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

asymptotic multiuser efficiencies for decision directed multiuser detectors the asymptotic multiuser efficiencies ames are derived for various classes of decision directed multiuser detectors including multistage detectors and decision feedback detectors novel classes of soft decision multistage detectors are proposed and analyzed each class is specified in part by a soft decision nonlinearity such as a symmetric quantizer or a linear clipper closed form expressions for two user ames are derived for soft decision two stage detectors and can be used as a design criterion to optimize the soft decision nonlinearities for a special case of two synchronous users the soft decision two stage detector using an optimized linear clipper with either conventional or decorrelated tentative decisions is shown to achieve optimum ame upper and lower bounds on the ame are obtained for decision feedback detectors using either conventional or decorrelated tentative decisions it is demonstrated that decision directed multiuser detectors with conventional tentative decisions have low near far resistance compared to those with decorrelated tentative decisions

min max game theory and nonstandard differential riccati equations for abstract hyperbolic like equations abstract we consider the abstract dynamical framework of lasiecka and triggiani 2000 1 chapter 9 which models a large variety of mixed pde problems see specific classes in the introduction with boundary or point control all defined on a smooth bounded domain r n n arbitrary this means that the input solution map is bounded on natural function spaces we then study min max game theory problem over a finite time horizon the solution is expressed in terms of a positive self adjoint time dependent riccati operator solution of a non standard differential riccati equation which expresses the optimal qualities in pointwise feedback form in concrete pde problems both control and deterministic disturbance may be applied on the boundary or as a dirac measure at a point the observation operator has some smoothing properties

regularity theory of hyperbolic equations with non homogeneous neumann boundary conditions ii general boundary data abstract this paper studies the regularity of solutions of general mixed second order time dependent hyperbolic problems of neumann type in a previous paper i lasiecka and r triggiani ann mat pura appl iv clvii 1990 285 367 using pseudo differential calculus we have provided sharp regularity results of the solutions and their traces when the non homogeneous data are in l 2 now we complement this study by providing a regularity when the non homogeneous data are more regular than as well as less regular than l 2 in contrast with our previous paper a functional analytic approach based on the l 2 results of our previous paper is used throughout

solving a class of optimum multiuser detection problems with polynomial complexity we identify a class of optimum multiuser detection problems which can be solved with polynomial complexity in the number of users the identification is based on transforming a quadratic 0 1 programming problem into an equivalent problem in graph theory for a synchronous direct sequence code division multiple access cdma system the result translates to designing a set of pseudorandom codes with the property that the cross correlation between every pair of codes in the set over one symbol period is nonpositive we give two sets of codes with good correlation properties that fall within this class finally we derive a bound on the cardinality of a signal set in an n dimensional space having the property that the cross correlation between every pair of signals in the set is nonpositive

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

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

cdma multiuser detection a nonlinear programming approach the optimum receiver to detect the bits of multiple code division multiple access cdma users has an exponential complexity in the number of active users in the system consequently many suboptimum receivers have been developed to achieve good performance with less complexity we take the approach of approximating the solution of the optimum multiuser detection problem omud using nonlinear programming relaxations first we observe that some popular suboptimum receivers indeed correspond to relaxations of the optimal detection problem in particular one proposed approximation method yields to iterative solutions which correspond to previously proposed heuristic nonlinear detectors using a nonlinear programming approach we identify the convergence properties of these iterative detectors secondly we propose a relaxation that yields a receiver which we call the generalized minimum mean squared error detector we give a simple iterative implementation of the detector its performance is evaluated and comparisons to other suboptimum detection schemes are given

chandrasekhar equations for infinite dimensional systems ii unbounded input and output case abstract a set of equations known as chandrasekhar equations arising in the linear quadratic optimal control problem is considered in this paper we consider the linear time invariant systems defined in hilbert spaces involving unbounded input and output operators for a general class of such systems we derive the chandrasekhar equations and establish the existence uniqueness and regularity results of their solutions

exact controllability of the euler bernoulli equation with boundary controls for displacement and moment abstract we consider the euler bernoulli problem 1 1 in the solution w t with boundary controls g1 and g2 acting in the dirichlet traces for w and w respectively we show two main exact controllability results both in the spaces of maximal regularity of the solution at t t see i lasiecka and r triggiani regularity theory for a class of euler bernoulli equations a cosine operator approach boll unione mat ital 7 3 b 1989 and both without geometrical conditions on the open bounded domain except for smoothness of its boundary one with g1 l2 0 t l2 and g2 h1 0 t l2 for any t 0 arbitrarily short and one with g1 h01 0 t l2 and g2 l2 0 t l2 for all t 0 sufficiently large an interpolation result between these two cases is also presented a direct approach is given based on two main steps first by means of an operator model i lasiecka and r triggiani regularity theory for a class of euler bernoulli equations a cosine operator approach boll unione mat ital 7 3 b 1989 for problem 1 1 and a functional analytic approach the question of exact controllability is shown to be equivalent to an a priori inequality for the corresponding homogeneous problem next this a priori inequality is proved to hold true by means of multiplier techniques these are inspired by recent progress on the maximal regularity exact controllability and uniform stabilization questions for second order hyperbolic equations

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

riccati equations for hyperbolic partial differential equations with l 2 0 t l 2 γ dirichlet boundary terms this paper studies the quadratic optimal control problem for second order linear hyperbolic partial differential equations defined on a bounded domain omega subset r n with boundary gamma both the finite interval case 0 t t infty and the infinite interval case t infty regulator problem are considered the distinguishing feature of the paper which differentiates it from previous scarce literature on the subject is that the controls are only l 2 0 t l 2 gamma functions which act in the dirichlet b c and that the corresponding solutions are penalized in the l 2 0 t l 2 omega norm smoother controls particularly in space were taken in the few previous works on this subject the well posedness of this formulation stems from recent results by the authors about regularity of second order hyperbolic mixed problems l t 1 l t 3 under minimal assumptions the optimal control is synthesized in a pointwise feedback form through an operator which is s

noncyclic division algebras over fields of brauer dimension one abstract let k be a complete discretely valued field of rank one with residue field q p it is well known that period equals index in br k we prove that when p 2 there exist noncyclic k division algebras of every 2 power degree divisible by four otherwise every k division algebra is cyclic this gives the first published example of a field whose brauer dimension and cyclic length are not equal

approximation of discrete time lqg compensators for distributed systems with boundary input and unbounded measurement abstract we consider the approximation of optimal discrete time linear quadratic gaussian lqg compensators for distributed parameter control systems with boundary input and unbounded measurement our approach applies to problems that can be formulated in a state space on which both the discrete time input and output operators are continuous approximating compensators are obtained via application of the lqg theory and associated approximation results for infinite dimensional discrete time control systems with bounded input and output numerical results for spline and modal approximation schemes used to compute optimal compensators for a one dimensional heat equation with either neumann or dirichlet boundary control and pointwise measurement of temperature are presented and discussed

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

uniform exponential energy decay of wave equations in a bounded region with l2 0 l2 γ feedback control in the dirichlet boundary conditions etant donne un ouvert borne r n n 2 on considere l equation d onde w tt w dans o avec des conditions initiales w o x w o x l 2 w 1 o x w 1 x h 1 et des conditions aux limites non homogenes de type dirichlet w t u t sur o etant la frontiere de

symbol error rate performance of box relaxation decoders in massive mimo the maximum likelihood ml decoder for symbol detection in large multiple input multiple output wireless communication systems is typically computationally prohibitive in this paper we study a popular and practical alternative namely the box relaxation optimization bro decoder which is a natural convex relaxation of the ml for independent identically distributed real gaussian channels with additive gaussian noise we obtain exact asymptotic expressions for the symbol error rate ser of the bro the formulas are particularly simple they yield useful insights and they allow accurate comparisons to the matched filter bound mfb and to linear decoders such as zero forcing and linear minimum mean square error for binary phase shift keying signals the ser performance of the bro is within 3 db of the mfb for square systems and it approaches the mfb as the number of receive antennas grows large compared to the number of transmit antennas our analysis further characterizes the empirical density function of the solution of the bro and shows that error events for any fixed number of symbols are asymptotically independent the fundamental tool behind the analysis is the convex gaussian min max theorem

global existence for an abstract riccati initial value problem with possibly unbounded coefficients abstract we consider operator valued riccati initial value problems of the form r t tr t r t t ta t tb t r t r t tc t r t td t r t r 0 r 0 here a t through d t and r 0 have values as nonnegative bounded linear operators in l 1 where is a finite measure and t is a closed nonnegative operator in l 1 satisfying additional technical conditions for such problems the notion of strongly mild solutions is defined the main result is a set of conditions under which with sufficiently small initial value has a global solution

semidefinite relaxation based multiuser detection for m ary psk multiuser systems because of the powerful symbol error performance of multiuser maximum likelihood ml detection recently there has been much interest in seeking effective ways of approximating multiuser ml detection mld with affordable computational costs it has been illustrated that for the synchronous code division multiple access cdma scenario the so called semidefinite relaxation sdr algorithm can accurately and efficiently approximate multiuser mld this sdr mld algorithm however can only handle binary and quadratic phase shift keying psk symbol constellations in this sequel we propose an extended sdr algorithm for mld with m ary psk mpsk constellations for the synchronous cdma scenario the proposed sdr algorithm provides an attractive polynomial time complexity order of k sup 3 5 where k is the number of users simulation results indicate that the proposed detector provides improved symbol error performance compared with several commonly used multiuser detectors