maximin joint optimization of transmitting code and receiving filter in radar and communications in this paper we conduct the joint design of transmitting sequence s and receiving filters subject to the peak to average ratio par constraint in radar and communications applications we consider optimizing the worst case performance and the resulting optimization problem takes a maximin format we propose two algorithms based on the mm majorization minimization or minorization maximization method as opposed to the traditional epigraph based smooth reformulation on top of that both algorithms are guaranteed to converge to a b oulingand stationary solution and b stationarity is the appropriate stationarity condition for problems with a nonconvex constraint set the proposed algorithms successively solve a series of simple convex problems that enjoy low computational complexity numerical simulations have shown that the proposed algorithms empirically achieve slightly higher objective values and converge faster in terms of cpu time than the existing methods

on the design of constant modulus probing signals for mimo radar probing signal waveforms play a central role in the signal processing performance of a multiple input multiple output mimo radar in practice for a given desired beam pattern we need to design a probing signal waveform whose beam pattern closely matches the desired one and whose autocorrelation and cross correlation sidelobes are kept low the latter properties are important to mitigate undesirable interference caused by multiple targets or scatterers in this correspondence we present an efficient optimization method to design a constant modulus probing signal which can synthesize a desired beam pattern while maximally suppressing both the autocorrelation and cross correlation sidelobes at between given spacial angles we formulate this problem as an unconstrained minimization of a fourth order trigonometric polynomial and propose an efficient quasi newton iterative algorithm to solve it besides we provide an analysis of the local minima of the fourth order trigonometric polynomial and prove that any local minima is a 1 2 approximation of its global optimal solution numerical examples show that the proposed approach compares favorably with the existing approach

from polynomial integrals of hamiltonian flows to a model of non linear elasticity abstract we prove non existence of smooth solutions of a quasi linear system suggested by ericksen in a model of non linear elasticity this system is of mixed elliptic hyperbolic type we discuss also a relation of such a system to polynomial integrals of classical hamiltonian systems

globally lipschitz continuous solutions to a class of quasilinear wave equations abstract this work investigates the existence of globally lipschitz continuous solutions to a class of cauchy problem of quasilinear wave equations applying lax s method and generalized glimm s method we construct the approximate solutions of the corresponding perturbed riemann problem and establish the global existence for the derivatives of solutions then the existence of global lipschitz continuous solutions can be carried out by showing the weak convergence of residuals for the source term of equation

mimo radar waveform design with constant modulus and similarity constraints we consider the problem of waveform design for multiple input multiple output mimo radar in the presence of signal dependent interference embedded in white gaussian disturbance we present two sequential optimization procedures to maximize the signal to interference plus noise ratio sinr accounting for a constant modulus constraint as well as a similarity constraint involving a known radar waveform with some desired properties e g in terms of pulse compression and ambiguity the presented sequential optimization algorithms based on a relaxation method yield solutions with good accuracy their computational complexity is linear in the number of iterations and trials in the randomized procedure and polynomial in the receive filter length finally we evaluate the proposed techniques by considering their sinr performance beam pattern as well as pulse compression property via numerical simulations

design of phase codes for radar performance optimization with a similarity constraint this paper deals with the design of coded waveforms which optimize radar performances in the presence of colored gaussian disturbance we focus on the class of phase coded pulse trains and determine the radar code which approximately maximizes the detection performance under a similarity constraint with a prefixed radar code this is tantamount to forcing a similarity between the ambiguity functions of the devised waveform and of the pulse train encoded with the prefixed sequence we consider the cases of both continuous and finite phase alphabet and formulate the code design in terms of a nonconvex np hard quadratic optimization problem in order to approximate the optimal solutions we propose techniques with polynomial computational complexity based on the method of semidefinite program sdp relaxation and randomization moreover we also derive approximation bounds yielding a ldquomeasure of goodnessrdquo of the devised algorithms at the analysis stage we assess the performance of the new encoding techniques both in terms of detection performance and ambiguity function under different choices for the similarity parameter we also show that the new algorithms achieve an accurate approximation of the optimal solution with a modest number of randomizations

the initial boundary value problem of hyperbolic integro differential systems of nonlinear balance laws abstract this research explores the initial boundary value problem for the 2 2 hyperbolic systems of balance laws whose sources are the time dependent and contain the integral of unknowns perturbed riemann and boundary riemann problems are provided to account for the time dependence of sources their approximation solutions are constructed by modified lax s method in addition we introduce a new version of glimm scheme ggs and study its stability which is proved by the wave interaction estimates in a dissipativity assumption with the consistency of ggs the existence of a global weak solution satisfying the entropy inequality is then achieved finally the lipschitz continuous solution to the problem is established by the weak convergence of the residual

smooth solutions to a class of quasilinear wave equations this article investigates the existence nonexistence of smooth solutions of nonlinear vibration equations which arise from the one dimensional motion of polytropic gas without external forces contained in a finite interval for any fixed arbitrarily long time we show that there are smooth small amplitude solutions of the nonlinear equations for which the periodic solutions of the linearized equation are the first order approximations on the other hand when the nonlinearity is strictly convex or concave there exists no time periodic solutions which are twice continuously differentiable an example of possible singularities which occur at the second derivatives is illustrated we also give another kind of exact solutions with singularity such that shocks occur after a finite time furthermore we get an estimate of the life span of smooth solutions to the initial boundary value problem

global solutions for initial boundary value problem of quasilinear wave equations abstract this work investigates the existence of globally lipschitz continuous solutions to a class of initial boundary value problem of quasilinear wave equations applying the lax s method and generalized glimm s method we construct the approximate solutions of initial boundary riemann problem near the boundary layer and perturbed riemann problem away from the boundary layer by showing the weak convergence of residuals for the approximate solutions we establish the global existence for the derivatives of solutions and obtain the existence of global lipschitz continuous solutions of the problem

compressible euler equations with general pressure law we study the hyperbolic system of euler equations for an isentropic compressible fluid governed by a general pressure law the existence and regularity of the entropy kernel that generates the family of weak entropies is established by solving a new euler poisson darboux equation which is highly singular when the density of the fluid vanishes new properties of cancellation of singularities in combinations of the entropy kernel and the associated entropy flux kernel are found

decay rates for nonconvex systems of conservation laws we study decay of solutions for hyperbolic systems of conservation laws which are not genuinely nonlinear for a generic class of such systems we determine sharp algebraic rates of decay in the total variation of the wave speed for solutions with compact initial support our analysis involves generalized characteristic arguments and the random choice difference scheme of glimm 1993 john wiley sons inc

design of optimized radar codes with a peak to average power ratio constraint this paper considers the problem of radar waveform design in the presence of colored gaussian disturbance under a peak to average power ratio par and an energy constraint first of all we focus on the selection of the radar signal optimizing the signal to noise ratio snr in correspondence of a given expected target doppler frequency algorithm 1 then through a max min approach we make robust the technique with respect to the received doppler algorithm 2 namely we optimize the worst case snr under the same constraints as in the previous problem since algorithms 1 and 2 do not impose any condition on the waveform phase we also devise their phase quantized versions algorithms 3 and 4 respectively which force the waveform phase to lie within a finite alphabet all the problems are formulated in terms of nonconvex quadratic optimization programs with either a finite or an infinite number of quadratic constraints we prove that these problems are np hard and hence introduce design techniques relying on semidefinite programming sdp relaxation and randomization as well as on the theory of trigonometric polynomials providing high quality suboptimal solutions with a polynomial time computational complexity finally we analyze the performance of the new waveform design algorithms in terms of detection performance and robustness with respect to doppler shifts

on mimo detection under non gaussian target scattering in this paper we consider a multiple input multiple output mimo detection problem with m widely spaced transmit antennas and l widely spaced receive antennas and we study the problem of designing the signal waveforms transmitted by each source node under non gaussian target scattering and temporally correlated gaussian clutter two figures of merit are investigated for space time code stc optimization under a semidefinite rank constraint 1 the lower chernoff bound lcb to the detection probability for fixed probability of false alarm and 2 the mutual information mi between the observations available at the receive nodes and the channel response generated by a point like target assumed present tout court both receive and transmit power constraints are discussed if the scattering distribution possesses some suitably defined properties of unitary invariance see both mi optimal and lcb optimal stcs have a simple canonical structure the same set of clutter dependant temporal codewords are employed at the transmit nodes the only difference among the many solutions being the amount of power radiated by each antenna such a spatial power allocation critically depends upon the adopted figure of merit the specified power constraint and the underlying scattering model sufficient conditions to determine the optimal power allocation for all design criteria are provided asymptotic power distributions are also derived in the limit of vanishingly small and increasingly large signal to clutter ratios proving that assuming gaussian scattering at the design stage is a robust choice a case study of relevant practical interest is examined in depth so as to compare the proposed design criteria and to assess the impact of signal non gaussianity on the system performances

code design to optimize radar detection performance under accuracy and similarity constraints this paper deals with the design of coded waveforms which optimize radar performances in the presence of colored gaussian disturbance we focus on the class of linearly coded pulse trains and determine the optimum radar code according to the following criterion maximization of the detection performance under a control on the region of achievable doppler estimation accuracies and imposing a similarity constraint with a prefixed radar code this last constraint is tantamount to requiring a similarity between the ambiguity functions of the devised waveform and of the pulse train encoded with the prefixed sequence the resulting optimization problem is nonconvex and quadratic in order to solve it we propose a technique with polynomial computational complexity based on the relaxation of the original problem into a semidefinite program thus the best code is determined through a rank one decomposition of an optimal solution of the relaxed problem at the analysis stage we assess the performance of the new encoding technique in terms of detection performance region of achievable doppler estimation accuracies and ambiguity function

waveform design for radar stap in signal dependent interference waveform design is a pivotal component of the fully adaptive radar construct in this paper we consider waveform design for radar space time adaptive processing stap accounting for the waveform dependence of the clutter correlation matrix due to this dependence in general the joint problem of receiver filter optimization and radar waveform design becomes an intractable nonconvex optimization problem nevertheless it is however shown to be individually convex either in the filter or in the waveform variables we derive constrained versions of a the alternating minimization algorithm b proximal alternating minimization and c the constant modulus alternating minimization which at each step iteratively optimizes either the stap filter or the waveform independently a fast and slow time model permits waveform design in radar stap but the primary bottleneck is the computational complexity of the algorithms

performance evaluation of finite normal mixture model based image segmentation techniques finite normal mixture fnm model based image segmentation techniques adopt the following detection estimation classification paradigm 1 detect the number of image regions by using theoretical information criteria 2 estimate model parameters by using expectation maximization em classification maximization cm algorithms and 3 classify pixels into regions by using various classifiers this paper presents a theoretical framework to evaluate the performance of this class of image segmentation techniques for the detection performance probabilities of over detection and under detection of the number of image regions are defined and the associated formulae in terms of model parameters and image quality are derived for the estimation performance both em and cm algorithms are showed to produce asymptotically unbiased ml estimates of model parameters in the case of no overlap cramer rao bounds of variances of these estimates are derived for the classification performance misclassification probability for the bayesian classifier is defined and a simple formula based on parameter estimates and classified data is derived to evaluate segmentation errors this evaluation method provides both theoretically approachable accuracy limits of the techniques and practically achievable performance of the given images theoretical and experimental results are in good agreement and indicate that for images of moderate quality the detection operation is robust the parameter estimates are accurate and the segmentation errors are small

global entropy solutions to a class of quasi linear wave equations with large time oscillating sources abstract this research explores the cauchy problem for a class of quasi linear wave equations with time dependent sources it can be transformed into the cauchy problem of hyperbolic integro differential systems of nonlinear balance laws we introduce the generalized glimm scheme in new version and study its stability which is proved by glimm type interaction estimates in a dissipativity assumption the generalized solutions to the perturbed riemann problems the building blocks of generalized glimm scheme are constructed by riemann problem method modeled on the source free equations the global existence for the lipschitz continuous solutions and weak solutions to the systems is established by the consistency of scheme and the weak convergence of source finally the weak solutions are also the entropy solutions which satisfy the entropy inequality

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

decay of entropy solutions of nonlinear conservation laws we are concerned with the asymptotic behavior of entropy solutions of nonlinear conservation laws the main objective of this paper is to present an analytical approach and to explore its applications to studying the large time behavior of periodic entropy solutions of hyperbolic conservation laws the asymptotic decay of periodic solutions of nonlinear hyperbolic conservation laws is an important nonlinear phenomenon it is observed that the genuine nonlinearity of equations forces the waves of each characteristic family to interact vigorously and to cancel each other the insightful analysis of glimm lax gl for scalar equations and 2 2 systems has indicated that the resultant mutual cancellation of interacting shock and rarefaction waves of the same family induces the decay of periodic solutions such a result was first shown by lax l1 in 1957 for one dimensional convex scalar conservation laws dafermos d1 applying his uniform processes proved the decay result for the case that the set of inflection points of the flux does not have an accumulation point the glimm lax theory gl indicates that for 2 2 strictly hyperbolic and genuinely nonlinear systems any periodic glimm solution decays like o 1 t this result was proved by using the approximate characteristic method in the glimm difference solutions provided that the oscillation of the corresponding initial data is small recently using the method of generalized characteristics dafermos d3 showed that any periodic solution with local bounded variation and small oscillation for 2 2 systems decays asymptotically with the same detailed structure pas found by lax l1 for the