficient conditions for a stable duality of a cone convex optimization problem where strong duality holds for each linear perturbation of a given convex objective function as an application we obtain stable duality results for convex semi definite programs and convex second order cone programs

convex optimization based time domain broadband beamforming with sidelobe control an approach to time domain broadband beamforming with sidelobe control is proposed the array response is expressed as a linear function of the finite impulse response filters tap weights the filters are designed by minimizing beamformer output power while maintaining the distortionless response in the direction of the desired signal and guaranteeing the sidelobes to be below some given threshold values norm constraint on tap weights is also imposed to improve the robustness of the beamformer computationally efficient convex formulation for the beamformer design problem is derived using second order cone programming simulation results demonstrate the satisfactory performance of the proposed approach

derivatives of any order of the confluent hypergeometric function f11 a b z with respect to the parameter a or b the derivatives to any order of the confluent hypergeometric kummer function f f11 a b z with respect to the parameter a or b are investigated and expressed in terms of generalizations of multivariable kampe de feriet functions various properties reduction formulas recurrence relations particular cases and series and integral representations of the defined hypergeometric functions are given finally an application to the two body coulomb problem is presented the derivatives of f with respect to a are used to write the scattering wave function as a power series of the sommerfeld parameter

synthesis of nonuniformly spaced linear arrays with frequency invariant patterns by the generalized matrix pencil methods this work extends the matrix pencil method mpm based synthesis technique to the case of nonuniformly spaced linear arrays with wideband frequency invariant fi patterns a new sampling strategy is proposed to obtain multiple pattern data of different frequencies having the same poles that correspond to the fi element positions the obtained multiple pattern sequences have the same shape for the fi pattern requirement but with different lengths the generalized mpm gmpm and its forward backward version gfbmpm are developed to estimate the best common element positions for different frequencies which can significantly reduce the number of elements required for the specified wideband pattern shape the element excitations are solved by the regularized least square ls method at each frequency then an efficient method by utilizing the fft is presented to obtain real coefficient finite impulse response fir filters for implementing the frequency varying excitations a set of numerical examples for the fi synthesis of pencil beams shaped patterns scannable patterns and taylor patterns with low slls are presented to validate the effectiveness and advantages of the proposed methods the element saving is about 11 2 49 4 for usual cases