efficient estimation of class a noise parameters via the em algorithm the class a middleton noise model is a commonly used statistical physical parametric model for non gaussian interference superimposed on a gaussian background in this study the problem of efficient estimation of the class a parameters for small sample sizes is considered the proposed estimator is based on the em algorithm a two step iterative estimation technique that is ideally suited for the class a estimation problem since the observations can be readily treated as incomplete data for the single parameter estimation problem a closed form expression for the estimator is obtained furthermore for the single parameter estimation problem it is shown that the sequence of estimates obtained via the em algorithm converges and a characterization of the point to which the sequence converges is given in particular it is shown that if the limit point of this convergent sequence is an interior point of the parameter set of interest then it must be a stationary point of the traditional likelihood function in addition for both the single parameter and two parameter estimation problems the small sample size performance of the proposed em algorithm is examined via an extensive simulation study

equivalence relations on separated nets arising from linear toral flows in 1998 burago kleiner and mcmullen independently proved the existence of separated nets in r which are not bi lipschitz equivalent bl to a lattice a finer equivalence relation than bl is bounded displacement bd separated nets arise naturally as return times to a section for minimal r actions we analyze the separated nets which arise via these constructions focusing particularly on nets arising from linear r actions on tori we show that generically these nets are bl to a lattice and for some choices of dimensions and sections they are generically bd to a lattice we also show the existence of such nets which are not bd to a lattice

entire majorants via euler maclaurin summation it is the aim of this article to give extremal majorants of type 2 for the class of functions f n x sgn x x n where n n as applications we obtain positive definite extensions to r of it m defined on r 1 1 where m n optimal bounds in hilbert type inequalities for the class of functions it m and majorants of type 2 for functions whose graphs are trapezoids

extremal functions in de branges and euclidean spaces ii this paper presents the gaussian subordination framework to generate optimal one sided approximations to multidimensional real valued functions by functions of prescribed exponential type such extremal problems date back to the works of beurling and selberg and provide a variety of applications in analysis and analytic number theory here we majorize and minorize on bbb r n the gaussian bf x mapsto e pi lambda bf x 2 where lambda0 is a free parameter by functions with distributional fourier transforms supported on euclidean balls optimizing weighted l 1 errors by integrating the parameter lambda against suitable measures we solve the analogous problem for a wide class of radial functions applications to inequalities and periodic analogues are discussed the constructions presented here rely on the theory of de branges spaces of entire functions and on new interpolation tools derived from the theory of laplace transforms of laguerre p o lya functions

interpolation formulas with derivatives in de branges spaces ii abstract we investigate necessary and sufficient conditions under which entire functions in de branges spaces can be recovered from function values and values of derivatives our main focus is on spaces with a structure function whose logarithmic derivative is bounded in the upper half plane

a multiuser receiver for code division multiple access communications over multipath channels a multiuser communication system is considered where k users share a channel with multipath propagation by using code division for multiple access data modulation is carried out by binary phase shift keying and direct sequence spread spectrum signaling the micro cellular communication media is modeled as a frequency selective fading channel with multipath propagation the multipath diversity of the received signals from the k users is exploited by a bank of k rake correlators algorithms based on the maximum likelihood rule have been developed for estimating the complex channel coefficients as well as for detection of the desired data packets from the sufficient statistics provided by the rake correlators the performance of the resulting multiuser detector is evaluated analytically and via monte carlo simulations the results indicate that the estimator of the channel coefficients has a variance close to the cramer rao lower bound and that the proposed multiuser detector is capable of eliminating the near far effect as well as processing the signals propagated through multiple paths

pest regulation by means of impulsive controls in this paper we consider an integrated pest management model which is impulsively controlled by means of biological and chemical controls these controls are assumed to act in a periodic fashion a nonlinear incidence rate being used to account for the dynamics of the disease caused by the application of the biological control the floquet theory for impulsive ordinary differential equations is employed to obtain a condition in terms of an inequality involving the total action of the nonlinear force of infection in a period under which the susceptible pest eradication solution is globally asymptotically stable if the opposite inequality is satisfied then it is shown that the system under consideration becomes uniformly persistent a biological interpretation of the persistence condition is also provided

nonlinear group blind multiuser detection a nonlinear group blind technique is developed for joint detection of some given users data in a cdma uplink environment with the presence of unknown interference this method performs the so called slowest descent search over a likelihood function of the desired users starting from the estimate closest to the unconstrained maximizer of the likelihood function and along mutually orthogonal directions where this likelihood function drops to the slowest simulation results show that this new nonlinear technique offers substantial performance improvement over the previously proposed linear group blind multiuser detectors with little attendant increase in computational complexity the problem of group blind multiuser detection in the presence of both unknown interference and impulsive ambient noise is also treated under the framework of slowest descent search with the aid of a novel subspace based robust interference cancellation scheme it is seen that this robust group blind method significantly outperforms the robust blind multiuser detection scheme proposed previously

mmse interference suppression for direct sequence spread spectrum cdma we consider interference suppression for direct sequence spread spectrum code division multiple access cdma systems using the minimum mean squared error mmse performance criterion the conventional matched filter receiver suffers from the near far problem and requires strict power control typically involving feedback from receiver to transmitter for acceptable performance multiuser detection schemes previously proposed mitigate the near far problem but are complex and require explicit knowledge or estimates of the interference parameters in this paper we present and analyze several new mmse interference suppression schemes which have the advantage of being near far resistant to varying degrees depending on their complexity and can be implemented adaptively when interference parameters are unknown and or time varying numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver we conclude that mmse detectors can alleviate the need for stringent power control in cdma systems and may be a practical alternative to the matched filter receiver

bounding s t and s_1 t on the riemann hypothesis let pi s t denote the argument of the riemann zeta function zeta s at the point s frac 1 2 it assuming the riemann hypothesis we present two proofs of the bound begin aligned s t le left frac 1 4 o 1 right frac log t log log t end aligned for large t this improves a result of goldston and gonek by a factor of 2 the first method consists of bounding the auxiliary function s 1 t int 0 t s u text d u using extremal functions constructed by carneiro littmann and vaaler we then relate the size of s t to the size of the functions s 1 t pm h s 1 t when h asymp 1 log log t the alternative approach bounds s t directly relying on the solution of the beurling selberg extremal problem for the odd function f x arctan left frac 1 x right frac x 1 x 2 this draws upon recent work by carneiro and littmann

hilbert spaces and the pair correlation of zeros of the riemann zeta function montgomery s pair correlation conjecture predicts the asymptotic behavior of the function n t defined to be the number of pairs and of ordinates of nontrivial zeros of the riemann zetafunction satisfying 0 0 using montgomery s formula and some extremal functions of exponential type these functions are optimal in the sense that they majorize and minorize the characteristic function of the interval in a way to minimize the l1 r 1 sin x x 2 dx error we give a complete solution for this extremal problem using the framework of reproducing kernel hilbert spaces of entire functions this extends previous work of p x gallagher 18 in 1985 where the case 1 2 n was considered using non extremal majorants and minorants

extremal functions in de branges and euclidean spaces abstract in this work we obtain optimal majorants and minorants of exponential type for a wide class of radial functions on r n these extremal functions minimize the l 1 r n x 2 2 n d x distance to the original function where 1 is a free parameter to achieve this result we develop new interpolation tools to solve an associated extremal problem for the exponential function f x e x where 0 in the general framework of de branges spaces of entire functions we then specialize the construction to a particular family of homogeneous de branges spaces to approach the multidimensional euclidean case finally we extend the result from the exponential function to a class of subordinated radial functions via integration on the parameter 0 against suitable measures applications of the results presented here include multidimensional versions of hilbert type inequalities extremal one sided approximations by trigonometric polynomials for a class of even periodic functions and extremal one sided approximations by polynomials for a class of functions on the sphere s n 1 with an axis of symmetry

iterative multiuser receivers for cdma channels an em based approach maximum likelihood detection for the multiuser code division multiple access cdma channel is prohibitively complex this paper considers new iterative multiuser receivers based on the expectation maximization em algorithm and related more powerful space alternating algorithms the latter algorithms include the sage algorithm and a new missing parameter space alternating algorithm that alternately updates individual parameter components or treats them as probabilistic missing data application of these em based algorithms to the problem of discrete parameter estimation i e data detection in the gaussian multiple access channel leads to a variety of convergent receiver structures that incorporate soft decision feedback for interference cancellation and or sequential updating of iterative bit estimates convergence and performance analyses are based on well known properties of the em algorithm and on numerical simulation

gaussian subordination for the beurling selberg extremal problem we determine extremal entire functions for the problem of ma jorizing minorizing and approximating the gaussian function e x 2 by en tire functions of exponential type the combination of the gaussian and a general distribution approach provides the solution of the extremal problem for a wide class of even functions that includes most of the previously known examples for instance 3 4 10 and 17 plus a variety of new interesting functions such asjxj for 1 log x 2 2 x 2 2 for 0 log x2 2 andx2n logx2 forn2 n further applications to number theory include optimal approximations of theta functions by trigonometric polynomi als and optimal bounds for certain hilbert type inequalities related to the discrete hardy littlewood sobolev inequality in dimension one

a class of extremal functions for the fourier transform we determine a class of real valued integrable functions f x and corresponding functions m x such that f x 1 and the value of mfo is miimi several applications of these functions to number theory and analysis are given

blind multiuser detection a subspace approach a new multiuser detection scheme based on signal subspace estimation is proposed it is shown that under this scheme both the decorrelating detector and the linear minimum mean square error mmse detector can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform and timing of the user of interest the consistency and asymptotic variance of the estimates of the two linear detectors are examined a blind adaptive implementation based on a signal subspace tracking algorithm is also developed it is seen that compared with the previous minimum output energy blind adaptive multiuser detector the proposed subspace based blind adaptive detector offers lower computational complexity better performance and robustness against signature waveform mismatch two extensions are made within the framework of signal subspace estimation first a blind adaptive method is developed for estimating the effective user signature waveform in the multipath channel secondly a multiuser detection scheme using spatial diversity in the form of an antenna array is considered a blind adaptive technique for estimating the array response for diversity combining is proposed it is seen that under the proposed subspace approach blind adaptive channel estimation and blind adaptive array response estimation can be integrated with blind adaptive multiuser detection with little attendant increase in complexity

extremal problems in de branges spaces the case of truncated and odd functions in this paper we find extremal one sided approximations of exponential type for a class of truncated and odd functions with a certain exponential subordination these approximations optimize the l 1 mathbb r e x 2 mathrm d x error where e is an arbitrary hermite biehler entire function of bounded type in the upper half plane this extends the work of holt and vaaler duke math j 83 203 247 1996 for the signum function we also provide periodic analogues of these results finding optimal one sided approximations by trigonometric polynomials of a given degree to a class of periodic functions with exponential subordination these extremal trigonometric polynomials optimize the l 1 mathbb r mathbb z mathrm d vartheta error where vartheta is an arbitrary nontrivial measure on mathbb r mathbb z the periodic results extend the work of li and vaaler indiana univ math j 48 1 183 236 1999 who considered this problem for the sawtooth function with respect to jacobi measures our techniques are based on the theory of reproducing kernel hilbert spaces of entire functions and of polynomials and on the construction of suitable interpolations with nodes at the zeros of laguerre polya functions

adaptive bayesian multiuser detection for synchronous cdma with gaussian and impulsive noise we consider the problem of simultaneous parameter estimation and data restoration in a synchronous cdma system in the presence of either additive gaussian or additive impulsive white noise with unknown parameters the impulsive noise is modeled by a two term gaussian mixture distribution bayesian inference of all unknown quantities is made from the superimposed and noisy received signals the gibbs sampler a markov chain monte carlo procedure is employed to calculate the bayesian estimates the basic idea is to generate ergodic random samples from the joint posterior distribution of all unknown and then to average the appropriate samples to obtain the estimates of the unknown quantities adaptive bayesian multiuser detectors based on the gibbs sampler are derived for both the gaussian noise synchronous cdma channel and the impulsive noise synchronous cdma channel a salient feature of the proposed adaptive bayesian multiuser detectors is that they can incorporate the a priori symbol probabilities and they produce as output the a posteriori symbol probabilities that is they are soft input soft output algorithms hence these methods are well suited for iterative processing in a coded system which allows the adaptive bayesian multiuser detector to refine its processing based on the information from the decoding stage and vice versa a receiver structure termed the adaptive turbo multiuser detector

some extremal functions in fourier analysis ii we obtain extremal majorants and minorants of exponential type for a class of even functions on which includes log x and x where 1 1 we also give periodic versions of these results in which the majorants and minorants are trigonometric polynomials of bounded degree as applications we obtain optimal estimates for certain hermitian forms which include discrete analogues of the one dimensional hardy littlewood sobolev inequalities a further application provides an erdos turan type inequality that estimates the sup norm of algebraic polynomials on the unit disc in terms of power sums in the roots of the polynomials

joint transmitter receiver optimization for multi input multi output systems with decision feedback the joint transmit receive optimization problem for multiuser communication systems with decision feedback is investigated it is shown that minimization of the geometric mean squared error defined as the determinant of the error covariance matrix leads to a tractable transmitter optimization problem for general multi input multi output decision feedback systems several computational results are included that highlight system performance for a variety of useful transmission scenarios