filtering and frequency interpretations of singular spectrum analysis new filtering and spectral interpretations of singular spectrum analysis ssa are provided it is shown that the variables reconstructed from diagonal averaging of reduced rank approximations to the trajectory matrix can be obtained from a noncausal convolution filter with zero phase characteristics the reconstructed variables are readily constructed using a two pass filtering algorithm that is well known in the signal processing literature when the number of rows in the trajectory matrix is much larger than number of columns many results reported in the signal processing literature can be used to derive the properties of the resulting filters and their spectra new features of the reconstructed series are revealed using these results two examples are used to illustrate the results derived in this paper

fuzzy linear programming and applications abstract this paper presents a survey on methods for solving fuzzy linear programs first lp models with soft constraints are discussed then lp problems in which coefficients of constraints and or of the objective function may be fuzzy are outlined pivotal questions are the interpretation of the inequality relation in fuzzy constraints and the meaning of fuzzy objectives in addition to the commonly applied extended addition based on the min operator and used for the aggregation of the left hand sides of fuzzy constraints and fuzzy objectives a more flexible procedure based on yager s parametrized t norm t p is presented finally practical applications of fuzzy linear programs are listed

designing structured tight frames via an alternating projection method tight frames also known as general welch bound equality sequences generalize orthonormal systems numerous applications including communications coding and sparse approximation require finite dimensional tight frames that possess additional structural properties this paper proposes an alternating projection method that is versatile enough to solve a huge class of inverse eigenvalue problems ieps which includes the frame design problem to apply this method one needs only to solve a matrix nearness problem that arises naturally from the design specifications therefore it is the fast and easy to develop versions of the algorithm that target new design problems alternating projection will often succeed even if algebraic constructions are unavailable to demonstrate that alternating projection is an effective tool for frame design the paper studies some important structural properties in detail first it addresses the most basic design problem constructing tight frames with prescribed vector norms then it discusses equiangular tight frames which are natural dictionaries for sparse approximation finally it examines tight frames whose individual vectors have low peak to average power ratio par which is a valuable property for code division multiple access cdma applications numerical experiments show that the proposed algorithm succeeds in each of these three cases the appendices investigate the convergence properties of the algorithm

a column generation algorithm for the estimation of origin destination matrices in congested traffic networks abstract the general problem of estimating origin destination o d matrices in congested traffic networks is formulated as a mathematical programme with equilibrium constraints referred to as the demand adjustment problem dap this approach integrates the o d matrix estimation and the network equilibrium assignment into one process in this paper a column generation algorithm for the dap is presented this algorithm iteratively solves a deterministic user equilibrium model for a given o d matrix and a dap restricted to the previously generated paths whose solution generates a new o d trip matrix estimation the restricted dap is formulated via a single level optimization problem the convergence on local minimum of the proposed algorithm requires only the continuity of the link travel cost functions and the gauges used in the definition of the dap in order to analyze the convergence and performance of the proposed algorithm various numerical tests were carried out on small scale problems

sequence set design with good correlation properties via majorization minimization sets of sequences with good correlation properties are desired in many active sensing and communication systems e g multiple input multiple output mimo radar systems and code division multiple access cdma cellular systems in this paper we consider the problems of designing complementary sets of sequences css and also sequence sets with both good auto and cross correlation properties algorithms based on the general majorization minimization method are developed to tackle the optimization problems arising from the sequence set design problems all the proposed algorithms can be implemented by means of the fast fourier transform fft and thus are computationally efficient and capable of designing sets of very long sequences a number of numerical examples are provided to demonstrate the performance of the proposed algorithms

designing sequence with minimum psl using chebyshev distance and its application for chaotic mimo radar waveform design controlling peak side lobe level psl is of great importance in high resolution applications of multiple input multiple output mimo radars in this paper designing sequences with good autocorrelation properties are studied the psl of the autocorrelation is regarded as the main merit and is optimized through newly introduced cyclic algorithms namely psl minimization quadratic approach psl minimization algorithm where the smallest rectangular and psl optimization cyclic algorithm it is revealed that minimizing psl results in better sequences in terms of autocorrelation side lobes when compared with traditional integrated side lobe level minimization in order to improve the performance of these algorithms fast randomized singular value decomposition is utilized to achieve waveform design for mimo radars this algorithm is applied to the waveform generated from a modified bernoulli chaotic system the numerical experiments confirm the superiority of the newly developed algorithms compared to high performance algorithms in monostatic and mimo radars

a new systematic construction of zero correlation zone sequences based on interleaved perfect sequences in the literature many constructions of zero correlation zone zcz sequences have been reported while most of them are suboptimal with respect to the known upper bound some constructed by matsufuji et al and torii et al respectively are almost optimal or even optimal in this paper we propose a systematic construction of almost optimal zcz sequence sets which generalizes the aforementioned constructions so that more flexible relationships between the set size and the sequence length are allowed in particular the obtained almost optimal zcz sequence sets of size m and length mn are new for 1 gcd m n min m n in addition their alphabets can be binary or nonbinary since our construction is only based on interleaving perfect sequences according to a certain orthogonal matrix

the peak sidelobe level of families of binary sequences a numerical investigation is presented for the peak sidelobe level psl of legendre sequences maximal length shift register sequences m sequences and rudin shapiro sequences the psl gives an alternative to the merit factor for measuring the collective smallness of the aperiodic autocorrelations of a binary sequence the growth of the psl of these infinite families of binary sequences is tested against the desired growth rate o spl radic nlnn for sequence length n the claim that the psl of m sequences grows like o spl radic n which appears frequently in the radar literature is concluded to be unproven and not currently supported by data notable similarities are uncovered between the psl and merit factor behavior under cyclic rotations of the sequences

estimation of a signal waveform from noisy data using low rank approximation to a data matrix an analysis and improvement of a data adaptive signal estimation algorithm are presented perturbation analysis of a reduced rank data matrix is used to reveal its statistical properties the obtained information is used for calculating the performance of the toeplitz restoration algorithm of d tufts et al 1982 this analysis leads to improvements of the methods and the predicted improvements are demonstrated by simulation and comparison with the cramer rao bounds

analytic hierarchy process hesitant group decision making in this paper we consider that the judgments provided by the decision makers dms cannot be aggregated and revised then define them as hesitant judgments to describe the hesitancy experienced by the dms in decision making if there exist hesitant judgments in analytic hierarchy process group decision making ahp gdm then we call it ahp hesitant group decision making ahp hgdm as an extension of ahp gdm based on hesitant multiplicative preference relations hmprs to collect the hesitant judgments we develop a hesitant multiplicative programming method hmpm as a new prioritization method to derive ratio scale priorities from hmprs the hmpm is discussed in detail with examples to show its advantages and characteristics the practicality and effectiveness of our methods are illustrated by an example of the water conservancy in china

a parameter estimation scheme for damped sinusoidal signals based on low rank hankel approximation most of the existing algorithms for parameter estimation of damped sinusoidal signals are based only on the low rank approximation of the prediction matrix and ignore the hankel property of the prediction matrix we propose a modified kumaresan tufts mkt algorithm exploiting both rank deficient and hankel properties of the prediction matrix computer simulation results demonstrate that compared with the original kumaresan tufts 1982 algorithm and the matrix pencil algorithm the mkt algorithm has a lower noise threshold and can estimate the parameters of signal with larger damping factors

continuity of closest rank p approximations to matrices in signal processing the singular value decomposition and rank characterization of matrices play prominent roles the mapping which associates with any complex m n matrix x its closest rank p approximation x p need not be continuous when the pth and the p 1 st singular values of x are equal this mapping maps in fact a matrix to a set of matrices furthermore an example is given to show that large errors in computing x p can be expected when p is sufficiently close to p 1 it is finally shown that this mapping is closed in the sense of zangwill the property of closedness is an essential assumption of a global convergence proof for algorithms involving this mapping e g see 1

the oscillation of differential transforms entire jacobi expansions abstract let l 1 x 2 d 2 2 x d with 1 2 1 2 and d d d x let f c 1 1 f x n 0 c n p n x with p n x normalized jacobi polynomials and the c n decrease sufficiently fast set l k l l k 1 k 2 let 1 if the number of sign changes of l k f x in 1 1 is o k 1 1 then f extends to be an entire function of logarithmic order 1 for legendre expansions the result holds with 1 1 replaced with 1

rational invariant subspace approximations with applications subspace methods such as music minimum norm and esprit have gained considerable attention due to their superior performance in sinusoidal and direction of arrival doa estimation but they are also known to be of high computational cost in this paper new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented these algorithms approximate the required subspace using rational and power like methods applied to the direct data or the sample covariance matrix several esprit as well as music type methods are developed based on these approximations a substantial computational saving can be gained comparing with those associated with the eigendecomposition based methods these methods are demonstrated to have performance comparable to that of music yet will require fewer computations to obtain the signal subspace matrix

a unified framework for low autocorrelation sequence design via majorization minimization in this paper we consider the low autocorrelation sequence design problem we optimize a unified metric over a general constraint set the unified metric includes the integrated sidelobe level isl and the peak sidelobe level psl as special cases and the general constraint set contains the unimodular constraint peak to average ratio par constraint and similarity constraint to name a few the optimization technique we employ is the majorization minimization mm method which is iterative and enjoys guaranteed convergence to a stationary solution we carry out the mm method in two stages in the majorization stage we propose three majorizing functions two for the unified metric and one for the isl metric in the minimization stage we give closed form solutions for algorithmic updates under different constraints the update step can be implemented with a few fast fourier transformations ffts and or inverse ffts iffts we also show the connections between the mm and gradient projection method under our algorithmic scheme numerical simulations have shown that the proposed mm based algorithms can produce sequences with low autocorrelation and converge faster than the traditional gradient projection method and the state of the art algorithms

super resolution reconstruction in frequency domain optical coherence tomography using the finite rate of innovation principle the standard approach to signal reconstruction in frequency domain optical coherence tomography fdoct is to apply the inverse fourier transform to the measurements this technique offers limited resolution due to heisenberg s uncertainty principle we propose a new super resolution reconstruction method based on a parametric representation we consider multilayer specimens wherein each layer has a constant refractive index and show that the backscattered signal from such a specimen fits accurately in to the framework of finite rate of innovation fri signal model and is represented by a finite number of free parameters we deploy the high resolution prony method and show that high quality super resolved reconstruction is possible with fewer measurements about one fourth of the number required for the standard fourier technique to further improve robustness to noise in practical scenarios we take advantage of an iterated singular value decomposition algorithm cadzow denoiser we present results of monte carlo analyses and assess statistical efficiency of the reconstruction techniques by comparing their performance against the cramer rao bound reconstruction results on experimental data obtained from technical as well as biological specimens show a distinct improvement in resolution and signal to reconstruction noise offered by the proposed method in comparison with the standard approach

unbiased risk estimates for singular value thresholding and spectral estimators in an increasing number of applications it is of interest to recover an approximately low rank data matrix from noisy observations this paper develops an unbiased risk estimate holding in a gaussian model for any spectral estimator obeying some mild regularity assumptions in particular we give an unbiased risk estimate formula for singular value thresholding svt a popular estimation strategy that applies a soft thresholding rule to the singular values of the noisy observations among other things our formulas offer a principled and automated way of selecting regularization parameters in a variety of problems in particular we demonstrate the utility of the unbiased risk estimation for svt based denoising of real clinical cardiac mri series data we also give new results concerning the differentiability of certain matrix valued functions

computationally efficient maximum likelihood estimation of structured covariance matrices by invoking the extended invariance principle exip we present herein a computationally efficient method that provides asymptotic for large samples maximum likelihood aml estimation for structured covariance matrices and is referred to as the aml algorithm a closed form formula for estimating the hermitian toeplitz covariance matrices that makes aml computationally simpler than most existing hermitian toeplitz matrix estimation algorithms is derived although the aml covariance matrix estimator can be used in a variety of applications we focus on array processing our simulation study shows that aml enhances the performance of angle estimation algorithms such as music by making them very close to the corresponding cramer rao bound crb for uncorrelated signals numerical comparisons with several structured and unstructured covariance matrix estimators are also presented

signal enhancement a composite property mapping algorithm a signal enhancement algorithm is developed that seeks to recover a signal from noise contaminated distorted measurements made on that signal this object is achieved by utilizing a set of properties which the signal is known or is hypothesized as possessing the measured signal is modified to the smallest degree necessary to sequentially possess each of the individual properties conditions for the algorithm s convergence are established in which the primary requirement is that a composite property mapping be closed this is a relatively unrestricted condition in comparison to that required of most existing signal enhancement algorithms

mimo radar transmit beampattern matching design in this paper a novel transmit beampattern matching design method is proposed for a multiple input multiple output mimo radar system whereas previous approaches first solve the correlation matrix r and then use r to design the transmit signal s the proposed one step method obtains the transmit signal s directly through solving the waveform matrix p since mimo radar transmit beampattern matching design is an inverse problem of the transmit beampattern in this paper we first discuss some important properties of the transmit beampattern and standardize the beampattern matching design problem we then theoretically explain the value of the signal waveform matrix p followed by an unconstrained optimization problem to solve p numerical examples demonstrate the advantages of the proposed one step method for the mimo radar transmit beampattern matching design problem including uniform and non uniform linear arrays

design of par constrained sequences for mimo channel estimation via majorization minimization communication systems and radars widely employ sequences of low peak to average power ratio par or unimodulus to meet the hardware constraints and maximize the power efficiency numerous works have probed the unimodular sequence design especially attempting to obtain good correlation properties regarding channel estimation however sequences of such properties do not necessarily qualify for the mission and tailored unimodular sequences for the specific criterion concerned are more desirable when we have access to the prior knowledge of the channel impulse response in this paper we formulate the problem of unimodular sequence design by optimizing minimum mean square error and conditional mutual information respectively the problems turn out nonconvex and we develop efficient algorithms based on the majorization minimization framework with convergence guaranteed more general we also examine optimal sequence design with low par constraints numerical examples demonstrate the improved results of mean square error signal to noise ratio and conditional mutual information by using our proposed training sequences with the efficiency of the derived algorithms illustrated

estimating localized sources of diffusion fields using spatiotemporal sensor measurements we consider diffusion fields induced by a finite number of spatially localized sources and address the problem of estimating these sources using spatiotemporal samples of the field obtained with a sensor network within this framework we consider two different time evolutions the case where the sources are instantaneous as well as the case where the sources decay exponentially in time after activation we first derive novel exact inversion formulas for both source distributions through the use of green s second theorem and a family of sensing functions to compute generalized field samples these generalized samples can then be inverted using variations of existing algebraic methods such as prony s method next we develop a novel and robust reconstruction method for diffusion fields by properly extending these formulas to operate on the spatiotemporal samples of the field finally we present numerical results using both synthetic and real data to verify the algorithms proposed herein

fri sampling on structured nonuniform grids application to super resolved optical imaging the annihilating filter forms the core of many state of the art techniques for finite rate of innovation fri signal reconstruction and spectral estimation in its standard manifestation the annihilating filter is setup in the discrete time domain with uniform sampling and is used to estimate the parameters of a signal that is expressible as a sum of exponentials in this paper we consider annihilation in the continuous domain using translation operators codenamed opera and show that fri signals can be reconstructed using measurements taken on a structured nonuniform sampling sns grid the parameters are estimable uniquely under certain conditions the transition from uniform sampling to sns comes with specific advantages the measurements could be made in bursts from high signal to noise ratio snr regions which directly enhances parameter estimation accuracy the sampling interval could be made larger than in the uniform case which leads to a reduction in the mean squared error mse and closely spaced exponential parameters could be resolved better we present theoretical developments related to the sns grid and demonstrate accurate parameter estimation monte carlo performance analysis in the presence of noise shows that the opera with the sns approach yields a significant decrease in mse up to 10 to 20 db for certain snr ranges compared with the uniform sampling scenario considering an application to frequency domain optical coherence tomography we show that the proposed methodology results in higher resolution and higher reconstruction accuracy than the standard techniques

alternative formulations of a combined trip generation trip distribution modal split and trip assignment model abstract the traditional four step model has been widely used in travel demand forecasting by considering trip generation trip distribution modal split and traffic assignment sequentially in a fixed order however this sequential approach suffers from the inconsistency among the level of service and flow values in each step of the procedure in the last two decades this problem has been addressed by many researchers who have sought to develop combined or integrated models that can consider travelers choice on different stages simultaneously and give consistent results in this paper alternative formulations including mathematical programming mp formulation and variational inequality vi formulations are provided for a combined travel demand model that integrates trip generation trip distribution modal split and traffic assignment using the random utility theory framework thus the proposed alternative formulations not only allow a systematic and consistent treatment of travel choice over different dimensions but also have behavioral richness qualitative properties of the formulations are also given to ensure the existence and uniqueness of the solution particularly the model is analyzed for a special but useful case where the probabilistic travel choices are assumed to be a hierarchical logit model furthermore a self adaptive goldstein levitin polyak glp projection algorithm is adopted for solving this special case

on prime root of unity sequences with perfect periodic correlation in this paper perfect root of unity sequences prus with entries in alpha p x in complexc x p 1 where p is a prime are studied a lower bound on the number of distinct phase

on the oscillation of differential transforms of eigenfunction expansions this paper continues the study of p6lya and wiener wille and szegb into the connections between the oscillation of derivatives of a real function and its analytic character in the present paper a sturm liouville operator l is applied successively to an infinitely differentiable function which admits a certain eigenfunction expansion the eigenfunction expansion is assumed to be conservative in the sense of hille several theorems are given which link the frequency of oscillation of latf x to the size of the coefficients of f x and thus to its analytic character

an optimization model for area traffic control with link tolls in this paper an optimization model is established for the maximum increase in travel demands in a signal controlled road network with link tolls using the concept of reserve capacity of signal controlled junctions the problem of finding the maximum increase in traffic demands and link tolls can be formulated as a mathematical program with equilibrium constraints due to the non differentiability of the perturbed solutions in equilibrium constraints a non smooth optimization model is established a bundle subgradient projection method is proposed to effectively solve the optimization problem global convergence analysis for the proposed method is also established numerical computations are performed at various sets of initial signal settings encouraging results are obtained when compared to other alternatives

a coordinate descent framework to design low psl isl sequences this paper is focused on the design of phase sequences with good aperiodic autocorrelation properties in terms of peak sidelobe level and integrated sidelobe level the problem is formulated as a biobjective pareto optimization forcing either a continuous or a discrete phase constraint at the design stage an iterative procedure based on the coordinate descent method is introduced to deal with the resulting optimization problems that are nonconvex and np hard in general each iteration of the devised method requires the solution of a nonconvex min max problem it is handled either through a novel bisection or an fft based method respectively for the continuous and the discrete phase constraint additionally a heuristic approach to initialize the procedures employing the l p norm minimization technique is proposed simulation results illustrate that the proposed methodologies can outperform some counterparts providing sequences with good autocorrelation features especially in the discrete phase binary case

designing unimodular codes via quadratic optimization the np hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications to tackle this problem which we call unimodular quadratic program uqp several computational approaches are devised and studied power method like iterations are introduced for local optimization of uqp furthermore a monotonically error bound improving technique merit is proposed to obtain the global optimum or a local optimum of uqp with good sub optimality guarantees the provided sub optimality guarantees are case dependent and may outperform the 4 approximation guarantee of semi definite relaxation several numerical examples are presented to illustrate the performance of the proposed method the examples show that for several cases including rank deficient matrices the proposed methods can solve uqps efficiently in the sense of sub optimality guarantee and computational time

constructing binary sequences with good correlation properties an efficient analytical computational interplay binary sequence sets with asymptotically optimal auto cross correlation peak sidelobe level psl growth have been known in the literature for a long time and their construction has been studied both analytically and numerically in contrast it has been a long standing problem whether we can construct a family of binary sequences whose auto correlation psl grows in an optimal manner in this paper we devise a construction method of binary sequences with asymptotically optimal psl growth from the sequence sets with good correlation properties a key component of the design follows from the observation that if the psl of the sequence set grows optimally or nearly optimally then the psl of the constructed binary sequence will experience a similar growth as a consequence the proposed construction is simple to implement and is shown to be accomplished in polynomial time with such a construction we not only bridge the gap between analytical construction and computational search but also pave the way to settle the long standing design problem of binary sequences with an optimal growth of the auto correlation psl

solving the combined modal split and traffic assignment problem with two types of transit impedance function abstract the gradient projection gp algorithm has been shown as a successful path based algorithm for solving various traffic assignment problems in this paper the gp algorithm is adapted for solving the combined modal split and traffic assignment cmsta problem which can be viewed as an elastic demand traffic equilibrium problem edtep with two modes using the excess demand formulation of edtep the cmsta problem is reformulated and solved by a modified gp algorithm numerical results based on a real bi modal network in the city of winnipeg canada are provided to demonstrate the efficiency and robustness of the modified path based gp algorithm for solving the cmsta problem in addition the cmsta problem is investigated with two types of impedance function for the transit mode and with different degrees of dispersion for the modal split function the computational results show the modified gp algorithm outperforms the classical evan s algorithm for both types of transit impedance function and it can be as efficient as the original gp algorithm for solving the traffic assignment problem with fixed demand

sequences with positive semidefinite fourier transforms a sequence is said to be positive if its fourier transform exclusively takes on real nonnegative values as a function of frequency positive sequences play a prominent role in contemporary signal processing and system theory to illustrate this point it is well known that the factorization theorem is extensively used in studies related to wide sense stationary random signals and linear systems the ability to appropriately factorize a fourier transform is contingent on that transform being positive semidefinite this paper is partially tutorial in that some fundamental positive sequence properties found in dispersed sources are first reviewed this is followed by the development of several new properties these properties are in turn used to develop an efficient algorithm for finding that positive sequence which lies closest to a given nonpositive sequence in the least squares error sense interest in this approximation problem arises from the fact that although a given sequence may be theoretically positive practical considerations often result in its realization being nonpositive for instance unbiased autocorrelation lag estimates can lead to nonpositive spectral density function estimates

simultaneous estimation of the origin destination matrices and the parameters of a nested logit model in a combined network equilibrium model abstract this paper deals with the inverse problem of a type of traffic equilibrium models with combined modes this problem consists of obtaining a parametrization of the equilibrium model from a set of observations of the outputs for the model the inputs for the model are an origin destination o d trip matrix for the various alternatives that have been considered and a set of parameters for a nested logit model used as a demand model this model has been formulated by using a new approach called the calibration and demand adjustment model cdam based on bilevel programming which simultaneously estimates an o d matrix and the parameters for the nested logit model in this paper the cdam properties are studied and it is proved the cdam solution exists this paper develops a heuristic column paths hyperpaths generation algorithm for the cdam this algorithm iterates between the network equilibrium problem and that which is used to obtain a set of paths when equilibrium is attained and the cdam is restricted to the set of previously generated columns the so called restricted cdam the restricted cdam is formulated as a single level model under certain hypotheses and it furnishes a solution upon which to base a new estimation of the o d matrix and the vector of parameters the computational tests on the algorithm have been carried out using data from a multi modal network in madrid

formulation and solution of structured total least norm problems for parameter estimation the total least squares tls method is a generalization of the least squares ls method for solving overdetermined sets of linear equations ax spl ap b the tls method minimizes spl par e r spl par sub f where r b a e x so that b r spl isin range a e given a spl isin c sup m spl times n with m spl ges n and b spl isin c sup m spl times 1 the most common tls algorithm is based on the singular value decomposition svd of a b however the svd based methods may not be appropriate when the matrix a has a special structure since they do not preserve the structure previously a new problem formulation known as structured total least norm stln and the algorithm for computing the stln solution have been developed the stln method preserves the special structure of a or a b and can minimize the error in the discrete l sub p norm where p 1 2 or spl infin in this paper the stln problem formulation is generalized for computing the solution of stln problems with multiple right hand sides ax spl ap b it is shown that these problems can be converted to ordinary stln problems with one right hand side in addition the method is shown to converge to the optimal solution in certain model reduction problems furthermore the application of the stln method to various parameter estimation problems is studied in which the computed correction matrix applied to a or a b keeps the same toeplitz structure as the data matrix a of a b respectively in particular the l sub 2 norm stln method is compared with the ls and tls methods in deconvolution transfer function modeling and linear prediction problems

new algorithmic alternatives for the o d matrix adjustment problem on traffic networks abstract in the last years the o d matrix adjustment problem using link counts on a traffic network modelled by means of a static user equilibrium approach has been formulated advantageously by means of bilevel programs the algorithms developed to solve the problem present heuristic components in a lesser or greater degree in this paper two new algorithmic alternatives are presented for this problem the first alternative is an hybrid scheme proximal point steepest descent that is based on a development of codina for the approximation of the steepest descent direction of the upper level function and the second alternative is developed by garcia and marin and consists of solving a sequence of simplified bilevel programs in order to highlight the characteristics of the two methods a set of test problems have been solved in conjunction with other well known methods such as the method of spiess the method of chan the method of yang as well as with an adaptation of the wolfe s conjugate directions method for non differentiable optimization in order to provide a better perspective of their advantages and tradeoffs

almost difference sets and their sequences with optimal autocorrelation almost difference sets have interesting applications in cryptography and coding theory we give a well rounded treatment of known families of almost difference sets establish relations between some difference sets and some almost difference sets and determine the numerical multiplier group of some families of almost difference sets we also construct six new classes of almost difference sets and four classes of binary sequences of period n spl equiv 0 mod 4 with optimal autocorrelation we have also obtained two classes of relative difference sets and four classes of divisible difference sets ddss we also point out that a result due to jungnickel 1982 can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

polynomial roots from companion matrix eigenvalues in classical linear algebra the eigenvalues of a matrix are sometimes defined as the roots of the characteristic polynomial an algorithm to compute the roots of a polynomial by computing the eigenvalues of the corresponding companion matrix turns the tables on the usual definition we derive a first order error analysis of this algorithm that sheds light on both the underlying geometry of the problem as well as the numerical error of the algorithm our error analysis expands on work by van dooren and dewilde in that it states that the algorithm is backward normwise stable in a sense that must be defined carefully regarding the stronger concept of a small componentwise backward error our analysis predicts a small such error on a test suite of eight random polynomials suggested by toh and trefethen however we construct examples for which a small componentwise relative backward error is neither predicted nor obtained in practice we extend our results to polynomial matrices where the result is essentially the same but the geometry becomes more complicated

nonlinear optimization by successive linear programming successive linear programming slp which is also known as the method of approximation programming solves nonlinear optimization problems via a sequence of linear programs this paper reports on promising computational results with slp that contrast with the poor performance indicated by previously published comparative tests the paper provides a detailed description of an efficient reliable slp algorithm along with a convergence theorem for linearly constrained problems and extensive computational results it also discusses several alternative strategies for implementing slp the computational results show that slp compares favorably with the generalized reduced gradient code grg2 and with minos grg it appears that slp will be most successful when applied to large problems with low degrees of freedom

adjustment of o d trip matrices from observed volumes an algorithmic approach based on conjugate directions abstract this paper presents a new algorithmic alternative to the o d matrix adjustment problem from observed link volumes when it is formulated as a mathematical programming problem with a bilevel structure the algorithmic approach presented is based on a method for nondifferentiable optimization due to wolfe that can be interpreted as a conjugate directions method with better convergence properties as shown with a set of computational tests closely related to the algorithm presented the problem of approximating gradients of the upper level function is discussed and a new and consistent approach is presented and analyzed with a detailed description of the algorithmic aspects involved

relative entropy based waveform design for mimo radar detection in the presence of clutter and interference this paper considers the waveform design problem for multiple input multiple output mimo radars in order to improve the detection performance of the systems we assume that target echoes are embedded in signal dependent clutter as well as colored interference considering the optimal neyman pearson detector obtaining waveforms which maximize the detection probability for a fixed value of the probability of false alarm is intractable therefore we employ relative entropy associated with the detection problem as the figure of merit for the waveform design we devise an iterative method based on minorization maximization mm technique to tackle the nonconvex design problem this method also includes a novel trick for replacing a nonconvex constraint set associated with an equivalent form of the design problem with a convex one iteratively the proposed method increases the design metric monotonically and is guaranteed to converge we extend the devised method for using in design with peak to average power ratio par and similarity constraints the method can be applied to both statistical and colocated mimo radars several numerical examples are included to demonstrate the effectiveness of the proposed method

new algorithms for designing unimodular sequences with good correlation properties unimodular i e constant modulus sequences with good autocorrelation properties are useful in several areas including communications and radar the integrated sidelobe level isl of the correlation function is often used to express the goodness of the correlation properties of a given sequence in this paper we present several cyclic algorithms for the local minimization of isl related metrics these cyclic algorithms can be initialized with a good existing sequence such as a golomb sequence a frank sequence or even a pseudo random sequence to illustrate the performance of the proposed algorithms we present a number of examples including the design of sequences that have virtually zero autocorrelation sidelobes in a specified lag interval and of long sequences that could hardly be handled by means of other algorithms previously suggested in the literature

paley wiener characterization of kernels for finite rate of innovation sampling exact reconstruction of finite rate of innovation signals can be achieved by employing customized sampling kernels that satisfy certain frequency domain properties we impose compact support in time as an additional constraint considering frequency domain reconstruction we derive conditions for admissible sampling kernels and corresponding sampling rates our constructive kernel design methodology is based on the paley wiener theorem for compactly supported functions the new kernels satisfy generalized strang fix conditions and have specific polynomial modulated exponential reproducing properties unlike exponential splines which have a support that is directly proportional to the number of exponentials they can generate the proposed kernels have a support that is independent of that number to analyze noise robustness we consider a special member of the class that has a sum of modulated splines sms form in the time domain and optimize its parameters to minimize the noise variance the sum of sincs sos kernel reported in the literature is an instance of this construction in noise robustness analysis sms kernels show improvement in mean squared error mse compared with the state of the art alternatives in continuous time noise the improvement in mse is about 2 db for low signal to noise ratio snr and 7 db for high snr in the case of discrete white gaussian noise the mse is lower by as much as 25 db by using a higher order sms kernel compared with the sos kernel for snrs in the range of 10 15 db

complementary sequences for isi channel estimation a merit factor based on the sequence autocorrelation function whose minimization leads to the reduction in the cramer rao lower bound crlb for the variance of two sided intersymbol interference isi channel estimation is introduced pairs of binary pilot symbol sequences a preamble and a postamble for channel estimation are jointly designed to minimize this merit factor given that the number of channel taps is l and the length of a pilot symbol sequence is n l 1 where n spl ges l we distinguish between the case when n is even and the case when it is odd for even n we show that complementary sequences not only minimize the merit factor but also the crlb for a subset of odd n we construct almost complementary periodic sequence pairs that minimize the merit factor the optimal pilot symbol block signaling requires alternating between two in most cases different binary sequences that form the merit minimizing pair

an information theoretic approach to robust constrained code design for mimo radars the problem of transmit code design in multiple input multiple output mimo radar systems is addressed in this paper the problem is considered in both colocated and widely separated antenna radars in the presence of signal dependent interference and target mobility due to complexity of exact expressions of the optimal detector in the mimo radars information theoretic criteria are employed as design metrics which results in a general form of nonconvex optimization problems in order to tackle the problem a novel technique based on the minorization maximization algorithm is proposed and solutions are presented under practical constraints on the transmit code namely energy constraint peak to average power ratio constraint and similarity constraint furthermore the devised method is extended to be robust against uncertainties of the clutter and interference statistics finally numerical examples are used to show the performance of the proposed technique in different situations

sequence design to minimize the weighted integrated and peak sidelobe levels sequences with low aperiodic autocorrelation sidelobes are well known to have extensive applications in active sensing and communication systems in this paper we first consider the problem of minimizing the weighted integrated sidelobe level wisl which can be used to design sequences with impulse like autocorrelation and a zero or low correlation zone two algorithms based on the general majorization minimization method are developed to tackle the wisl minimization problem with guaranteed convergence to a stationary point the proposed methods are then extended to optimize the ell p norm of the autocorrelation sidelobes which leads to a way to minimize the peak sidelobe level psl criterion all the proposed algorithms can be implemented via the fast fourier transform fft and thus are computationally efficient an acceleration scheme is considered to further accelerate the algorithms numerical experiments show that the proposed algorithms can efficiently generate sequences with virtually zero autocorrelation sidelobes in a specified lag interval and can also produce very long sequences with much smaller psl compared with some well known analytical sequences

resource allocation in mimo radar with multiple targets for non coherent localization in an mimo radar network the multiple transmit elements may emit waveforms that differ on power and bandwidth in this paper we are asking given that these two resources are limited what is the optimal power optimal bandwidth and optimal joint power and bandwidth allocation for best localization of multiple targets the well known cramer rao lower bound for target localization accuracy is used as a figure of merit and approximate solutions are found by minimizing a sequence of convex problems their quality is assessed through extensive numerical simulations and with the help of a lower bound on the true solution simulations results reveal that bandwidth allocation policies have a definitely stronger impact on performance than power

structured low rank approximation this paper concerns the construction of a structured low rank matrix that is nearest to a given matrix the notion of structured low rank approximation arises in various applications ranging from signal enhancement to protein folding to computer algebra where the empirical data collected in a matrix do not maintain either the specified structure or the desirable rank as is expected in the original system the task to retrieve useful information while maintaining the underlying physical feasibility often necessitates the search for a good structured lower rank approximation of the data matrix this paper addresses some of the theoretical and numerical issues involved in the problem two procedures for constructing the nearest structured low rank matrix are proposed the procedures are flexible enough that they can be applied to any lower rank any linear structure and any matrix norm in the measurement of nearness the techniques can also be easily implemented by utilizing available optimization packages the special case of symmetric toeplitz structure using the frobenius matrix norm is used to exemplify the ideas throughout the discussion the concept rather than the implementation details is the main emphasis of the paper

sampling curves with finite rate of innovation in this paper we extend the theory of sampling signals with finite rate of innovation fri to a specific class of two dimensional curves which are defined implicitly as the zeros of a mask function here the mask function has a parametric representation as a weighted summation of a finite number of complex exponentials and therefore has finite rate of innovation an associated edge image which is discontinuous on the predefined parametric curve is proved to satisfy a set of linear annihilation equations we show that it is possible to reconstruct the parameters of the curve i e to detect the exact edge positions in the continuous domain based on the annihilation equations robust reconstruction algorithms are also developed to cope with scenarios with model mismatch moreover the annihilation equations that characterize the curve are linear constraints that can be easily exploited in optimization problems for further image processing e g image up sampling we demonstrate one potential application of the annihilation algorithm with examples in edge preserving interpolation experimental results with both synthetic curves as well as edges of natural images clearly show the effectiveness of the annihilation constraint in preserving sharp edges and improving snrs

asymmetric pulse modeling for fri sampling we consider sampling and reconstruction of finite rate of innovation fri signals such as a train of pulses where the pulses have varying degrees of asymmetry we address the problem of asymmetry modeling starting from a given symmetric prototype we show that among the class of unitary operators that are linear and invariant to translation and scale the fractional hilbert frh operator is unique for parametrically modeling pulse asymmetry the frh operator is obtained by a trigonometric interpolation between the standard hilbert and identity operators where the interpolation weights are determined by the degree of asymmetry the frh operators are also steerable which allows for estimation of the asymmetry factors in addition to the delays and amplitudes using the high resolution spectral estimation techniques that are used for solving standard fri problems we also develop the discrete counterpart using discrete frh operators and show that all the desirable properties carry over smoothly to the discrete setting as well we derive closed form expressions for the cramer rao bounds and hammersley chapman robbins bound on the variances of the estimators for continuous and discrete parameters respectively experimental results show that the proposed estimators have variances that meet the lower bounds we demonstrate an application of the proposed discrete frh methodology on real electrocardiogram ecg signals in the presence of noise specifically we show how the asymmetry of qrs complexes in various channels of an ecg signal could be modeled accurately

exploring trust region method for the solution of logit based stochastic user equilibrium problem abstract in this research paper we explored using the trust region method to solve the logit based sue problem we proposed a modified trust region newton mtrn algorithm for this problem when solving the trust region sue subproblem we showed that applying the well known steihaug toint method is inappropriate since it may make the convergence rate of the major iteration very slow in the early stage of the computation to overcome this drawback a modified steihaug toint method was proposed we proved the convergence of our mtrn algorithm and showed its convergence rate is superlinear for the implication of our algorithm we proposed an important principle on how to select the basic route for each od pair we indicated that it is a crucial principle to accelerate the convergence rate of the minor iteration i e trust region subproblem solving iteration in this study other implication issues for the sue problem are also considered including the computation of the trial step and the strategy to ensure strict feasibility iteration point we compared the mtrn algorithm with the gradient projection gp algorithm on the sioux falls network some results of numerical analysis are also reported

a heuristic for the od matrix adjustment problem in a congested transport network abstract we study the demand adjustment problem dap associated to the urban traffic planning the framework for the formulation of the dap is mathematical programming with equilibrium constraints in particular if we consider the optimization problem equivalent to the equilibrium problem the dap becomes a bilevel optimization problem in this work we present a descent scheme based on the approximation of the gradient of the objective function of dap

efficient denoising algorithms for large experimental datasets and their applications in fourier transform ion cyclotron resonance mass spectrometry modern scientific research produces datasets of increasing size and complexity that require dedicated numerical methods to be processed in many cases the analysis of spectroscopic data involves the denoising of raw data before any further processing current efficient denoising algorithms require the singular value decomposition of a matrix with a size that scales up as the square of the data length preventing their use on very large datasets taking advantage of recent progress on random projection and probabilistic algorithms we developed a simple and efficient method for the denoising of very large datasets based on the qr decomposition of a matrix randomly sampled from the data this approach allows a gain of nearly three orders of magnitude in processing time compared with classical singular value decomposition denoising this procedure called urqrd uncoiled random qr denoising strongly reduces the computer memory footprint and allows the denoising algorithm to be applied to virtually unlimited data size the efficiency of these numerical tools is demonstrated on experimental data from high resolution broadband fourier transform ion cyclotron resonance mass spectrometry which has applications in proteomics and metabolomics we show that robust denoising is achieved in 2d spectra whose interpretation is severely impaired by scintillation noise these denoising procedures can be adapted to many other data analysis domains where the size and or the processing time are crucial

on meeting the peak correlation bounds in this paper we study the problem of meeting peak periodic or aperiodic correlation bounds for complex valued sets of sequences to this end the welch levenstein and exponential bounds on the peak inner product of sequence sets are considered and used to provide compound peak correlation bounds in both periodic and aperiodic cases the peak aperiodic correlation bound is further improved by using the intrinsic dimension deficiencies associated with its formulation in comparison to the compound bound the new aperiodic bound contributes an improvement of more than 35 for some specific values of the sequence length n and set cardinality m we study the tightness of the provided bounds by using both analytical and computational tools in particular novel algorithms based on alternating projections are devised to approach a given peak periodic or aperiodic correlation bound several numerical examples are presented to assess the tightness of the provided correlation bounds as well as to illustrate the effectiveness of the proposed methods for meeting these bounds

a comparison of linear reformulations for multinomial logit choice probabilities in facility location models abstract in the last decade several papers appeared on facility location problems that incorporate customer demand by the multinomial logit model three linear reformulations of the original non linear model have been proposed so far in this paper we discuss these models in terms of solvability we present empirical findings based on synthetic data

a fuzzy set based approach to origin destination matrix estimation in urban traffic networks with imprecise data abstract an important issue in the management of urban traffic networks is the estimation of origin destination o d matrices whose entries represent the travel demands of network users we discuss the challenges of o d matrix estimation with incomplete imprecise data we propose a fuzzy set based approach that utilises successive linear approximation the fuzzy sets used have triangular membership functions that are easy to interpret and enable straightforward calibration of the parameters that weight the discrepancy between observed data and those predicted by the proposed approach the method is potentially useful when prior o d matrix entry estimates are unavailable or scarce requiring trip generation information on origin departures and or destination arrivals leading to multiple modelling alternatives the method may also be useful when there is no o d matrix that can be user optimally assigned to the network to reproduce observed link counts exactly the method has been tested on some numerical examples from the literature and the results compare favourably with the results of earlier methods it has also been successfully used to estimate o d matrices for a practical urban traffic network in brazil

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

an algorithm for the ranking of shortest paths an efficient computational implementation of a path deletion k shortest paths algorithm and a new algorithm for the same problem are presented in a path deletion k shortest paths algorithm a sequence g1 g2 gk of networks is is defined such that g1 is given network and its k th shortes path is trivially determined from the shortest path in gk in essence as soon as the shortest path in gk is determined it is excluded from gk in such a way that no new paths are formed and no more paths are deleted so far each gk two procedures are executed a shortest path algorithm and a path deletion algorithm in the presented computational implementation all the information resulting from the determination of the k th shortest path is carried throughout gk 1 gk 2 gk the new algorithm not only keeps this characteristics but also avoids the last k 1 executions of a shortest path algorithm which results in a suprising and very substantial reduction in the execution time in fact for randomly generated networks with 104 nodes and 105 arcs once the shortest the new algorithm computes the next 100 shortest paths in times of the order of 10 1 seconds to illustrate the efficiency of this algorithm comparative computational experiments are reported

cognitive radar based sequence design via sinr maximization the ambiguity function plays an important role in radar systems in fact many radar design problems can be interpreted from the perspective of persuing desired ambiguity functions to adapt to various application scenes in this paper we consider designing a radar sequence subject to a peak to average power ratio par constraint to maximize the signal to interference plus noise ratio which can also be interpreted as designing a sequence with a desired ambiguity function from an optimization point of view this is equivalent to optimizing a complex quartic function with the par constraint an efficient algorithm based on the general majorization minimization mm method is developed to solve this problem with guaranteed convergence to a stationary point under some mild conditions in addition the unit modulus constraint as a special case is considered and another algorithm is proposed which is the combination of the general mm and the coordinate descent method numerical experiments show that the proposed algorithms can shape a desired ambiguity function based on the prior information and the performance is much better compared with the existing methods

traffic assignment model with fuzzy level of travel demand an efficient algorithm based on quasi logit formulas abstract the place of fuzzy concepts in traffic assignment ta models has been studied in recent literature keeping fuzzy level of travel demand in mind we propose a new ta model in which the travel costs of links are depended on their congestion from the results of such fuzzy ta model network planners are able to estimate the number of travelers on network links by using zero one variables the proposed model is transformed into a crisp mixed integer problem with respect to path flow variables in order to produce the logit flows from this problem damberg et al algorithm is modified then the level of certainty is maximized and perceived travel delays are minimized for a fixed certainty degree the obtained solution which is named the fuzzy equilibrium flow satisfies a quasi logit formula similar to ordinary expression of the logit route choice model eventually we examine the quality of different path enumeration techniques in the proposed model

designing unimodular sequence sets with good correlations including an application to mimo radar a multiple input multiple output mimo radar system that transmits orthogonal waveforms via its antennas can achieve a greatly increased virtual aperture compared with its phased array counterpart this increased virtual aperture enables many of the mimo radar advantages including enhanced parameter identifiability and improved resolution practical radar requirements such as unit peak to average power ratio and range compression dictate that we use mimo radar waveforms that have constant modulus and good auto and cross correlation properties we present in this paper new computationally efficient cyclic algorithms for mimo radar waveform synthesis these algorithms can be used for the design of unimodular mimo sequences that have very low auto and cross correlation sidelobes in a specified lag interval and of very long sequences that could hardly be handled by other algorithms previously suggested in the literature a number of examples are provided to demonstrate the performances of the new waveform synthesis algorithms

the mimo radar and jammer games the interaction between a smart target and a smart mimo radar is investigated from a game theory perspective since the target and the radar form an adversarial system their interaction is modeled as a two person zero sum game the mutual information criterion is used in formulating the utility functions the unilateral hierarchical and symmetric games are studied and the equilibria solutions are derived

ambiguity function shaping for cognitive radar via complex quartic optimization in this paper we propose a cognitive approach to design phase only modulated waveforms sharing a desired range doppler response the idea is to minimize the average value of the ambiguity function of the transmitted signal over some range doppler bins which are identified exploiting a plurality of knowledge sources from a technical point of view this is tantamount to optimizing a real and homogeneous complex quartic order polynomial with a constant modulus constraint on each optimization variable after proving some interesting properties of the considered problem we devise a polynomial time waveform optimization procedure based on the maximum block improvement mbi method and the theory of conjugate partial symmetric conjugate super symmetric fourth order tensors at the analysis stage we assess the performance of the proposed technique showing its capability to properly shape the range doppler response of the transmitted waveform

quadratic optimization with similarity constraint for unimodular sequence synthesis this paper considers unimodular sequence synthesis under similarity constraint for both the continuous and discrete phase cases a computationally efficient iterative algorithm for the continuous phase case ia cpc is proposed to sequentially optimize the quadratic objective function the quadratic optimization problem is turned into multiple one dimensional optimization problems with closed form solutions for the discrete phase case we present an iterative block optimization algorithm specifically we partition the design variables into k blocks and then we sequentially optimize each block via exhaustive search while fixing the remaining k 1 blocks finally we evaluate the computational costs and performance gains of the proposed algorithms in comparison with power method like and semidefinite relaxation related techniques

a unified description of iterative algorithms for traffic equilibria the purpose of this paper is to provide a unified description of iterative algorithms for the solution of traffic equilibrium problems we demonstrate that a large number of well known solution techniques can be described in a unified manner through the concept of partial linearization and establish close relationships with other algorithmic classes for nonlinear programming and variational inequalities in the case of nonseparable travel costs the class of partial linearization algorithms are shown to yield new results in the theory of finite dimensional variational inequalities the possibility of applying truncated algorithms within the framework is also discussed

computational design of sequences with good correlation properties in this paper we introduce a computational framework based on an iterative twisted approximation itrox and a set of associated algorithms for various sequence design problems the proposed computational framework can be used to obtain sequences or complementary sets of sequences possessing good periodic or aperiodic correlation properties and in an extended form to construct zero or low correlation zone sequences furthermore as constrained e g finite alphabets are of interest in many applications we introduce a modified version of our general framework that can be useful in these cases several applications of itrox are studied and numerical examples focusing on the construction of real valued and binary sequences are provided to illustrate the performance of itrox for each application

the oscillation of derivatives the bernstein problem for fourier integrals in 1914 s bernstein discovered that if a real valued function f x and all its derivatives are of a constant sign in a closed interval z then f is the restriction to z of an analytic function the problem of determining the analytic character of a function f x from the oscillatory properties of its derivatives has thus become known as the bernstein problem for functions periodic on the real axis the important results are due to polya and wiener and ego

fast subspace decomposition many recent signal processing techniques in various areas e g array signal processing system identification and spectrum estimation require a step of extracting the low dimensional subspace from a large space this step is usually called subspace decomposition which is conventionally accomplished by an eigendecomposition ed since an ed requires o m sup 3 flops for an m spl times m matrix it may represent a barrier to the real time implementation of these algorithms the authors present a fast algorithm for signal subspace decomposition which is termed fsd that exploits the special matrix structure low rank plus identity associated with signal subspace algorithms and requires only o m sup 2 d flops where d often spl lt m denotes the signal subspace dimension unlike most of alternatives the dimension of the signal subspace is not assumed known apriori and is estimated as part of the procedure moreover theoretical analysis has been conducted and its results show the strong consistency of the new detection scheme and the asymptotic equivalence between fsd and ed in estimating the signal subspace their new approach can also exploit other matrix structure common in signal processing areas e g toeplitz or hankel and thus achieve another order of computational reduction moreover it can be easily implemented in parallel to reduce further the computation time to as little as o md using o m simple processors

alternating projections for designing locally orthogonal waveform pairs we propose an approach to design locally orthogonal waveform pairs lowp the approach is based on alternating projection in which an algorithm framework called alternating projections to synthesize lowp aplowp is derived two specialized versions of aplowp namely aplowp dynamic ideal autocorrelation construction diac and aplowp inner product constraint ipc are developed aplowp diac is used to synthesize waveform pairs for instantaneous polarization radar because its designed waveforms have very low auto and cross correlation magnitudes in specified lag intervals aplowp ipc is used for joint transmit receive optimization the ipc of aplowp ipc guarantees that the signal to noise ratio snr loss is below the specified bound even though a mismatched filter leads to snr loss the effectiveness of the proposed algorithms is demonstrated by using numerical simulations

complex spreading sequences with a wide range of correlation properties this paper presents a new family of complex valued pseudo random sequences for use in coded multiple access communication systems the family offers a very wide range of values for both auto correlation ac and cross correlation cc functions allowing great flexibility in the selection of characteristics of sequence sets based on the measure described in this paper for the mean square aperiodic ac and cc values of a set of sequences the correlation properties of sets of these sequences are compared to well known sequence sets and it is shown that sets from the new family of sequences have superior qualities tables of parameters for various sequence sets are presented to enable the construction and comparison of sets from this new family

a new construction framework for polyphase complete complementary codes with various lengths complete complementary codes ccc with equal sequence lengths have found numerous applications in wireless communications owing to their ideal correlation properties in modern multi user multi rate communication systems cccs with various sequence lengths for different complementary codes are desirable in this paper we propose a new construction of polyphase ccc with various lengths by using unimodular paraunitary pu matrices our key idea is to decompose a large square pu matrix into direct sum of matrices with smaller sizes which is equivalent to block diagonalization of matrices in order to construct ccc with various lengths we show that our proposed constructions not only generalize several previously known methods but also lead us to new cccs with both equal and various lengths