on lower bounds to the maximum correlation of complex roots of unity sequences it is shown how the welch bound 1974 on the maximum correlation of families of complex sequences of fixed norm can be modified to provide an improved bound for the case when the sequence symbols are roots of unity as in the welch bound the improved bound is based on a useful expression for the even correlation moments an analysis of the ratio of successive even moments using this expression is shown to yield a small improvement over a similarly derived bound due to v m sidelnikov 1971 interestingly the expression for the moments reduces in the binary q 2 case to a version of the pless power moment identities the derivation also provides insight into the problem of optimal sequence design

norm constrained capon beamforming using multirank signal models with kalman filter implementation the performance of the capon beamforming is known to degrade dramatically in the presence of model mismatches especially when the desired signal is present in the training data to improve the robustness the diagonal loading technique was introduced however the major drawback is the selection of the diagonal loading level which is related to the unknown signal powers another way to alleviate performance degradation is to use a more accurate signal model of the array response in this paper a norm constrained capon beamforming using multirank signal models is proposed based on the pseudo observation method the quadratic constraints can be easily constructed the problem is solved by a nonlinear kalman filter which can be implemented on line the simulation results show that the design of the norm constraint value is less sensitive to the signal powers small angle mismatches and number of sensors with a standard linear array further it is shown that the use of a multirank signal model and kalman filter technique result in less self cancellation and performance degradation than that of the rank 1 signal model and the estimation of sample matrix

new families of binary sequences with low correlation for a positive integer n new families s and u of binary sequences of period 2 sup n 1 with low correlations are proposed where for some positive integer e s is defined for odd n e and u for even n e the family s has four valued correlations and is a generalization of the family of gold like sequences introduced by s boztas and p v kumar see ibid vol 40 p 532 7 1994 the family u which is also a generalization of the sequence family defined by p udaya polyphase and frequency hopping sequences obtained from finite rings ph d dissertation dept elec eng indian inst technol kanpur 1992 has six valued correlations the relationship between gold like sequences and gold sequences is the same as the relationship between the family s and the family constructed from the binary sequences partially contributed by r gold see ibid vol it 14 p 154 6 1968 t kasami see coordinated sci lab univ of illinois urbana champaign tech rep r 285 ad 632574 1966 and welch using a lifting idea no j s and kumar p v ibid vol 35 p 371 9 1989 for the families s and u families of binary sequences with the same correlation distributions and large linear span are also constructed

minimal linear equivalent analysis of a variable memory binary sequence generator starting from a memory based nonlinear generator due to p r geffe 1973 a binary sequence generator mem bsg consisting of three linear feedback shift registers and a variable memory is defined and analyzed the mem bsg is shown to be convenient for generating fast binary sequences of large period and linear complexity which may be useful in spread spectrum and cryptographic applications

bat chirps with good properties zak space construction of perfect polyphase sequences previously a discretization of the linear fm chirp of length n kl 2 l and kl isin z was given and the conditions for its minimal zak space support were derived chirps satisfying these conditions are known as finite chirps in this work subsets of finite chirps of length n l 2 l a prime are examined the investigation leads to a new zak space construction of general polyphase sequence sets of size l 1 with optimal auto and cross correlation properties known as perfect sequence sets it is shown that perfect sequence sets are closely related to sets of finite chirps and in particular include the sets of zadoff chu sequences which are identical with subsets of finite chirps and the sets of generalized frank sequences which are identical with sets of modulations of finite chirps as special cases the entire collection of perfect sequence sets is then given by a partition of the set of perfect auto correlation sequences obtained by right coset decomposition of the group of all permutations with respect to a certain cyclic group the construction suggests several further generalizations that can be obtained by operating exclusively on subgroups of the permutation group

doubly constrained robust capon beamformer the standard capon beamformer scb is known to have better resolution and much better interference rejection capability than the standard data independent beamformer when the array steering vector is accurately known however the major problem of the scb is that it lacks robustness in the presence of array steering vector errors in this paper we will first provide a complete analysis of a norm constrained capon beamforming nccb approach which uses a norm constraint on the weight vector to improve the robustness against array steering vector errors and noise our analysis of nccb is thorough and sheds more light on the choice of the norm constraint than what was commonly known we also provide a natural extension of the scb which has been obtained via covariance matrix fitting to the case of uncertain steering vectors by enforcing a double constraint on the array steering vector viz a constant norm constraint and a spherical uncertainty set constraint which we refer to as the doubly constrained robust capon beamformer dcrcb nccb and dcrcb can both be efficiently computed at a comparable cost with that of the scb performance comparisons of nccb dcrcb and several other adaptive beamformers via a number of numerical examples are also presented

several new infinite families of bent functions and their duals bent functions are optimal combinatorial objects since their introduction substantial efforts have been directed toward their study in the last three decades a complete classification of bent functions is elusive and looks hopeless today therefore not only their characterization but also their generation are challenging problems this paper is devoted to the construction of bent functions first we provide several new effective constructions of bent functions self dual bent functions and antiself dual bent functions second we provide seven new infinite families of bent functions by explicitly calculating their dual

tests for gaussian repeated measures with missing data in small samples for small samples of gaussian repeated measures with missing data barton and cramer recommended using the em algorithm for estimation and reducing the degrees of freedom for an analogue of rao s f approximation to wilks test computer simulations led to the conclusion that the modified test was slightly conservative for total sample size of n 40 here we consider additional methods and smaller sample sizes nin 12 24 we describe analogues of the pillai bartlett trace hotelling lawley trace and geisser greenhouse corrected univariate tests which allow for missing data eleven sample size adjustments were examined which replace n by some function of the numbers of non missing pairs of responses in computing error degrees of freedom overall simulation results allowed concluding that an adjusted test can always control test size at or below the nominal rate even with as few as 12 observations and up to 10 per cent missing data the choice of method varies with the test statistic replacing n by the mean number of non missing responses per variable works best for the geisser greenhouse test the pillai bartlett test requires the stronger adjustment of replacing n by the harmonic mean number of non missing pairs of responses for wilks and hotelling lawley an even more aggressive adjustment based on the minimum number of non missing pairs must be used

further results on generalized bent functions and their complete characterization this paper contributes to increase our knowledge on generalized bent functions including generalized bent boolean functions and generalized p ary bent functions with odd prime p by bringing new results on their characterization and construction in arbitrary characteristic more specifically we first investigate relations between generalized bent functions and bent functions by the decomposition of generalized bent functions this enables us to completely characterize generalized bent functions and mathbb z p k bent functions by some affine space associated with the generalized bent functions we also present the relationship between generalized bent boolean functions with an odd number of variables and generalized bent boolean functions with an even number of variables based on the well known maiorana mcfarland class of boolean functions we present some infinite classes of generalized bent boolean functions in addition we introduce a class of generalized hyperbent functions that can be seen as generalized dillon s ps functions finally we solve an open problem related to the description of the dual function of a weakly regular generalized bent boolean function with an odd number of variables via the walsh hadamard transform of their component functions and we generalize these results to the case of odd prime

a new binary sequence family with low correlation and large size for odd n 2l 1 and an integer spl rho with 1 spl les spl rho spl les l a new family s sub o spl rho of binary sequences of period 2 sup n 1 is constructed for a given spl rho s sub o spl rho has maximum correlation 1 2 sup n 2 spl rho 1 2 family size 2 sup n spl rho and maximum linear span n n 1 2 similarly a new family of s sub e spl rho of binary sequences of period 2 sup n 1 is also presented for even n 2l and an integer spl rho with 1 spl les spl rho l where maximum correlation family size and maximum linear span are 1 2 sup n 2 spl rho 2 sup n spl rho and n n 1 2 respectively the new family s sub o spl rho or s sub e spl rho contains boztas and kumar s construction or udaya s as a subset if m sequences are excluded from both constructions as a good candidate with low correlation and large family size the family s sub o 2 is discussed in detail by analyzing its distribution of correlation values

new families of m ary sequences with low correlation constructed from sidel nikov sequences in this correspondence for a positive integer m and a prime p such that m pn 1 three families of m ary sequences using the m ary sidel nikov sequences with period pn 1 are constructed two small families contain pn 1 2 m 2 or pn m 3 m ary sequences and both of their maximum magnitudes of correlation values are upper bounded by 2 radic pn 6 the largest family has its maximum magnitude of correlation values upper bounded by 3 radic pn 5 and the family size is m 1 2 2n 1 1 m 1 for p 2 or m 1 2 pn 3 2 m m 1 2 for an odd prime p

some relations between extended and unscented kalman filters the unscented kalman filter ukf has become a popular alternative to the extended kalman filter ekf during the last decade ukf propagates the so called sigma points by function evaluations using the unscented transformation ut and this is at first glance very different from the standard ekf algorithm which is based on a linearized model the claimed advantages with ukf are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model we point out several less known links between ekf and ukf in terms of two conceptually different implementations of the kalman filter the standard one based on the discrete riccati equation and one based on a formula on conditional expectations that does not involve an explicit riccati equation first it is shown that the sigma point function evaluations can be used in the classical ekf rather than an explicitly linearized model second a less cited version of the ekf based on a second order taylor expansion is shown to be quite closely related to ukf the different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications

semiparametric models for longitudinal data with application to cd4 cell numbers in hiv seroconverters summary the paper describes a semiparametric model for longitudinal data which is illustrated by its application to data on the time evolution of cd4 cell numbers in hiv seroconverters the essential ingredients of the model are a parametric linear model for covariate adjustment a nonparametric estimation of a smooth time trend serial correlation between measurements on an individual subject and random measurement error a back fitting algorithm is used in conjunction with a cross validation prescription to fit the model a notable feature in the application is that the onset of hiv infection is associated with a sudden drop in cd4 cells followed by a longer term slower decay the model is also used to estimate an individual s curve by combining his data with the population curve shrinkage toward the population mean trajectory is controlled in a natural way by the estimated covariance structure of the data

on quadratic bent functions in polynomial forms in this correspondence we construct some new quadratic bent functions in polynomial forms by using the theory of quadratic forms over finite fields the results improve some previous work moreover we solve a problem left by yu and gong in 2006

binary sequences with gold like correlation but larger linear span a new construction of optimal binary sequences identical to the well known family of gold sequences in terms of maximum nontrivial correlation magnitude and family size but having larger linear span is presented the distribution of correlation values is determined for every odd integer spl tau spl ges 3 the construction provides a family that contains 2 sup spl tau 1 cyclically distinct sequences each of period 2 sup spl tau 1 the maximum nontrivial correlation magnitude equals 2 spl tau 1 sup 2 1 with one exception each of the sequences in the family has linear span at least spl tau sup 2 spl tau 2 compared to 2 spl tau for gold sequences the sequences are easily implemented using a quaternary shift register followed by a simple feedforward nonlinearity

large families of sequences with near optimal correlations and large linear span in order to build spread spectrum communication systems based on the cdma paradigm it is necessary to have large families of binary sequences with low pairwise correlation values for these systems to have resistance to certain cryptanalytic attacks and resistance to jamming the sequences must have large linear span we describe certain families of sequences that have these desirable properties the sequences are based on families of quadratic forms over finite fields

on correlations of a family of generalized geometric sequences in this correspondence we study families of generalized geometric sequences formed bp applying a feedforward function to certain sums of decimated m sequences with elements in a finite field we compute their correlation functions which for certain families turn out to be close to the square root of the period the size of these families equals their period we also show that in the binary case the linear complexities of these sequences are much larger than those of cascaded geometric sequences although in these cases the maximum correlations are larger

systematic methods of constructing bent functions and 2 rotation symmetric bent functions in this paper we first present two systematic constructions of bent functions by modifying the truth tables of rothaus s bent function and maiorana mcfarland s bent function respectively the number of the newly constructed bent functions by modifying the truth table of rothaus s bent function is also determined the methods of constructing self dual bent functions are then given after the dual functions of these bent functions being determined finally as an application two constructions of 2 rotation symmetric bent functions are presented in this paper

on the cross correlation of a p ary m sequence of period p 2m 1 and its decimated sequences by p m 1 2 2 p 1 in this paper for an odd prime we investigate into the cross correlation of a p ary m sequence m t of period p n 1 and its d decimated sequences m dt l 0 l m 1 2 where d pm 1 2 2 p l n 2m and m is an odd integer there are pm 1 2 distinct decimated sequences m dt l since gcd d pn 1 pm 1 2 it is shown that the magnitude of the cross correlation values is upper bounded by p 1 2 pn 2 1 we also construct the sequence family f from these sequences where the family size is pm and the correlation magnitude is upper bounded by pm 1 2 pn 2 1

a linear mixed effects model with heterogeneity in the random effects population abstract this article investigates the impact of the normality assumption for random effects on their estimates in the linear mixed effects model it shows that if the distribution of random effects is a finite mixture of normal distributions then the random effects may be badly estimated if normality is assumed and the current methods for inspecting the appropriateness of the model assumptions are not sound further it is argued that a better way to detect the components of the mixture is to build this assumption in the model and then compare the fitted model with the gaussian model all of this is illustrated on two practical examples

mixed effects smoothing spline analysis of variance we propose a general family of nonparametric mixed effects models smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function the random effects are generic and are modelled parametrically by assuming that the covariance function depends on a parsimonious set of parameters these parameters and the smoothing parameter are estimated simultaneously by the generalized maximum likelihood method we derive a connection between a nonparametric mixed effects model and a linear mixed effects model this connection suggests a way of fitting a nonparametric mixed effects model by using existing programs the classical two way mixed models and growth curve models are used as examples to demonstrate how to use smoothing spline analysis of variance decompositions to build nonparametric mixed effects models similarly to the classical analysis of variance components of these nonparametric mixed effects models can be interpreted as main effects and interactions the penalized likelihood estimates of the fixed effects in a two way mixed model are extensions of james stein shrinkage estimates to correlated observations in an example three nested nonparametric mixed effects models are fitted to a longitudinal data set

multiplicative characters the weil bound and polyphase sequence families with low correlation power residue and sidelnikov sequences are polyphase sequences with low correlation and variable alphabet sizes represented by multiplicative characters in this paper sequence families constructed from the shift and addition of the polyphase sequences are revisited initially 0 1 is assumed for multiplicative characters to represent power residue and sidelnikov sequences in a simple form the weil bound on multiplicative character sums is refined for the assumption where the character sums are equivalent to the correlations of sequences represented by multiplicative characters general constructions of polyphase sequence families that produce some of known families as the special cases are then presented the refined weil bound enables the efficient proofs on the maximum correlation magnitudes of the sequence families from the constructions it is shown that m ary known sequence families with large size can be partitioned into m 1 disjoint subsequence families with smaller maximum correlation magnitudes more generalized constructions are also considered by the addition of multiple cyclic shifts of power residue and sidelnikov sequences

signal set design with constrained amplitude spectrum and specified time bandwidth product a new method for designing signals with a given time bandwidth product such that all the signals in the set have a flat amplitude spectrum and have low cross correlation function values is introduced it is shown that these signals lie on a signal parameter space ellipse for a given duration and bandwidth it is possible to trade off the cardinality of the set for better cross correlation properties between remaining members of the set proof that the cross correlation between these signals is bounded from above by a factor proportional to the square root of inverse distance between these signals along one of the axes of the ellipse is given it is also shown that the cross correlation between two signals that are furthest apart is bounded by the square root of inverse time bandwidth product of the signals in the set an example design is then given and a comparison of this signal set to some well known signal sets illustrates that it performs better when the metric is maximum cross correlation value the proposed signal set also has the advantage that it can be designed for any time bandwidth product instead of discrete values

4 phase sequences with near optimum correlation properties two families of four phase sequences are constructed using irreducible polynomials over z sub 4 family a has period l 2 sup r 1 size l 2 and maximum nontrivial correlation magnitude c sub max

a distribution free test of constant mean in linear mixed effects models we propose a distribution free procedure an analogy of the dip test in non parametric regression to test whether the means of responses are constant over time in repeated measures data unlike the existing tests the proposed procedure requires very minimal assumptions to the distributions of both random effects and errors we study the asymptotic reference distribution of the test statistic analytically and propose a permutation procedure to approximate the finite sample reference distribution the size and power of the proposed test are illustrated and compared with competitors through several simulation studies we find that it performs well for data of small sizes regardless of model specification finally we apply our test to a data example to compare the effect of fatigue in two different methods used for cardiopulmonary resuscitation

the dip test of unimodality the dip test measures multimodality in a sample by the maximum difference over all sample points between the empirical distribution function and the unimodal distribution function that minimizes that maximum difference the uniform distribution is the asymptotically least favorable unimodal distribution and the distribution of the test statistic is determined asymptotically and empirically when sampling from the uniform

systematic constructions of rotation symmetric bent functions 2 rotation symmetric bent functions and bent idempotent functions rotation symmetric bent functions and their generation two rotation symmetric bent functions are two classes of cryptographically significant boolean functions however few constructions have been presented in the literature which either have restriction on integer n or have algebraic degree no more than 4 in this paper for any even integer n ge 4 three classes of bent functions are presented respectively most notably the proposed n variable rotation symmetric bent functions and two rotation symmetric bent functions can have any possible algebraic degree ranging from 2 to n 2 besides we obtain bent idempotent functions with the maximal algebraic degree n 2

bent function sequences in this paper we construct a new family of nonlinear binary signal sets which achieve welch s lower bound on simultaneous cross correlation and autocorrelation magnitudes given a parameter n with n 0 pmod 4 the period of the sequences is 2 n 1 the number of sequences in the set is 2 n 2 and the cross auto correlation function has three values with magnitudes leq 2 n 2 1 the equivalent linear span of the codes is bound above by sum i 1 n 4 left stackrel n i right these new signal sets have the same size and correlation properties as the small set of kasami codes but they have important advantages for use in spread spectrum multiple access communications systems first the sequences are balances which represents only a slight advantage second the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly hopped from sequence to sequence for code division multiple access operation most importantly the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it this high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing

constructions of quadratic bent functions in polynomial forms in this correspondence the constructions and enumerations of all bent functions represented by a polynomial form of f x spl sigma sub i 1 sup n 2 1 c sub i tr x sup 1 2 i c sub n 2 tr sub 1 sup n sup 2 x sup 1 2 n 2 c sub i spl isin sub 2 f sub 2 are presented for special cases of n using an iterative approach the construction of bent functions of n variables with degree n 2 is also provided using the constructed quadratic bent functions

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

adaptive beamforming using the constrained kalman filter from the viewpoint of achieving rapid convergence application of a kalman filter to an adaptive array is considered compared with the frost s 1972 constrained least mean square algorithm the constrained kalman algorithm for adaptive beamforming is proposed to overcome the problem of signal distortion along the look direction which occurs in the unconstrained kalman beamformer of baird 1974 a constraint on the array response along the look direction is added to the measurement equation of the kalman filter the weight vector of the constrained kalman beamformer is derived and shown to converge to that of the minimum variance distortionless response beamformer the convergence rate of the proposed algorithm is also analyzed compared to baird s algorithm and the sidelobe canceller with one step kalman predictor simulation results show the effectiveness of the proposed algorithm

prime phase sequences with periodic correlation properties better than binary sequences for the case where p is an odd prime n or 2 is an integer and omega is a complex primitive pth root of unity a construction is presented for a family of p sup n p phase sequences symbols of the form omega sup i where each sequence has length p sup n 1 and where the maximum nontrivial correlation value c sub max does not exceed 1 square root p sup n a complete distribution of correlation values is provided as a special case of this construction a previous construction due to sidelnikov 1971 is obtained the family of sequences is asymptotically optimum with respect to its correlation properties and in comparison with many previous nonbinary designs the present design has the additional advantage of not requiring an alphabet of size larger than three the new sequences are suitable for achieving code division multiple access and are easily implemented using shift registers they wee discovered through an application of deligne s bound 1974 on exponential sums of the weil type in several variables the sequences are also shown to have strong identification with certain bent functions

d form sequences families of sequences with low correlation values and large linear spans large families of binary sequences with low correlation values and large linear span are critical for spread spectrum communication systems the author describes a method for constructing such families from families of homogeneous functions over finite fields satisfying certain properties he then uses this general method to construct specific families of sequences with optimal correlations and exponentially better linear span than no sequences no 1988

inference for smooth curves in longitudinal data with application to an aids clinical trial we discuss a longitudinal study where data for many subjects are collected at irregular intervals the study is a randomized trial of hiv infected subjects and the response variable of interest is serum neopterin the mean of the outcome variable taken over patients in each treatment group is assumed to follow a smooth curve piecewise cubic polynomials with a moderate number of knots are used to model the curves a general parametric form is assumed for the covariance structure maximum penalized likelihood estimation is used to smooth the over parameterized curves statistical inference for the mean curves including confidence bands and hypothesis tests is discussed two approaches one using a bayesian interpretation of the penalized likelihood and the other based on the asymptotic distribution of the maximum penalized likelihood estimates are discussed and contrasted the properties of the confidence bands obtained from these two approaches are evaluated by examining their coverage rates in a simulation study

kernel regression estimation using repeated measurements data abstract the estimation of growth curves has been studied extensively in parametric situations here we consider the nonparametric estimation of an average growth curve suppose that there are observations from several experimental units each following the regression model y xi f xj e j 1 n where e1 e n are correlated zero mean errors and 0 x1 xn 1 are fixed constants we study some of the properties of a kernel estimator of f x asymptotic and finite sample results concerning the mean squared error of the estimator are obtained in particular the influence of correlation on the bandwidth minimizing mean squared error is discussed a data based method for selecting the bandwidth is illustrated in a data analysis most previous research on kernel regression estimators has involved uncorrelated errors we investigate how dependence of the errors changes the behavior of a kernel estimator our theorems concerning the asymptotic mean squared error show that the estimator cannot be consistent un

a robust null space method for linear equality constrained state estimation we present a robust null space method for linear equality constrained state space estimation exploiting a degeneracy in the estimator statistics an orthogonal factorization is used to decompose the problem into stochastic and deterministic components which are then solved separately the resulting dimension reduction algorithm has enhanced numerical stability solves the constrained problem completely and can reduce computational load by reducing the problem size the new method addresses deficiencies in commonly used pseudo observation or projection methods which either do not solve the constrained problem completely or have unstable numerical implementations due in part to the degeneracy in the estimator statistics we present a numerical example demonstrating the effectiveness of the new method compared to other current methods

on kalman filtering with nonlinear equality constraints the state space description of some physical systems possess nonlinear equality constraints between some state variables in this paper we consider the problem of applying a kalman filter type estimator in the presence of such constraints we categorize previous approaches into pseudo observation and projection methods and identify two types of constraints those that act on the entire distribution and those that act on the mean of the distribution we argue that the pseudo observation approach enforces neither type of constraint and that the projection method enforces the first type of constraint only we propose a new method that utilizes the projection method twice once to constrain the entire distribution and once to constrain the statistics of the distribution we illustrate these algorithms in a tracking system that uses unit quaternions to encode orientation

signal set design for band limited memoryless multiple access channels with soft decision demodulation signal sets are identified that maximize the cutoff rate region for a multiple access channel with an additive white gaussian noise in which the demodulator output alphabet is allowed to be infinite infinitely soft decisions the optimizing designs consist of a simplex signal set for each sender such that each sender s set is orthogonal to those of the other senders for second moment and for fractional out of band energy bandwidth constraints on the signals of each sender conditions are derived under which mutually orthogonal simplex sets are still optimal for the second moment constraint simplex sets derived from sinusoidal functions yield an optimal design and for the out of band energy constraint simplex sets derived from prolate spheroidal wave functions are optimal choices of signal sets that maximize the cutoff rate region for an additive shot noise limited multiple access optical channel subject to average energy and peak amplitude constraints are also identified

robust adaptive beamforming for general rank signal models the performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment sources or sensor array this is especially true when the desired signal components are present in the beamformer training data snapshots because in this case the adaptive array performance is very sensitive to array and model imperfections the similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly but the training sample size is small we propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary type mismatches of the desired signal array response our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank one point source and higher rank scattered source fluctuating wavefront desired signal models the proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst case performance optimization simple closed form solutions to the considered robust adaptive beamforming problems are derived our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms while at the same time offer a significantly improved robustness and faster convergence rates

eigenvalue beamforming using a multirank mvdr beamformer and subspace selection we derive eigenvalue beamformers to resolve an unknown signal of interest whose spatial signature lies in a known subspace but whose orientation in that subspace is otherwise unknown the unknown orientation may be fixed in which case the signal covariance is rank 1 or it may be random in which case the signal covariance is multirank we present a systematic treatment of such signal models and explain their relevance for modeling signal uncertainties we then present a multirank generalization of the mvdr beamformer the idea is to minimize the power at the output of a matrix beamformer while enforcing a data dependent distortionless constraint in the signal subspace which we design based on the type of signal we wish to resolve we show that the eigenvalues of an error covariance matrix are fundamental for resolving signals of interest signals with rank 1 covariances are resolved by the largest eigenvalues of the error covariance while signals with multirank covariances are resolved by the smallest eigenvalues thus the beamformers we design are eigenvalue beamformers which extract signal information from eigen modes of an error covariance we address the tradeoff between angular resolution of eigenvalue beamformers and the fraction of the signal power they capture

a generalization of the family of p ary decimated sequences with low correlation let p be a prime and n a positive integer let e pn 1 and n pn 1 e in this paper we construct a family s of e2n p ary sequences each member of s has period n and the magnitudes of correlations of members of s are upper bounded by 2 pn 2 en 1

multichannel post filtering in nonstationary noise environments in this paper we present a multichannel post filtering approach for minimizing the log spectral amplitude distortion in nonstationary noise environments the beamformer is realistically assumed to have a steering error a blocking matrix that is unable to block all of the desired signal components and a noise canceller that is adapted to the pseudo stationary noise but not modified during transient interferences a mild assumption is made that a desired signal component is stronger at the beamformer output than at any reference noise signal and a noise component is strongest at one of the reference signals the ratio between the transient power at the beamformer output and the transient power at the reference noise signals is used to indicate whether such a transient is desired or interfering based on a gaussian statistical model and combined with an appropriate spectral enhancement technique we derive estimators for the signal presence probability the noise power spectral density and the clean signal the proposed method is tested in various nonstationary noise environments compared with single channel post filtering a significantly reduced level of nonstationary noise is achieved without further distorting the desired signal components

a recursive least squares implementation for lcmp beamforming under quadratic constraint quadratic constraints on the weight vector of an adaptive linearly constrained minimum power lcmp beamformer can improve robustness to pointing errors and to random perturbations in sensor parameters we propose a technique for implementing a quadratic inequality constraint with recursive least squares rls updating a variable diagonal loading term is added at each step where the amount of loading has a closed form solution simulations under different scenarios demonstrate that this algorithm has better interference suppression than both the rls beamformer with no quadratic constraint and the rls beamformer using the scaled projection technique as well as faster convergence than lms beamformers

cross correlation of p ary gmw sequences the cross correlation function of p ary p prime gmw sequences is investigated the well known m sequences are incorporated in these sequences gmw sequences also have the two level autocorrelation function but their linear span may be much larger than those of m sequences the calculation of the cross correlation function of gmw sequences is reduced to the cross correlation of the m sequences because many results on this kind of sequence are known in the literature only the cross correlation function of an m sequence with a gmw sequence has been known up to now

a new family of quadriphase sequences for cdma the construction of a family of quadriphase sequences that are suitable for code division multiple access spread spectrum cma ss communication is described for a given parameter n where n 2 mod 4 the period of the sequence is 2 sup n 1 chips the set of sequences asymptotically achieves welch s lower bound on simultaneous cross correlation and autocorrelation magnitudes all of them being bounded by a value 2 sup n 2 1 the cardinality of this family of sequencies is 2 sup n 2

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

a wide family of nonlinear filter functions with a large linear span a broad collection of pseudorandom sequence generators is introduced these generators are based on nonlinear functions applied to maximal length lfsrs and are not constrained in the length l of the lfsrs or the nonlinear order k of the functions the linear span of the resulting sequences is proved to be as large as the linear span of the sequences obtained from a product of equidistant phases that is to say at least lk a count of the number of functions is evaluated and compared with the corresponding count of products of equidistant phases

efficient subspace based estimator for localization of multiple incoherently distributed sources in this paper a new subspace based algorithm for parametric estimation of angular parameters of multiple incoherently distributed sources is proposed this approach consists of using the subspace principle without any eigendecomposition of the covariance matrix so that it does not require the knowledge of the effective dimension of the pseudosignal subspace and therefore the main difficulty of the existing subspace estimators can be avoided the proposed idea relies on the use of the property of the inverse of the covariance matrix to exploit approximately the orthogonality property between column vectors of the noise free covariance matrix and the sample pseudonoise subspace the resulting estimator can be considered as a generalization of the pisarenko s extended version of capon s estimator from the case of point sources to the case of incoherently distributed sources theoretical expressions are derived for the variance and the bias of the proposed estimator due to finite sample effect compared with other known methods with comparable complexity the proposed algorithm exhibits a better estimation performance especially for close source separation for large angular spread and for low signal to noise ratio

generic construction of bent functions and bent idempotents with any possible algebraic degrees as a class of optimal combinatorial objects bent functions have important applications in cryptography sequence design and coding theory bent idempotents are a subclass of bent functions and of great interest since they can be stored in less space and allow faster computation of the walsh hadamard transform the objective of this paper is to present a generic construction of bent functions from known ones it includes the previous constructions of bent functions by mesnager and xu et al as special cases and produces new bent functions which cannot be produced by earlier ones in particular it also generates infinite families of bent idempotents over f 2 2m of any algebraic degree between 2 and m this together with a recent construction by su and tang gives a positive answer to an open problem on bent idempotents proposed by carlet in addition an infinite family of anti self dual bent functions is obtained in which the sum of any three distinct functions is again an anti self dual bent function in this family this solves an open problem recently proposed by mesnager

constructions of bent negabent functions and their relation to the completed maiorana mcfarland class the problem of constructing bent negabent functions that do not belong to the completed maiorana mcfarland class emerges implicitly through a series of construction methods proposed recently these approaches manage to optimize the algebraic degree of bent negabent functions but all of the constructed bent negabent functions belong to the completed maiorana mcfarland class in this paper we use the indirect sum construction proposed by carlet in 2004 for constructing the bent negabent functions that are not provably contained in this class which is the first significant attempt in this direction to achieve this we first provide a class of bent functions with certain desirable properties that does not belong to this class and demonstrate the existence of the class members then embedding these functions in the framework of the indirect sum construction we are able to specify sufficient conditions for bent negabent functions not being contained in the completed maiorana mcfarland class

optimum tests for fixed effects and variance components in balanced models abstract for any analysis of variance model with balanced data involving both fixed and random effects uniformly most powerful unbiased umpu and uniformly most powerful invariant unbiased umpiu tests are derived for the significance of a fixed effect or a variance component under the assumption of normality of random effects the tests coincide with the usual f tests robustness of the umpiu test against suitable deviations from normality is established

parametric localization of distributed sources most array processing algorithms are based on the assumption that the signals are generated by point sources this is a mathematical constraint that is not satisfied in many applications in this paper we consider situations where the sources are distributed in space with a parametric angular cross correlation kernel we propose an algorithm that estimates the parameters of this model using a generalization of the music algorithm the method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors we study two particular cases coherent and incoherent spatial source distributions the spatial correlation function for a uniformly distributed signal is derived from this we find the array gain and show that in contrast to point sources it does not increase linearly with the number of sources we compare our method to the conventional point source music algorithm the simulation studies show that the new method outperforms the music algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources it is also shown that the threshold signal to noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method

decimations of the frank heimiller sequences the frank heimiller sequence of period n2with n phases is constructed by writing the n by n discrete fourier transform matrix by rows the periodic autocorrelation sidelobes for such a sequence are all zero small families of n phase sequences with optimal periodic cross correlations can be formed by judicious selection of decimations of the frank heimiller sequence

on the existence of square dot matrix patterns having a specific three valued periodic correlation function the author examines square matrices of size n containing dot patterns satisfying the following two restrictions 1 each column contain precisely one dot and 2 if the pattern is moved around over a plane tied by the same pattern when in all positions except the home position there is at most one overlap in dots from differing viewpoints there matrices are the characteristic functions of either a certain class of relative difference sets or else a select subset of bent functions also the existence of such an n n matrix implies the existence of a finite projective plane of order n a family of constructions for such matrices is available when n is prime a polynomial equation characterizing such matrices and resembling the hall polynomial equation of cyclic difference sets is presented analogs of known existence tests for cyclic difference sets are then applied to rule out existence for most nonprime values of n it is shown how such patterns can be used to provide hopping patterns for a frequency hopped multiple access system