continuous time equivalents of welch bound equality sequences the theory developed on the sequence optimization for equal power code division multiple access cdma systems is generalized in this paper unlike previous works where discrete time or vector channel models are predominantly employed the overloaded channels are modeled as strictly band limited continuous time multiple access channels corrupted by additive white gaussian noise awgn after being posed as a multiple input single output miso joint transmitter and receiver optimization problem with the total mean squared error mse as the objective functional to be minimized the variational problem is solved by using a frequency domain approach it is shown that there exist continuous time equivalents of welch bound equality cte wbe sequences as the jointly optimum transmit waveforms and that the matched filters are the jointly optimum receivers the user capacity of the band limited channels is characterized by a necessary and sufficient condition for the admissibility of users into the system in terms of the channel load the received signal to noise ratio and the signal to interference plus noise ratio sinr requirement it is also shown that cte wbe sequences achieve the lower bound on the continuous time equivalent of total squared correlation cte tsc

minimum probability of error for asynchronous gaussian multiple access channels consider a gaussian multiple access channel shared by k users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms the uncoded probability of error achievable by optimum multiuser detectors is investigated it is shown that the k user maximum likelihood sequence detector consists of a bank of single user matched filters followed by a viterbi algorithm whose complexity per binary decision is o 2 k the upper bound analysis of this detector follows an approach based on the decomposition of error sequences the issues of convergence and tightness of the bounds are examined and it is shown that the minimum multiuser error probability is equivalent in the iow noise region to that of a single user system with reduced power these results show that the proposed multiuser detectors afford important performance gains over conventional single user systems in which the signal constellation carries the entire burden of complexity required to achieve a given performance level

intrinsic ultracontractivity and eigenfunction estimates for schrodinger operators let d be a domain in rn n 2 and let h h0 v where h0 is a divergence form uniformly elliptic operator with dirichlet boundary conditions and v is in the kato class intrinsic ultracontractivity is proved for the semigroup of h when d is holder domain of order 0 or a uniformly holder domain of order for 0 2 for every 2 there exists a uniformly holder domain of order for which the dirichlet laplacian is not intrinsically ultracontractive for a large class of domains it is shown that the heat kernels for h0 and h decay at the same rate at the boundary applications are given to the lifetime of conditioned brownian motion some of our results seem to be new even for smooth domains

an optimal orthogonal overlay for a cyclostationary legacy signal in this paper the design of an overlay system is considered that operates on a channel already occupied by a legacy system it is assumed that the legacy transmitter generates a cyclostationary signal and that the legacy receiver is equipped with a linear filter followed by a uniform sampler under a zero interference constraint at the legacy receiver the meansquared error at the overlay receiver is minimized to find the optimal overlay system that employs linear modulation and demodulation for the trade off between performance and rate of the overlay system the problem is formulated to allow a transmission rate that is a fraction of the fundamental cycle frequency of the legacy signal the notion of a virtual legacy receiver is devised to incorporate cases with non identical frequency bands for the transmission and reception of the overlay signal using the vectorized fourier transform technique the problem is reformulated the solution is derived and a necessary and sufficient condition for the existence of the optimal solution is found all in the frequency domain numerical results show that the proposed scheme significantly improves the spectral efficiency by effectively exploiting the cyclostationarity of the legacy signal

solvability of the divergence equation implies john via poincare inequality abstract let r 2 be a bounded simply connected domain we show that for a fixed every p 1 the divergence equation div v f is solvable in w 0 1 p 2 for every f l 0 p if and only if is a john domain if and only if the weighted poincare inequality u x u q d x c u x q dist x q d x holds for some every q 1 this gives a positive answer to a question raised by russ 2013 in the case of bounded simply connected domains in higher dimensions similar results are proved under some additional assumptions on the domain in question

a linear receiver for direct sequence spread spectrum multiple access systems with antenna arrays and blind adaptation a linear receiver for direct sequence spread spectrum multiple access communication systems under the aperiodic random sequence model is considered the receiver consists of the conventional matched filter followed by a tapped delay line with the provision of incorporating the use of antenna arrays it has the ability of suppressing multiple access interference mai and narrowband interference in some weighted proportions as well as combining multipath components without explicit estimation of any channel conditions under some specific simplified channel models the receiver reduces to the minimum variance distortionless response beamformer the rake receiver a notch filter or an mai suppressor the interference rejection capability is made possible through a suitable choice of weights in the tapped delay line the optimal weights can be obtained by straightforward but computationally complex eigenanalysis in order to reduce the computational complexity a simple blind adaptive algorithm is also developed

generalized hardy inequality for the magnetic dirichlet forms we obtain lower bounds for the magnetic dirichlet form in dimensions d 2 for d 2 the results generalize a well known lower bound by the magnetic field strength we replace the actual magnetic field bby an non vanishing effective field which decays outside the support of bas dist x suppb 2 in the case d 3 we establish that the magnetic form is bounded from below by the magnetic field strength if one assumes that the field does not vanish and its direction is slowly varying

performance of binary and quaternary direct sequence spread spectrum multiple access systems with random signature sequences the performance of synchronous and asynchronous binary and quaternary with and without offset direct sequence spread spectrum multiple access ds ssma communication systems using random signature sequences and arbitrary chip waveforms is investigated the average probability of error at the output of the correlation receiver is evaluated using a characteristic function approach for these systems numerical results are presented that illustrate performance comparisons between systems using random and deterministic signature sequences synchronous and asynchronous systems systems with rectangular or sinewave chip waveforms and binary and quaternary systems with the same data rates and bandwidth in all cases the accuracy of the gaussian approximation is also examined

analyzing iterations in identification with application to nonparametric h norm estimation many iterative approaches in the field of system identification for control have been developed although successful implementations have been reported a solid analysis with respect to the convergence of these iterations has not been established the aim of this paper is to present a thorough analysis of a specific iterative algorithm that involves nonparametric h norm estimation the pursued methodology involves a novel frequency domain approach that addresses both additive stochastic disturbances and input normalization the results of the convergence analysis are twofold 1 the presence of additive disturbances introduces a bias in the estimation procedure and 2 the iterative procedure can be interpreted as experiment design for h norm estimation revealing the value of iterations and limits of accuracy in terms of the fisher information matrix the results are confirmed by means of a simulation example

gauss green theorem for weakly differentiable vector fields sets of finite perimeter and balance laws we analyze a class of weakly differentiable vector fields f w r n r n with the property that f 2 l 1 and div f is a signed radon measure these fields are called bounded divergence measure fields the primary focus of our inves tigation is to introduce a suitable notion of the normal trace of any divergence measure field f over the boundary of an arbitrary set of finite perimeter that en sures the validity of the gauss green theorem to achieve this we first establish a fundamental approximation theorem which states that given a signed radon measurethat is absolutely continuous with respect to h n 1 on r n a ny set of finite perimeter can be approximated by a family of sets with smooth boundary essentially from the measure theoretic interior of the set with respect to the mea sure kk the total variation measure we employ this approximation theorem to derive the normal trace of f on the boundary of any set of finite perimeter e as the limit of the normal traces of f on the boundaries of the approximate sets with smooth boundary so that the gauss green theorem for f holds one with these results we analyze the cauchy flux that is bounded by a nonnegative radon measure over any oriented surface i e an n 1 dimensional surface that is a part of the boundary of a set of finite perimeter and thereby develop a general mathematical formulation of the physical principle of the balance law through the cauchy flux finally we apply this framework to the derivation of systems of balance laws with measure valued source terms from the formulation of the balance law this framework also allows the recovery of cauchy entropy flux through the lax entropy inequality for entropy solutions of hyperbolic con servation laws c 2008 wiley periodicals inc

nonparametric methods for the estimation of l2 gain and gains at sample frequencies using bandpass filters this paper describes a method of estimating the gains at sample frequencies and the l2 gain for a linear time invariant discrete time system using a truncated step response the gain is estimated using a bandpass filter at each sample frequency and the filter parameter is optimized by maximizing the estimate of the l2 gain near the peak gain this filtering method is extended to multivariable systems another method of making an optimal bandpass filter is derived from the iterative experiment method the filtering method is compared with other estimation methods in terms of noise sensitivity through a series of numerical experiments

a theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity the energy functional of nonlinear plate theory is a curvature functional for surfaces rst proposed on physical grounds by g kirchhoff in 1850 we show that it arises as a 0 limit of three dimensional nonlinear elasticity theory as the thickness of a plate goes to zero a key ingredient in the proof is a sharp rigidity estimate for maps v v u r n u r n we show that the l 2 distance of rv from a single rotation matrix is bounded by a multiple of the l 2 distance from

uniformly fat sets in this paper we study closed sets e which are locally uniformly fat with respect to a certain nonlinear riesz capacity we show that e is actually locally uniformly fat with respect to a weaker riesz capacity two applications of this result are given the first application is concerned with proving sobolev type inequalities in domains whose complements are uniformly fat the second application is concerned with the fekete points of e introduction let x x x2 x be a point in euclidean n space rn with jxl the norm of x for a 0 let i x ixi a n denote the riesz kernel of order a and put i f x f ix y f n f y dy x e r rn ic u x fr yj c n d u y x e r rn when f is a lebesgue integrable function and u a borel measure on rn here dy denotes lebesgue measure on rn if e c rn 0 1 define the a p outer riesz capacity of e by ra p e inf jfllfp ia f 1 on el where if lip is the lebesgue p norm of f we note that a 1 p 2 is the classical newtonian capacity if ap n we let rc p e inf jfjjf j f 1 on el where jc is the truncated riesz kernel defined by je x ixi a n 100 a n x 100 0 lxl 100 we shall say that a property holds a p quasi everywhere abbreviated a p q e on a set e if it holds on e except perhaps for a set of rop capacity zero next we list some properties of riesz capacities to simplify the writing we state these properties only for 0 u l p l 1 a p q e on e and p 1 a p q e on supp u c e moreover e jjli pi ujj rop e received by the editors march 11 1987 1980 mathematic3 subject cla33ification 1985 revi3ion primary 31c15 31b15 1988 american mathematical society 0002 9947 88 1 00 25 per page

bit to bit error dependence in slotted ds ssma packet systems with random signature sequences a technique is developed to find an accurate approximation to the probability of data bit error and the probability of packet success in a direct sequence spread spectrum multiple access ds ssma packet radio system with random signature sequences an improved gaussian approximation to the probability of data bit error is performed packet performance is analyzed by using the theory of moment spaces to gain insight into the effect of bit to bit error dependence caused by interfering signal relative delays and phases which are assumed constant over the duration of a desired packet numerical results show that if no error control exists in the desired packet or if block error control is used when multiple access interference is high the error dependence increases the average probability of packet success beyond that predicted by models which use independent bit errors however when block error control is used and the multiple access interference is low the bit error dependencies cause a reduction in packet error performance

brief paper non parametric methods for l2 gain estimation using iterative experiments in this paper we develop non parametric methods to estimate the l 2 gain h norm of a linear dynamical system from iterative experiments this work is mainly motivated by model error modeling where the error dynamics are more complex than can be captured by a low order parametric model the standard system identification approach to the gain estimation problem is to estimate a parametric model of the system which is then used to calculate the gain if it is possible to update the input signal during the experiment an alternative way is to iteratively optimize the input signal in order to maximize the estimated input to output gain a key observation is that the gradient of the gain with respect to the input signal can without knowing a model be found from two experiments iterative numerical methods for calculation of eigenvalues of matrices e g the power method or the lanczos method can then be applied to update the input signal sequence between experiments in order to find the maximum gain the main difficulty compared to the corresponding eigenvalue problem in numerical analysis is the effects of additive measurement noise which require modified schemes that avoid bias errors three such related methods are derived and evaluated by a numerical example partial results on convergence and statistical properties of the gain estimator are given a constrained stochastic gradient method with local optimization of step length gives the best numerical results in the case of noisy data

windowing for multicarrier cdma systems the windows for achieving good multiple access performance of multicarrier code division multiple access mccdma systems employing minimum mean squared error receivers are studied the mean squared error mse is used as the performance metric for the optimization in a simplified two user system the rectangular window is found to be optimum while regarded as an inferior window in orthogonal frequency division multiplexing systems because of its spectral inefficiency necessary conditions are given for improving the performances of spectrally efficient windows by exploiting the cyclic prefix and oversampling in the frequency domain

time domain identification for robust control abstract in this paper we are concerned with a problem of robust control oriented system identification in the time domain based on the well known schur takagi aak theorem we propose a linear algorithm to obtain the nominal model of the plant to be identified and the minimal bound of the uncertainty of the nominal model error which is measured by h norm it is also shown that in the model set defined by the nominal model and the uncertainty bound there exists at least one model which matches the prescribed input output data given in the time domain

multiple access interference suppression for mc cdma by frequency domain oversampling a technique for interference suppression in multicarrier code division multiple access mc cdma systems is proposed which exploits the structural differences in signals that arrive at the receiver with doppler shifts or carrier offsets oversampling the received signal in the frequency domain and properly combining the samples provides the interference suppression frequency domain oversampling is accomplished by using a time extension of the conventional mc cdma signal or unconsumed portions of the cyclic prefix furthermore a receiver structure is introduced that despreads and combines groups of samples so that a linear minimum mean squared error solution for combining the groups is easily found this combining scheme increases the signal to interference ratio experienced by the desired user in the mc cdma system in addition the receiver performs well in severe near far scenarios when there is sufficient frequency separation between the signals of the desired user and an interferer numerical results show that the proposed receiver significantly outperforms the conventional mc cdma receiver in many channel realizations

error probability for direct sequence spread spectrum multiple access communications part ii approximations approximations are obtained for the average probability of error in an asynchronous direct sequence spread spectrum multiple access communications system both binary and quaternary systems are considered and the chip waveforms are allowed to be arbitrary time limited waveforms with time duration equal to the inverse of the chip rate the approximation is based on the integration of the characteristic function of the multiple access interference the amount of computation required to evaluate this approximation grows only linearly with the product of the number of simultaneous transmitters and the number of chips per bit the accuracy of the approximation is extremely good in most cases but it can be improved if necessary by an application of a series expansion numerical results are presented for specific chip waveforms and signature sequences

error probabilities for binary direct sequence spread spectrum communications with random signature sequences binary direct sequence spread spectrum multiple access communications an additive white gaussian noise channel and a coherent correlation receiver are considered an expression for the output of the receiver is obtained for the case of random signature sequences and the corresponding characteristic function is determined the expression is used to study the density function of the multiple access interference and to determine arbitrarily tight upper and lower bounds on the average probability of error the bounds which are obtained without making a gaussian approximation are compared to results obtained using a gaussian approximation the effects of transmitter power the length of the signature sequences and the number of interfering transmitters are illustrated each transmitter is assumed to have the same power although the general approach can accommodate the case of transmitters with unequal powers

average bit error rate performance of band limited ds ssma communications direct sequence spread spectrum multiple access ds ssma communications strictly band limited transmitter chip waveforms with excess bandwidth in the interval between zero and one pseudo random spreading sequences an additive white gaussian noise channel and matched filter receivers are considered first a new expression for the average bit error rate ber is derived for systems with quaternary phase shift keying qpsk spreading the conventional matched filter receiver a coherent detector for binary phase shift keying bpsk data symbols and chip waveforms that result in no interchip interference the expression consists of a well known ber expression based on the standard gaussian approximation to multiple access interference and a few correction terms it enables accurate ber evaluations without any numerical integration for various choices of system parameters of interest the accuracy of the expression is guaranteed as long as the conditional gaussian approximation to the cross correlation coefficients between the desired user s spreading sequence and the interfering users spreading sequences is valid the expression well reflects the effect of filtering on the system performance extensions of the expression are discussed for systems with qpsk spreading and different detection schemes systems with bpsk spreading and systems with different transmit and receive filters monte carlo simulation results are also provided to verify the accuracy

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

linear multiuser detectors for synchronous code division multiple access channels under the assumptions of symbol synchronous transmissions and white gaussian noise the authors analyze the detection mechanism at the receiver comparing different detectors by their bit error rates in the low background noise region and by their worst case behavior in a near far environment where the received energies of the users are not necessarily similar optimum multiuser detection achieves important performance gains over conventional single user detection at the expense of computational complexity that grows exponentially with the number of users it is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations and on the optimum linear detector it is shown that the generalized inverse detectors exhibit the same degree of near far resistance as the optimum multiuser detectors the optimum linear detector is obtained

the equivalence between pointwise hardy inequalities and uniform fatness we prove an equivalence result between the validity of a pointwise hardy inequality in a domain and uniform capacity density of the complement this result is new even in euclidean spaces but our methods apply in general metric spaces as well we also present a new transparent proof for the fact that uniform capacity density implies the classical integral version of the hardy inequality in the setting of metric spaces in addition we consider the relations between the above concepts and certain hausdorff content conditions

holder estimates of p harmonic extension operators it is now a well known fact that for 1 p the p harmonic functions on domains in metric measure spaces equipped with a doubling measure supporting a 1 p poincare inequality are locally holder continuous in this note we provide a characterization of domains in such metric spaces for which p harmonic extensions of holder continuous boundary data are globally holder continuous we also provide a link between this regularity property of the domain and the uniform p fatness of the complement of the domain

self improvement of weighted pointwise inequalities on open sets abstract we prove a general self improvement property for a family of weighted pointwise inequalities on open sets including pointwise hardy inequalities with distance weights for this purpose we introduce and study the classes of p poincare and p hardy weights for an open set x where x is a metric measure space we also apply the self improvement of weighted pointwise hardy inequalities in connection with usual integral versions of hardy inequalities

reverse holder inequalities for singular parabolic equations near the boundary abstract we show that weak solutions to a singular parabolic partial differential equation globally belong to a higher sobolev space than assumed a priori to this end we prove that the gradients satisfy a reverse holder inequality near the boundary the results extend to singular parabolic systems as well motivation for studying reverse holder inequalities comes partly from applications to regularity theory

sharp hardy inequalities on the solid torus abstract in this paper we establish the classical hardy inequality in the solid torus and some variants of it the general idea is to use the fact that sobolev embeddings can be improved in the presence of symmetries in all cases using techniques that exploit the symmetry presented by the solid torus we calculate the displayed best constants and we prove that they are the same as the standard hardy best constants which appear in convex domains although the solid torus is not convex

equivalence and self improvement of p fatness and hardy s inequality and association with uniform perfectness we present an easy proof that p hardy s inequality implies uniform p fatness of the boundary when p n the proof works also in metric space setting and demonstrates the self improving phenomenon of the p fatness we also explore the relationship between p fatness p hardy inequality and the uniform perfectness for all p 1 and demonstrate that in the ahlfors q regular metric measure space setting with p q these three properties are equivalent when p 2 our results are new evenin the euclidean setting

a time domain approach to model validation in this paper we offer a novel approach to control oriented model validation problems the problem is to decide whether a postulated nominal model with bounded uncertainty is consistent with measured input output data our approach directly uses time domain input output data to validate uncertainty models the algorithms we develop are computationally tractable and reduce to generally nondifferentiable convex feasibility problems or to linear programming problems in special cases we give analytical solutions to these problems

an asymptotic analysis of ds ssma communication systems with random polyphase signature sequences direct sequence spread spectrum multiple access ds ssma communication systems with random m phase sequences for even m are considered by examining the asymptotic behavior of the normalized multiple access interference mai the authors find that a system with random m phase sequences for m 4 should have the same performance as one with random quadriphase sequences asymptotically however a system with random m phase sequences for m spl ges 4 may perform better than one with random binary sequences when the number of simultaneous users is relatively small a new gaussian approximation is proposed to estimate the probabilities of error in these systems in two cases the new approximation reduces to established results which have been shown to provide close estimates to the probabilities of error

an asymptotic analysis of ds ssma communication systems with general linear modulation and error control coding we investigate direct sequence spread spectrum multiple access ds ssma communication systems with general linear modulation and error control coding by the central limit theorem for martingale difference arrays it is proved that under general conditions the overall multiple access interference mai across different symbol intervals tends to a jointly complex gaussian random vector as both the number of chips per symbol interval and the number of interferers tend to infinity the result allows the calculation of the limiting exact error probabilities and justifies the use of the popular standard gaussian approximation the asymptotic properties of the mai from each individual interferer are also examined the results lead to another approximation the conditional gaussian approximation which provides better estimates to the error probabilities especially in near far situations

regularity and free boundary regularity for the p laplace operator in reifenberg flat and ahlfors regular domains regularity and free boundary regularity for the p laplace operator in reifenberg flat and ahlfors regular domains

performance evaluation for band limited ds cdma systems based on simplified improved gaussian approximation the standard gaussian approximation sga for error analysis of direct sequence code division multiple access ds cdma systems is very optimistic in many cases improved gaussian approximation iga is a technique that produces accurate error probabilities but is still computationally intensive simplified iga siga has complexity similar to that of sga and at the same time provides sufficient accuracy in this paper we consider siga for ds cdma systems employing random sequences in a band limited scenario the validity of iga for band limited systems is established in a rigorous mathematical sense then a key parameter in siga is derived via a frequency domain approach applications to a number of typical chip waveforms including the popular sinc and raised cosine pulses are investigated performance comparison with iga based lower and upper bounds shows that siga yields very accurate probability of error

self improvement of uniform fatness revisited we give a new proof for the self improvement of uniform p fatness in the setting of general metric spaces our proof is based on rather standard methods of geometric analysis and in particular the proof avoids the use of deep results from potential theory and analysis on metric spaces that have been indispensable in the previous proofs of the self improvement a key ingredient in the proof is a self improvement property for local hardy inequalities

in between the inequalities of sobolev and hardy abstract we establish both sufficient and necessary conditions for the validity of the so called hardy sobolev inequalities on open sets of the euclidean space these inequalities form a natural interpolating scale between the weighted sobolev inequalities and the weighted hardy inequalities the assouad dimension of the complement of the open set turns out to play an important role in both sufficient and necessary conditions

ber performance of bandlimited ds cdma systems in nakagami fading accurate average bit error rate analysis of asynchronous bandlimited binary direct sequence code division multiple access ds cdma systems in nakagami m fading is studied the fading is assumed to be flat and slow the spectrum raised cosine src and beaulieu tan damen btd pulse shapes are employed a new method which combines the characteristic function cf method with the improved gaussian approximation ga is proposed for evaluating the ber of bandlimited ds cdma a substantial computational complexity reduction is achieved the well known standard ga holtzman s simplified improved ga and improved holtzman s ga methods are also considered the accuracies of the approximation methods are assessed using monte carlo simulation for a system employing a deterministic sequence for the desired user and random sequences for the active interfering users a cf method is employed to derive precise ber results the new btd pulse outperforms the src pulse in all situations

performance bounds on chip matched filter receivers for bandlimited ds ssma communications performance bounds on chip matched filter cmf receivers for bandlimited direct sequence spread spectrum multiple access bl ds ssma systems with aperiodic random spreading sequences are obtained first the optimum transmit receive chip waveform pairs that maximize the conditional signal to interference ratio are derived this leads to performance bounds on cmf receivers when the conditional gaussian approximation for cyclostationary multiple access interference mai is exploited the bounds are used to examine the dependence of the mai suppression capability of the cmf receivers on the excess bandwidth of the system and the delay profile of multiple access users the system employing the flat spectrum chip waveform pair is shown to have near optimum average bit error rate performance among the fixed cmf fcmf receiver systems numerical results are provided for an adaptive cmf receiver and for fcmf receivers employing several different fixed chip waveforms

an optimal signal design for band limited asynchronous ds cdma communications an optimal signal design for band limited asynchronous direct sequence code division multiple access ds cdma communications with aperiodic random spreading sequences and a conventional matched filter receiver is considered in an additive white gaussian noise awgn channel with bandwidth defined in the strict sense two optimization problems are solved under finite bandwidth and zero interchip interference constraints first a chip waveform optimization is performed given the system bandwidth the data symbol transmission rate and the processing gain a technique to characterize a band limited chip waveform with a finite number of parameters is developed and it is used to derive optimum chip waveforms which minimize the effect of multiple access interference mai for any energy and delay profile of users next a joint optimization of the processing gain and the chip waveform is performed given the system bandwidth and the data symbol transmission rate a sufficient condition for a system to have lower average probability of bit error for any energy profile is found and it is used to derive some design strategies it is shown that the flat spectrum pulse with the processing gain leading to zero excess bandwidth results in the minimum average probability of bit error design examples and numerical results are also provided

weighted hardy inequalities abstract for bounded lipschitz domains d in r n it is known that if 1 p then for all 0 0 where 0 p 1 0 there is a constant c with d u x p dist x d p d x c d u x p dist x d d x for all u c 0 d we show that if d is merely assumed to be a bounded domain in r n that satisfies a whitney cube counting condition with exponent and has plump complement then the same inequality holds with 0 now taken to be p n n p n p 2 n further we extend the known results see h brezis m marcus hardy s inequalities revisited dedicated to ennio de giorgi ann scuola norm sup pisa cl sci 4 25 1997 1998 217 237 m hoffmann ostenhof t hoffmann ostenhof a laptev a geometrical version of hardy s inequality j funct anal 189 2002 537 548 j tidblom a geometrical version of hardy s inequality for w 1 p proc amer math soc 132 2004 2265 2271 concerning the improved hardy inequality d u x p dist x d p d x d p n d u x p d x c d u x p d x c c n p by showing that the class of domains for which the inequality holds is larger than that of all bounded convex domains

multiuser constrained water pouring for continuous time overloaded gaussian multiple access channels in this paper signature waveforms and signal powers are jointly optimized for multiuser communications over strictly bandlimited continuous time overloaded channels corrupted by additive white gaussian noise awgn the total signal power is minimized subject to general asymmetric signal to interference plus noise ratio sinr constraints at the output of linear minimum mean squared error lmmse receivers using vectorized fourier transform vft technique the optimal solutions as well as a necessary and sufficient condition for the existence of a feasible solution are derived in the frequency domain it turns out that every optimal solution performs the same as the optimal frequency division multiple access fdma system a geometric procedure called multiuser constrained water pouring is developed to construct every possible optimal solution of which profiles of signal power and equivalent bandwidth are respectively the same as those of signal power and physical bandwidth of the optimal fdma system it is shown that orthogonal signature waveforms are assigned to oversized users and continuous time equivalents of generalized welch bound equality cte gwbe sequences are assigned to non oversized users

global gradient estimates for non quadratic vector valued parabolic quasi minimizers abstract we establish local and global higher integrability estimates for the gradient of vector valued parabolic quasi minimizers of integral functionals with polynomial p growth p 2 n n 2 on a parabolic domain t in r n 1 n 2 and under a weak regularity assumption on the parabolic boundary of t

the kato square root problem for mixed boundary conditions we consider the negative laplacian subject to mixed boundary conditions on a bounded domain we prove under very general geometric assumptions that slightly above the critical exponent 12 its fractional power domains still coincide with suitable sobolev spaces of optimal regularity in combination with a reduction theorem recently obtained by the authors this solves the kato square root problem for elliptic second order operators and systems in divergence form under the same geometric assumptions thereby we answer a question posed by j l lions in 1962 30

performance of multicarrier ds ssma over fast rayleigh fading channels with doppler diversity the significant loss in performance of multicarrier direct sequence spread spectrum multiple access systems over fast fading channels is investigated first the channel model for individual subchannels is obtained using a canonical decomposition to a wide sense stationary wss uncorrelated scattering channel next a receiver structure which features both doppler diversity and frequency diversity is presented and analyzed it is found that large doppler spreads cause the average magnitude of the desired signals to diminish dramatically expressions for the bit error rate are derived for both uncoded and coded systems by applying the standard gaussian approximation numerical results which show that doppler diversity is preferable over frequency diversity in fast fading channels are provided for different combinations of the diversity orders numerical results which show that the intersymbol and intersubchannel interference can be effectively suppressed and the multiple access interference tends to degenerate into a wss process with the statistical periodicity destroyed by the fast fading channels are also provided