three transmit antenna space time codes based on su 3 fully diverse constellations i e a set of unitary matrices whose pairwise differences are nonsingular are useful in multiantenna communications especially in multiantenna differential modulation since they have good pairwise error properties recently group theoretic ideas especially fixed point free fpf groups have been used to design fully diverse constellations of unitary matrices here we give systematic design methods of space time codes which are appropriate for three transmit antenna differential modulation the structures of the codes are motivated by the special unitary lie group su 3 one of the codes which is called the ab code has a fast maximum likelihood ml decoding algorithm using complex sphere decoding diversity products of the codes can be easily calculated and simulated performance shows that they are better than group based codes especially at high rates and as good as the elaborately designed nongroup code

communication on the grassmann manifold a geometric approach to the noncoherent multiple antenna channel we study the capacity of multiple antenna fading channels we focus on the scenario where the fading coefficients vary quickly thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver we use a noncoherent block fading model proposed by marzetta and hochwald see ibid vol 45 p 139 57 1999 the model does not assume any channel side information at the receiver or at the transmitter but assumes that the coefficients remain constant for a coherence interval of length t symbol periods we compute the asymptotic capacity of this channel at high signal to noise ratio snr in terms of the coherence time t the number of transmit antennas m and the number of receive antennas n while the capacity gain of the coherent multiple antenna channel is min m n bits per second per hertz for every 3 db increase in snr the corresponding gain for the noncoherent channel turns out to be m 1 m t bits per second per hertz where m min m n t 2 the capacity expression has a geometric interpretation as sphere packing in the grassmann manifold

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

markowitz s mean variance portfolio selection with regime switching a continuous time model a continuous time version of the markowitz mean variance portfolio selection model is proposed and analyzed for a market consisting of one bank account and multiple stocks the market parameters including the bank interest rate and the appreciation and volatility rates of the stocks depend on the market mode that switches among a finite number of states the random regime switching is assumed to be independent of the underlying brownian motion this essentially renders the underlying market incomplete a markov chain modulated diffusion formulation is employed to model the problem using techniques of stochastic linear quadratic control mean variance efficient portfolios and efficient frontiers are derived explicitly in closed forms based on solutions of two systems of linear ordinary differential equations related issues such as a minimum variance portfolio and a mutual fund theorem are also addressed all the results are markedly different from those for the case when there is no regime switching an interesting observation is however that if the interest rate is deterministic then the results exhibit rather unexpected similarity to their no regime switching counterparts even if the stock appreciation and volatility rates are markov modulated

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

some 2 spl times 2 unitary space time codes from sphere packing theory with optimal diversity product of code size 6 in this correspondence we propose some new designs of 2 spl times 2 unitary space time codes of sizes 6 32 48 64 with best known diversity products or product distances by partially using sphere packing theory in particular we present an optimal 2 spl times 2 unitary space time code of size 6 in the sense that it reaches the maximal possible diversity product for 2 spl times 2 unitary space time codes of size 6 the construction and the optimality of the code of size 6 provide the precise value of the maximal diversity product of a 2 spl times 2 unitary space time code of size 6

tree search multiple symbol differential decoding for unitary space time modulation differential space time modulation dstm using unitary matrix signal constellations is an attractive solution for transmission over multiple input multiple output mimo fading channels without requiring channel state information csi at the receiver to avoid a high error floor for dstm in relatively fast mimo fading channels multiple symbol differential detection msdd has to be applied at the receiver msdd jointly processes blocks of several received matrix symbols and power efficiency improves as the blocksize increases but since the search space of msdd grows exponentially with the blocksize and also with the number of transmit antennas and the data rate the complexity of msdd quickly becomes prohibitive in this paper we investigate the application of tree search algorithms to overcome the complexity limitation of msdd we devise a nested msdd structure consisting of an outer and a number of inner tree search decoders which renders msdd feasible for wide ranges of system parameters decoder designs tailored for diagonal and orthogonal dstm codes are given and a more power efficient variant of msdd so called subset msdd is proposed furthermore we derive a tight symbol error rate approximation for msdd which lends itself to efficient numerical evaluation numerical and simulation results for different dstm constellations and fading channel scenarios show that the new tree search msdd achieves a significantly better performance complexity tradeoff than benchmark decoders

fast multiple antenna differential decoding we present an algorithm based on lattice reduction for the fast decoding of diagonal differential modulation across multiple antenna while the complexity of the maximum likelihood ml algorithm is exponential both in the number of antenna and the rate the complexity of our approximate lattice algorithm is polynomial in the number of antennas and the rate we show that the error performance of our lattice algorithm is very close to the ml algorithm

dynamic nulling and canceling for efficient near ml decoding of mimo systems it is known that conventional nulling and canceling nc detection for multiple input multiple output mimo systems cannot exploit all of the available diversity and thus its performance is significantly inferior to that of maximum likelihood ml detection conventional nc employs the layerwise postequalization signal to noise ratios snrs as reliability measures for layer sorting these snrs are average quantities that do not depend on the received vector in this paper we propose the novel dynamic nulling and canceling dnc technique that uses approximate a posteriori probabilities as measures of layer reliability the dnc technique is a minimum mean square error mmse nulling scheme combined with an improved dynamic layer sorting rule that exploits the information contained in the current received vector we calculate the error probability of dnc for a simple special case and show that it is upper bounded by the error probability of conventional nc simulation results are presented for spatial multiplexing systems and for systems using linear dispersion codes it is demonstrated that the dnc technique can yield near ml performance for a wide range of system sizes and channel snrs at a fraction of the computational complexity of the sphere decoding algorithm for ml detection

cyclic algebras for noncoherent differential space time coding we investigate cyclic algebras for coding over the differential noncoherent channel cyclic algebras are an algebraic object that became popular for coherent space time coding since it naturally yields linear families of matrices with full diversity coding for the differential noncoherent channel has a similar flavor in the sense that it asks for matrices that achieve full diversity except that these matrices furthermore have to be unitary in this work we give a systematic way to find infinitely many unitary matrices inside cyclic algebras which holds for all dimensions we show how cyclic algebras generalize previous families of unitary matrices obtained using the representation of fixed point free groups as an application of our technique we present families of codes for three and four antennas that achieve high coding gain

robust jump linear quadratic control a mode stabilizing solution this correspondence is concerned with optimal feedback control of a class of linear stochastic systems for a quadratic performance index the solution to this problem is known but the resulting optimal regulator does not ensure stability in every mode of operation to improve robustness a new mode stabilizing solution is defined an example illustrates the advantages of the proposed controller

cayley differential unitary space time codes one method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter and to decode differentially without knowing the channel coefficients at the receiver since channel knowledge is not required at the receiver differential schemes are ideal for use on wireless links where channel tracking is undesirable or infeasible either because of rapid changes in the channel characteristics or because of limited system resources although this basic principle is well understood it is not known how to generate good performing constellations of unitary matrices for any number of transmit and receive antennas and for any rate this is especially true at high rates where the constellations must be rapidly encoded and decoded we propose a class of cayley codes that works with any number of antennas and has efficient encoding and decoding at any rate the codes are named for their use of the cayley transform which maps the highly nonlinear stiefel manifold of unitary matrices to the linear space of skew hermitian matrices this transformation leads to a simple linear constellation structure in the cayley transform domain and to an information theoretic design criterion based on emulating a cauchy random matrix moreover the resulting cayley codes allow polynomial time near maximum likelihood ml decoding based on either successive nulling canceling or sphere decoding simulations show that the cayley codes allow efficient and effective high rate data transmission in multiantenna communication systems without knowing the channel

algebraic cayley differential space time codes cayley space time codes have been proposed as a solution for coding over noncoherent differential multiple input multiple output mimo channels based on the cayley transform that maps the space of hermitian matrices to the manifold of unitary matrices cayley codes are particularly suitable for high data rate since they have an easy encoding and can be decoded using a sphere decoder algorithm however at high rate the problem of evaluating if a cayley code is fully diverse may become intractable and previous work has focused instead on maximizing a mutual information criterion the drawback of this approach is that it requires heavy optimization which depends on the number of antennas and rate in this work we study cayley codes in the context of division algebras an algebraic tool that allows to get fully diverse codes we present an algebraic construction of fully diverse cayley codes and show that this approach naturally yields without further optimization codes that perform similarly or closely to previous unitary differential codes including previous cayley codes and codes built from lie groups

differential space time modulation space time coding and modulation exploit the presence of multiple transmit antennas to improve the performance on multipath radio channels thus far most work on space time coding has assumed that perfect channel estimates are available at the receiver in certain situations however it may be difficult or costly to estimate the channel accurately in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver we propose a general approach to differential modulation for multiple transmit antennas based on group codes this approach ran be applied to any number of transmit and receive antennas and any signal constellation we also derive low complexity differential receivers error bounds and modulator design criteria which we use to construct optimal differential modulation schemes for two transmit antennas these schemes can be demodulated with or without channel estimates this permits the receiver to exploit channel estimates when they are available the performance degrades by approximately 3 db when estimates are not available

ergodicity of filtering process by vanishing discount approach a new approach to study ergodicity of filtering processes is presented it is based on the vanishing discount approach to discounted functional of filtering process we show that limit superior of the cesaro averages of the functionals is the same for all initial conditions from which the uniqueness of invariant measures of filtering processes follows the approach is based on certain assumption for which we provide a sufficient condition using concavity arguments in addition we show the existence of solutions to the poisson equation corresponding to filtering process with concave functional the assumptions are then extended to the controlled case and using similar concave arguments we obtain the existence of solutions to the bellman equation corresponding to partially observed average cost per unit time problem

an implicit scheme for solving the convection diffusion reaction equation in two dimensions in this paper we consider a passive scalar transported in two dimensional flow the governing equation is that of the convection diffusion reaction equation for purposes of computational efficiency we apply an alternating direction implicit scheme akin to that proposed by polezhaev use of this implicit operator splitting scheme allows the application of a tridiagonal thomas solver to obtain the solution within each solution step a semidiscretization scheme is applied to discretize the differential equation in one dimension we approximate the time derivative term using a forward time stepping scheme the resulting inhomogeneous differential equation has only the spatial derivative terms and is solved using a newly proposed nodally exact steady state convection diffusion reaction scheme details on the development of the flux discretization scheme are provided modified equation analysis fourier stability analysis and a study on scheme monotonicity are also performed to shed further light on the proposed transient scheme to validate the proposed scheme we first consider test problems which are amenable to analytic solutions good agreement is obtained with both one and two dimensional steady unsteady problems thus demonstrating the validity of the method c 2000 academic press

representation theory for high rate multiple antenna code design multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment but the practical success of using multiple antennas depends crucially on our ability to design high rate space time constellations with low encoding and decoding complexity it has been shown that full transmitter diversity where the constellation is a set of unitary matrices whose differences have nonzero determinant is a desirable property for good performance we use the powerful theory of fixed point free groups and their representations to design high rate constellations with full diversity furthermore we thereby classify all full diversity constellations that form a group for all rates and numbers of transmitter antennas the group structure makes the constellations especially suitable for differential modulation and low complexity decoding algorithms the classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd we therefore also consider extensions of the constellation designs to nongroups we conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels

necessary and sufficient conditions for analysis and synthesis of markov jump linear systems with incomplete transition descriptions this technical note is concerned with exploring a new approach for the analysis and synthesis for markov jump linear systems with incomplete transition descriptions in the study not all the elements of the transition rate matrices trms in continuous time domain or transition probability matrices tpms in discrete time domain are assumed to be known by fully considering the properties of the trms and tpms and the convexity of the uncertain domains necessary and sufficient criteria of stability and stabilization are obtained in both continuous and discrete time numerical examples are used to illustrate the results

applications of convex optimization in signal processing and digital communication in the last two decades the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization these advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential this paper focuses on two such fields digital signal processing and communication in the past the widely used optimization methods in both fields had been the gradient descent or least squares methods both of which are known to suffer from the usual headaches of stepsize selection algorithm initialization and local minima with the recent advances in conic and robust optimization the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication this paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields the successful applications considered in this paper include adaptive filtering robust beamforming design and analysis of multi user communication system channel equalization decoding and detection throughout our emphasis is on how to exploit the hidden convexity convex reformulation of semi infinite constraints analysis of convergence complexity and performance as well as efficient practical implementation

feedback control of switched stochastic systems using randomly available active mode information almost sure asymptotic stabilization of a discrete time switched stochastic system is investigated information on the active operation mode of the switched system is assumed to be available for control purposes only at random time instants we propose a stabilizing feedback control framework that utilizes the information obtained through mode observations we first consider the case where stochastic properties of mode observation instants are fully known we obtain sufficient asymptotic stabilization conditions for the closed loop switched stochastic system under our proposed control law we then explore the case where exact knowledge of the stochastic properties of mode observation instants is not available we present a set of alternative stabilization conditions for this case the results for both cases are predicated on the analysis of a sequence valued process that encapsulates the stochastic nature of the evolution of active operation mode between mode observation instants finally we demonstrate the efficacy of our results with numerical examples

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

a least squares method for the helmholtz equation abstract we investigate the use of least squares methods to approximate the helmholtz equation the basis used in the discrete method consists of solutions of the helmholtz equation either consisting of plane waves or bessel functions on each element of a finite element grid unlike previous methods of this type we do not use polynomial based finite elements the use of small elements and relatively few basis functions per element allows us to prove convergence theorems for the method and to some extent control the conditioning of the resulting linear sy stem numerical results show the efficiency of the new method and suggest that it may be possible to obtain accurate results with a coarser grid than is usual for standard finite element methods

a galerkin least squares finite element method for the two dimensional helmholtz equation in this paper a galerkin least squares gls finite element method in which residuals in least squares form are added to the standard galerkin variational equation is developed to solve the helmholtz equation in two dimensions an important feature of gls methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes previous work has accomplished this for the one dimensional helmholtz equation using dispersion analysis in this paper the selection of the gls mesh parameter for two dimensions is considered and leads to elements that exhibit improved phase accuracy for any given direction of wave propagation an optimal gls mesh parameter is determined using two dimensional fourier analysis in general problems the direction of wave propagation will not be known a priori in this case an optimal gls parameter is found which reduces phase error for all possible wave vector orientations over elements the optimal gls parameters are derived for both consistent and lumped mass approximations several numerical examples are given and the results compared with those obtained from the galerkin method the extension of gls to higher order quadratic interpolations is also presented

structured unitary space time autocoding constellations we previously showed that arbitrarily reliable communication is possible within a single coherence interval in rayleigh flat fading as the symbol duration of the coherence interval and the number of transmit antennas grow simultaneously this effect where the space time signals act as their own channel codes is called autocoding for relatively short e g 16 symbol coherence intervals a codebook of independent isotropically random unitary space time signals theoretically supports transmission rates that are a significant fraction of autocapacity with an extremely low probability of error the exploitation of space time autocoding requires the creation and decoding of extraordinarily large constellations typically l 2 sup 80 we make progress on the first part of the problem through a random but highly structured constellation that is completely specified by log sub 2 l independent isotropically distributed unitary matrices the distinguishing property of this construction is that any two signals in the constellation are pairwise statistically independent and isotropically distributed thus the pairwise probability of error and hence the union bound on the block probability of error of the structured constellation is identical to that of a fully random constellation of independent signals we establish the limitations of an earlier construction through a subsidiary result that is interesting in its own right the square or for that matter any integer power greater than one of an isotropically random unitary matrix is not isotropically random with the sole exception of the one by one unitary matrix

systematic design of unitary space time constellations we propose a systematic method for creating constellations of unitary space time signals for multiple antenna communication links unitary space time signals which are orthonormal in time across the antennas have been shown to be well tailored to a rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients the signals can achieve low probability of error by exploiting multiple antenna diversity because the fading coefficients are not known the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum euclidean distance norm our construction begins with the first signal in the constellation an oblong complex valued matrix whose columns are orthonormal and systematically produces the remaining signals by successively rotating this signal in a high dimensional complex space this construction easily produces large constellations of high dimensional signals we demonstrate its efficacy through examples involving one two and three transmitter antennas

solution and asymptotic behavior of coupled riccati equations in jump linear systems a new necessary and sufficient condition for the existence of a positive semidefinite solution of coupled riccati equations occurring in jump linear systems is derived by verifying a riccati inequality it is shown that such a solution exists in addition two numerical algorithms are given to compute it an example is given to illustrate the proposed method

on the optimum design of unitary cyclic group space time codes in this letter based on the exact pairwise error probability we derive the union bound on the symbol error probability sep of the differential unitary space time dust modulation employing group codes instead of using the rank and determinant or euclidean distance criteria we optimize the cyclic group codes such that the union bound on the sep is minimized for a predetermined scenario taking into account the number of transmit and receive antennas and the operating signal to noise ratio snr our simulation results show that for a wide range of snrs the codes with the minimum union bound for a particular snr outperform the codes designed based on rank and determinant or euclidean distance criteria

on the design of layered space time systems for autocoding hochwald et al see ieee trans inform theory nov 2001 have recognized that arbitrarily reliable communication is possible in multiantenna systems with coding over only a single coherence interval in particular they showed that reliable communication is possible for all rates r spl les c sub a with code words that extend over a single coherence interval when the number of transmit antennas and coherence interval n t spl rarr spl infin they coined the names autocoding for this phenomenon and autocapacity for c sub a they also proposed a signalling scheme based on random unitary matrices that achieves a significant fraction of this capacity the main limitation however is that currently no decoder of reasonable complexity is known for this signalling scheme we investigate the application of space time layering to autocoding we show that properly constructed layered systems can achieve the autocapacity with a reasonable complexity receiver composed of minimum mean square error mmse decision feedback multiuser detectors and single user decoders in addition to this asymptotic result we propose a specific layering approach the threaded space time layering that combines generalized bit interleaved space time coded modulation iterative signal processing and pilot symbol assisted channel estimation we show that this approach is well suited for practical systems with limited numbers of transmit antennas and small coherence intervals finally we report simulation results that demonstrate the ability of the threaded approach to achieve significant fractions of the autocapacity with a realizable receiver the simulation results also indicate significant performance gains over the cayley differential space time signalling scheme in certain scenarios

optimal space time constellations from groups we consider the design of space time constellations based on group codes for fading channels with multiple transmit and receive antennas these codes can be viewed as multiantenna extensions of phase shift keying psk in the sense that all codewords have equal energy all are rotations of a fixed codeword and there is a simple differential transmission rule that allows data to be sent without channel estimates at the transmitter or receiver for coherent detection we show that all optimal full rank space time group codes are unitary each code matrix has equal energy orthogonal rows this leads to a simpler code design criterion and suggests that unitary codes may play an important role in coherent as well as noncoherent communication for any number of transmit antennas t we then use the design criterion to characterize all full rank unitary space time group codes of minimum block length also t which have 2 sup p codewords these results allow us to characterize all optimal 2 sup p ary unitary group codes with square code matrices this restricted class of block codes matches the class proposed for differential modulation by hughes see ieee trans inform theory vol 46 p 2567 78 nov 2000 and by hochwald and sweldens see ieee trans commun vol 48 p 2041 2052 dec 2000

iterative decoding of space time differentially coded unitary matrix modulation noncoherent communication over the rayleigh flat fading channel with multiple transmit and receive antennas is investigated codes achieving bit error rate ber lower than 10 sup 4 at bit energy over the noise spectral density ratio e sub b n sub 0 of 0 8 to 2 8 db from the capacity limit were found with coding rates of 0 5 to 2 25 bits per channel use the codes are serial concatenation of a turbo code and a unitary matrix differential modulation code the receiver is based on a high performance joint iterative decoding of the turbo code and the modulation code information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

optimization of extrapolated cayley transform with non hermitian positive definite matrix abstract for the extrapolated cayley transform we give necessary and sufficient conditions for guaranteeing its convergence and contraction in the euclidean norm we derive upper bounds for the convergence and the contraction factors and compute the optimal parameters minimizing these upper bounds and the corresponding optimal values of these upper bounds numerical computations show that these upper bounds are reasonably sharp compared with the exact convergence and the exact contraction factors of the extrapolated cayley transform respectively

svd iterative decision feedback demodulation and detection of coded space time unitary differential modulation a new suboptimal demodulator based on iterative decision feedback demodulation dfd and a singular value decomposition svd for estimation of unitary matrices is introduced noncoherent communication over the rayleigh flat fading channel with multiple transmit and receive antennas where no channel state information csi is available at the receiver is investigated with four transmit antennas codes achieving bit error rate ber lower than 10 sup 4 at bit energy over the noise spectral density ratio e sub b n sub o of 0 25 db up to 3 5 db with coding rates of 1 6875 to 5 06 bits per channel use were found the performance is compared to the mutual information upper bound of the capacity attaining isotropically random ir unitary transmit matrices the codes achieve ber lower than 10 sup 4 at e sub b n sub o of 3 2 db to 5 8 db from this bound system performance including the iterative dfd algorithm is compared to the one using euclidean distance as a reliability measure for demodulation the dfd system presents a performance gain of up to 1 5 db uncoded systems doing iterative dfd demodulation and idealized pilot sequence assisted modulation psam detection are compared iterative dfd introduces a gain of more than 1 2 db the coded system comprises a serial concatenation of turbo code and a unitary matrix differential modulation code the receiver employs the high performance coupled iterative decoding of the turbo code and the modulation code information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder

svd iterative detection of turbo coded multiantenna unitary differential modulation a new suboptimal demodulator based on a singular value decomposition for estimation of unitary matrices is introduced noncoherent communication over the rayleigh flat fading channel with multiple transmit and receive antennas where no channel state information is available at the receiver is investigated codes achieving bit error rate ber lower than 10 sup 4 at bit energy over the noise spectral density ratio e sub b n sub 0 of 1 6 1 9 db from code restricted capacity limit were found at higher data rates computation of code restricted capacity is impractical therefore the mutual information upper bound of the capacity attaining isotropically random unitary transmit matrices was used the codes achieve ber lower than 10 sup 4 at e sub b n sub 0 of 3 2 6 db from this bound with coding rates of 1 125 5 06 bits per channel use and different modulation decoding complexities the codes comprise a serial concatenation of turbo code and a unitary matrix differential modulation code the receiver employs the high performance coupled iterative decoding of the turbo code and the modulation code information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder

spectrally efficient noncoherent communication this paper considers noncoherent communication over a frequency nonselective channel in which the time varying channel gain is unknown a priori but is approximately constant over a coherence interval unless the coherence interval is large coherent communication which requires explicit channel estimation and tracking prior to detection incurs training overhead which may be excessive especially for multiple antenna communication in contrast noncoherent detection may be viewed as a generalized likelihood ratio test glrt which jointly estimates the channel and the data and hence does not require separate training the main results in this paper are as follows 1 we develop a signal space criterion for signal and code design for noncoherent communication in terms of the distances of signal points from the decision boundaries 2 the noncoherent metric thus obtained is used to guide the design of signals for noncoherent communication that are based on amplitude phase constellations these are significantly more efficient than conventional differential phase shift keying psk especially at high signal to noise ratio snr also known results on the high snr performance of multiple symbol demodulation of differential psk are easily inferred from the noncoherent metric 3 the glrt interpretation is used to obtain near optimal low complexity implementations of noncoherent block demodulation in particular this gives an implementation of multiple symbol demodulation of differential psk which is of linear complexity in the block length and whose degradation from the exact exponential complexity implementation can be made as small as desired

coherent and differential space time shift keying a dispersion matrix approach motivated by the recent concept of spatial modulation sm we propose a novel space time shift keying stsk modulation scheme for multiple input multiple output mimo communication systems where the concept of sm is extended to include both the space and time dimensions in order to provide a general shift keying framework more specifically in the proposed stsk scheme one out of q dispersion matrices is activated during each transmitted block which enables us to strike a flexible diversity and multiplexing tradeoff this is achieved by optimizing both the space time block duration as well as the number of the dispersion matrices in addition to the number of transmit and receive antennas we will demonstrate that the resultant equivalent system model does not impose any inter channel interference ici and hence the employment of single stream maximum likelihood ml detection becomes realistic at a low complexity furthermore we propose a differential stsk dstsk scheme assisted by the cayley unitary transform which does not require any channel state information csi at the receiver here the usual error doubling caused by the differential decoding gives rise to 3 db performance penalty in comparison to coherent stsk cstsk additionally we introduce an enhanced cstsk scheme which avoids the requirement of inter antenna synchronization ias between the rf chains associated with the transmit antenna elements aes by imposing a certain constraint on the dispersion matrix design where each column of the dispersion matrices includes only a single non zero component moreover according to the turbo coding principle the proposed cstsk and dstsk schemes are combined with multiple serially concatenated codes and an iterative bit to symbol soft demapper more specifically the associated stsk parameters are optimized with the aid of extrinsic information transfer exit charts for the sake of achieving a near capacity performance

full diversity non coherent alamouti based toeplitz space time block codes recently the liu zhang wong s toeplitz space time block code and the shang xia s alamouti code based overlapped space time block code have been developed to enable coherent full diversity with the linear receivers for a wireless communication system having multiple transmitter antennas and a single receiver antenna in this paper such a noncoherent system is considered in which channel state information is unavailable at both the transmitter and receiver using the alamouti coding scheme and the toeplitz matrix structure a novel noncoherent nonunitary space time block code which is called an alamouti based toeplitz space time block code is proposed by the fundamentals of galois theory and algebraic number theory two important properties on the two alamouti codes generated from a pair of coprime phase shift keying psk constellations i e the uniqueness of factorization itself and the shift invariant uniqueness of factorization are first revealed and rigorously proved then it is further shown that it is these two kinds of unique factorizations that enable the unique blind identification of both the channel coefficients and the transmitted signals by only processing two block received signals as well as noncoherent full diversity with a generalized likelihood ratio test glrt receiver in addition a full diversity unitary code design is also proposed by simply applying the qr decomposition to the full diversity nonunitary alamouti based toeplitz space time block code computer simulations demonstrate that the nonunitary and unitary codes presented in this paper outperform the differential codes and the signal to noise ratio snr efficient training scheme based on the coherent orthogonal space time block codes in the current literature

a high order compact finite difference scheme and precise integration method based on modified hopf cole transformation for numerical simulation of n dimensional burgers system abstract this paper modifies a n dimensional hopf cole transformation to the n dimensional burgers system we obtain the n dimensional heat conduction equation through the modification of the hopf cole transformation then the fourth order precise integration method pim in combination with a spatially global sixth order compact finite difference cfd scheme is presented to solve the equation with high accuracy moreover coupling with the strang splitting method the scheme is extended to multi dimensional two three dimensional burgers system numerical results show that the proposed method appreciably improves the computational accuracy compared with the existing numerical method moreover the two dimensional and three dimensional examples demonstrate excellent adaptability and the numerical simulation results also have very high accuracy in medium reynolds numbers

multidimensional orthogonal filter bank characterization and design using the cayley transform we present a complete characterization and design of orthogonal infinite impulse response iir and finite impulse response fir filter banks in any dimension using the cayley transform ct traditional design methods for one dimensional orthogonal filter banks cannot be extended to higher dimensions directly due to the lack of a multidimensional md spectral factorization theorem in the polyphase domain orthogonal filter banks are equivalent to paraunitary matrices and lead to solving a set of nonlinear equations the ct establishes a one to one mapping between paraunitary matrices and para skew hermitian matrices in contrast to the paraunitary condition the para skew hermitian condition amounts to linear constraints on the matrix entries which are much easier to solve based on this characterization we propose efficient methods to design md orthogonal filter banks and present new design results for both iir and fir cases

finite difference methods for the reduced water wave equation abstract a comparative study of various finite difference schemes for numerical solution of the reduced water wave equation is carried out the nine point optimal scheme is newly derived and the derivation involves a tactical combination of the taylor expansions of wave function at the relevant nodes of a representative grid element it is demonstrated that there is a proper range of the relative grid size for each scheme in practical computations beyond which a numerical solution is either inaccurate due to the fact that approximations adopted by the scheme are valid only when the ratio of the grid size to the local wave length is small or unobtainable due to the ill condition of the difference equation system a high order scheme is shown to be advantageous in terms of not only the numerical accuracy but also the validity when relatively large grid elements are employed

stabilizing control law for hybrid models this note is concerned with the adaptive stabilizing control problem for jump markov systems a new control law is proposed based on a simple set of algebraic sufficient conditions it is shown that this approach can be used for a class of stochastic models for which the more restrictive solution proposed by caines and zhang 1992 does not apply

recursive space time trellis codes using differential encoding differential space time modulation dstm has been recently proposed by hughes and hochwald and sweldens when the channel information is not known at the receiver where the demodulation is in fact the same as the coherent demodulation of space time block coding by replacing the channel matrix with the previously received signal matrix on the other hand the dstm also needs a recursive memory of a matrix block at the encoder and therefore provides a trellis structure when the channel information is known at the receiver which is the interest of this paper this recursive structure of the dstm has been adopted lately by schlegel and grant in joint with a conventional binary code and joint iterative decoding demodulation with a superior performance the number of states of the trellis from the recursive structure depends on both the memory size which is fixed in this case and the unitary space time code ustc when a ustc for the dstm forms a group the number of states is the same as the size of the ustc otherwise the number of the states is the size of the semi group generated by the ustc from all the multiplications of the matrices in the ustc it is well known in the conventional convolutional coding cc or the trellis coded modulation tcm the free hamming or euclidean distance or the performance increases when the number of states increases by adding more memory with a properly designed cc or tcm in this paper we systematically study and design the ustc dstm for the recursive space time trellis modulation and show that the diversity product increases when the number of states increases which is not because of the memory size but because of the different ustc designs that generate different sizes of semi groups we propose a new ustc design criterion to ensure that the trellis structure improves the diversity product over the ustc as a block code based on the new criterion we propose a new class of ustc design for an arbitrary number of transmit antennas that has an analytical diversity product formula for two transmit antennas we then follow schlegel and grant s approach for joint encoding and iterative decoding of a binary coded dstm turbo space time coding and numerically show that our new ustc designs for the recursive space time trellis modulation outperforms the group ustc used by schlegel and grant

orthogonal space time block codes with sphere packing orthogonal designs have received considerable attention in the development of efficient modulation and coding methods for future multi antenna wireless communication systems due to their special properties in this paper we propose a class of space time block codes constructed by combining orthogonal designs with sphere packing for an arbitrary number of transmit antennas the structure of the orthogonal designs is exploited to guarantee full diversity and sphere packing is used to improve the coding advantage space time block code construction from block orthogonal designs is also considered the full diversity property is ensured by rotating the sphere packing underlying the code and the optimal rotation angle is determined for a class of sphere packing code design examples are provided for two and four transmit antennas and various transmission rates the simulation results show that by jointly designing the symbols in the orthogonal designs the performance of the block codes can be significantly increased

the reference prior for complex covariance matrices with efficient implementation strategies the paper derives the reference prior for complex covariance matrices the reference prior is a noninformative prior that circumvents some of the weaknesses of common alternatives in multidimensional settings as a consequence inference based on this prior renders well behaving solutions that in many cases outperform traditionally used approaches the main obstacle is that inference based on this prior require integration over high dimensional spaces which have no closed form solutions a focus of the paper is therefore to discuss efficient implementation strategies based on markov chain monte carlo methods it is identified that certain structures can be treated analytically both for the case where the parameter of interest is the covariance matrix itself but also for cases in which the covariance matrix is a nuisance parameter that characterizes noise color evaluation in both these settings also verify the superior performance obtained by using the proposed prior as compared to traditional techniques to treat unknown covariance matrices

on exponential almost sure stability of random jump systems this paper is concerned with a class of random jump systems represented by transition operators which includes switched linear systems with strictly stationary switching signals in infinite modes space as its special case a series of necessary and sufficient conditions are established for almost sure stability of this class of random jump systems under different scenarios the stability criteria obtained are further extended to markov jump linear systems with infinite states and hence a unified approach to describing the almost sure stability of mjlss is addressed under this context all the results in the work are developed for both the continuous and discrete time systems

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

the new numerical method for solving the system of two dimensional burgers equations in this paper the system of two dimensional burgers equations are solved by local discontinuous galerkin ldg finite element method the new method is based on the two dimensional hopf cole transformations which transform the system of two dimensional burgers equations into a linear heat equation then the linear heat equation is solved by the ldg finite element method the numerical solution of the heat equation is used to derive the numerical solutions of burgers equations directly such a ldg method can also be used to find the numerical solution of the two dimensional burgers equation by rewriting burgers equation as a system of the two dimensional burgers equations three numerical examples are used to demonstrate the efficiency and accuracy of the method

development of a sixth order two dimensional convection diffusion scheme via cole hopf transformation abstract in this paper we develop a two dimensional finite difference scheme for solving the time dependent convection diffusion equation the numerical method exploits cole hopf equation to transform the nonlinear scalar transport equation into the linear heat conduction equation within the semi discretization context the time derivative term in the transformed parabolic equation is approximated by a second order accurate time stepping scheme resulting in an inhomogeneous helmholtz equation we apply the alternating direction implicit scheme of polezhaev to solve the helmholtz equation as the key to success in the present simulation we develop a helmholtz scheme with sixth order spatial accuracy as is standard practice we validated the code against test problems which were amenable to exact solutions results show excellent agreement for the one dimensional test problems and good agreement with the analytical solution for the two dimensional problem

full diversity blind alamouti space time block codes for unique identification of flat fading channels in this paper we consider a systematic design of a full diversity blind alamouti space time block code for a wireless communication system having two transmitter antennas and a single receiver antenna in which the channel is completely unknown at both the transmitter and the receiver the key idea is to alternatively transmit alamouti codes with different phase shift keying psk constellations say with p psk and q psk to provide the theoretical analysis of its unique identification and full diversity conditions we first establish a general theorem for factorizing a pq psk constellation into a product of a p psk constellation and a q psk constellation then we prove that a necessary and sufficient condition for both the factorization and a set of solutions of the resulting alamouti diophantine equation from our code design to be unique is that p and q are coprime the same condition assures that the channel and the transmitted signal can be blindly and uniquely identified furthermore a closed form solution to determine the channel coefficients and the transmitted symbols are obtained also we prove that our code enables full diversity for the generalized likelihood ratio test glrt receiver if p and q are coprime when finite length of the received data is available the unitarity and linearity of our code design allow us to utilize the semi definite relaxation sdr decoder or the sphere decoder so that the joint estimation of the channel and symbols can be efficiently implemented

unitary space time constellation designs from group codes in this correspondence we propose new unitary space time constellation designs with high diversity products our hamiltonian and product constellations are based on slepian s group codes and can be used for any number of antennas and any data rate our hamiltonian constellations achieve the theoretical upper bound of diversity product when the number of transmitter antennas is even and the cardinality of the signal constellation is less than or equal to 5 many of our hamiltonian and product constellations outperform and have higher diversity products than the best known designs in the literature these include orthogonal designs dicyclic groups cyclic groups parametric codes numerical approaches nongroup designs cayley codes tast codes and some constellations obtained from fixed point free groups

unitary space time constellation design based on the chernoff bound of the pairwise error probability unitary space time constellation design is considered for noncoherent multiple antenna communications where neither the transmitter nor the receiver knows the fading coefficients of the channel by employing the clarke s subdifferential theorem of the sum of the kappa largest singular values of a unitary matrix we present a numerical optimization procedure for finding unitary space time signal constellations of any dimension the chernoff bound of the pairwise error probability is used directly as a design criterion the constellations are found by performing gradient descent search on a family ldquosurrogaterdquo functions that converge to the maximum pairwise error probability the complexity of the search procedure increases with the dimension and the size of the constellation but it can be considered to be acceptable for an off line design procedure since the designed constellations are unstructured and thus require an exhaustive search over all codewords in decoding their main practical value is to serve as constellation design performance benchmarks we compare the performance of the new constellations to that of some other well known constellations computer simulation results illustrate typically about 0 4 3 5 db performance gains

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

almost sure stabilization for feedback controls of regime switching linear systems with a hidden markov chain this work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown markov chain the control system displays continuous dynamics represented by differential equations and discrete events given by a hidden markov chain in the previous investigation on this class of problems averaging criteria were used which provides only the system behavior in some expectation sense a closer scrutiny of the system behavior necessarily requires the consideration of sample path properties different from previous work on stabilization of adaptive controlled systems with a hidden markov chain where average criteria were considered this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes under simple conditions it is shown that as long as the feedback controls have linear growth in the continuous component the resulting process is regular moreover by appropriate choice of the lyapunov functions it is shown that the adaptive system is stabilizable almost surely as a by product it is also established that the controlled process is positive recurrent

leveraging coherent space time codes for noncoherent communication via training training codes are introduced for the multiple antenna noncoherent multiple block rayleigh fading channel in which the fading coefficients which are constant over a fixed number of dimensions coherence interval for each block and then change independently to a new realization are known neither at the transmitter nor at the receiver each codeword of a training code consists of a part known to the receiver used to form a minimum mean squared error mmse estimate of the channel and a part that contains codeword s of a space time block or trellis code designed for the coherent channel in which the receiver has perfect knowledge of the channel the channel estimate is used as if it were error free for decoding the information bearing part of the training codeword training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable conditions for which the estimator detector e d receiver is equivalent to the optimal noncoherent receiver are established a key performance analysis result of this paper is that the training codes when decoded with the e d receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code in some cases the performance of training codes can be measured relative to coherent reception via training efficiency which is then optimized over the energy allocation between the training and data phases in the limit of increasing block lengths training codes always achieve the performance of coherent reception the examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available even though the latter require exponential decoding complexity

on the adaptive control for jump parameter systems vianonlinear filtering in this paper we first present an error analysis for the process of estimates generated by the wonham filter when it is used for the estimation of the finite set valued jump markov parameters of a random parameter linear stochastic system and further give bounds on certain functions of these estimates we then consider a certainty equivalence adaptive linear quadratic gaussian feedback control law using the estimates generated by the nonlinear filter and demonstrate the global existence of solutions to the resulting closed loop system a stochastic lyapunov analysis establishes that the certainty equivalence law stabilizes the markov jump parameter linear system in the mean square average sense the conditions for this result are that certain products of i the parameter process jump rate and ii the solution of the control riccati equation and its second derivatives should be less than certain given bounds an example is given where the controlled linear system has state dimension 2 finally the stabilizing properties of certainty equivalence laws which depend on i the maximum likelihood estimate of the parameter value and ii a modified version of this estimate are established under certain conditions

systematic and optimal cyclotomic lattices and diagonal space time block code designs in this correspondence a new and systematic design of cyclotomic lattices with full diversity is proposed by using some algebraic number theory this design provides infinitely many full diversity cyclotomic lattices for a given lattice size based on the packing theory and the concrete form of the design optimal cyclotomic lattices are presented by minimizing the mean transmission signal power for a given minimum diversity product or equivalently maximizing the minimum product for a given mean transmission signal power the newly proposed cyclotomic lattices can be applied to both space time code designs for multi antenna systems and linear precode design for signal space diversity in single antenna systems over fast rayleigh fading channels although there are some cyclotomic lattices space time codes existing in the literature most of them are not optimal

effects of non identical rayleigh fading on differential unitary space time modulation non identical fading distribution in a multiple input multiple output mimo channel including unequal average channel gains and fade rates often occurs when antennas are not co located in this paper we present an analytical study of the effects of non identical rayleigh fading on the error performance of differential unitary space time modulation dustm the fading processes for different transmit receive antenna pairs are assumed to be independent and time variant we find that the maximum likelihood ml differential detector of dustm over such channels is involved except for differential cyclic group codes the conventional detector is proved to be asymptotically optimal in the limit of high signal to noise ratio snr over static fading channels applying the distribution of quadratic forms of gaussian vectors we then derive closed form expressions for the exact error probabilities of two specific unitary classes namely cyclic group codes and orthogonal codes simple and useful asymptotic bounds on error probabilities are also obtained our analysis leads to the following general findings 1 equal power allocation is asymptotically optimal and 2 non identical channel gain distribution degrades the error performance finally we also introduce a water filling based power allocation to exploit the transmit non identical fading statistics

energy efficient full diversity collaborative unitary space time block code designs via unique factorization of signals in this paper a novel concept called a uniquely factorable constellation pair ufcp is proposed for the systematic design of a noncoherent full diversity collaborative unitary space time block code by normalizing two alamouti codes for a wireless communication system having two transmitter antennas and a single receiver antenna it is proved that such a unitary ufcp code assures the unique identification of both channel coefficients and transmitted signals in a noise free case as well as full diversity for the noncoherent maximum likelihood receiver in a noise case to further improve error performance an optimal unitary ufcp code is designed by appropriately and uniquely factorizing a pair of energy efficient cross quadrature amplitude modulation qam constellations to maximize the coding gain subject to a transmission bit rate constraint after a deep investigation of the fractional coding gain function a technical approach developed in this paper to maximizing the coding gain is to carefully design an energy scale to compress the first three largest energy points in the corner of the qam constellations in the denominator of the objective as well as carefully design a constellation triple forming two ufcps with one collaborating with the other two so as to make the accumulated minimum euclidean distance along the two transmitter antennas in the numerator of the objective as large as possible and at the same time to avoid as many corner points of the qam constellations with the largest energy as possible to achieve the minimum of the numerator in other words the optimal coding gain is attained by intelligent constellations collaboration and efficient energy compression computer simulations demonstrate that error performance of the optimal unitary ufcp code presented in this paper outperforms those of the differential code and the signal to noise ratio efficient training code

block differential encoding for rapidly fading channels rapidly fading channels provide doppler induced diversity but are also challenging to estimate to bypass channel estimation we derive two novel block differential bd codecs relying on a basis expansion model for time varying channels our differential designs are easy to implement and can achieve the maximum possible doppler diversity the first design bd i relies on a time frequency duality based on which we convert a time varying channel into multiple frequency selective channels and subsequently into multiple flat fading channels using orthogonal frequency division multiplexing combined with a group partitioning scheme bd i offers flexibility to trade off decoding complexity with performance our second block differential design bd ii improves the bandwidth efficiency of bd i at the price of increased complexity at the receiver which relies on decision feedback decoding simulation results corroborate our theoretical analysis and compare with competing alternatives

asymptotic properties of hybrid diffusion systems in response to the increasing needs for control and optimization of hybrid systems this work is concerned with such asymptotic properties as recurrence also known as weak stochastic stability in the literature and ergodicity of regime switching diffusions using liapunov functions necessary and sufficient conditions for positive recurrence are developed then ergodicity of positive recurrent regime switching diffusions is obtained by constructing cycles using the associated discrete time markov chains

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

unitary space time modulation via cayley transform a prevoiusly proposed method for communicating with multiple antennas over block fading channels is unitary space time modulation ustm in this method the signals transmitted from the antennas viewed as a matrix with spatial and temporal dimensions form a unitary matrix i e one with orthonormal columns since channel knowledge is not required at the receiver ustm schemes are suitable for use on wireless links where channel tracking is undesirable or infeasible either because of rapid changes in the channel characteristics or because of limited system resources previous results have shown that if suitably designed ustm schemes can achieve full channel capacity at high snr and moreover that all this can be done over a single coherence interval provided the coherence interval and number of transmit antennas are sufficiently large which is a phenomenon referred to as autocoding while all this is well recognized what is not clear is how to generate good performing constellations of nonsquare unitary matrices that lend themselves to efficient encoding decoding the schemes proposed so far either exhibit poor performance especially at high rates or have no efficient decoding algorithms we propose to use the cayley transform to design ustm constellations this work can be viewed as a generalization to the nonsquare case of the cayley codes that have been proposed for differential ustm the codes are designed based on an information theoretic criterion and lend themselves to polynomial time often cubic near maximum likelihood decoding using a sphere decoding algorithm simulations suggest that the resulting codes allow for effective high rate data transmission in multiantenna communication systems without knowing the channel however our preliminary results do not show a substantial advantage over training based schemes

double differential space time block coding for time selective fading channels most existing space time coding schemes assume time invariant fading channels and offer antenna diversity gains relying on accurate channel estimates at the receiver other single differential space time block coding schemes forego channel estimation but are less effective in rapidly fading environments based on a diagonal unitary matrix group a novel double differential space time block coding approach is derived in this paper for time selective fading channels without estimating the channels at the receiver information symbols are recovered with antenna diversity gains regardless of frequency offsets the resulting transceiver has very low complexity and is applicable to an arbitrary number of transmit and receive antennas approximately optimal space time codes are also designed to minimize bit error rate system performance is evaluated both analytically and with simulations

unitary signal constellations for differential space time modulation with two transmit antennas parametric codes optimal designs and bounds we focus on the design of unitary signal constellations for differential space time modulation with double transmit antennas by using the parametric form of a two by two unitary matrix we present a class of unitary space time codes called parametric codes and show that this class of unitary space time codes leads to a five signal constellation with the largest possible diversity product and a 16 signal constellation with the largest known diversity product although the parametric code of size 16 is not a group by itself we show that it is a subset of a group of order 32 furthermore the unitary signal constellations of sizes 32 64 128 and 256 obtained by taking the subsets of the parametric codes of sizes 37 75 135 and 273 respectively have the largest known diversity products we also use large diversity sum of unitary space time signal constellations as another significant property for the signal constellations to have good performance in low snr scenarios the newly introduced unitary space time codes can lead to signal constellations with sizes of 5 and 9 through 16 that have the largest possible diversity sums subsequently we construct a few sporadic unitary signal constellations with the largest possible diversity product or diversity sum a four signal constellation which has both the largest possible diversity product and the largest possible diversity sum and three unitary signal constellations with the largest possible diversity sums for sizes of 6 7 and 8 are constructed respectively furthermore by making use of the existing results in sphere packing and spherical codes we provide several upper and lower bounds on the largest possible diversity product and the largest possible diversity sum that unitary signal constellations of any size can achieve

a new family of unitary space time codes with a fast parallel sphere decoder algorithm in this paper we propose a new design criterion and a new class of unitary signal constellations for differential space time modulation for multiple antenna systems over rayleigh flat fading channels with unknown fading coefficients extensive simulations show that the new codes have significantly better performance than existing codes we have compared the performance of our codes with differential detection schemes using orthogonal design cayley differential codes fixed point free group codes and product of groups and for the same bit error rate our codes allow smaller signal to noise ratio snr by as much as 10 db the design of the new codes is accomplished in a systematic way through the optimization of a performance index that closely describes the bit error rate as a function of the snr the new performance index is computationally simple and we have derived analytical expressions for its gradient with respect to constellation parameters decoding of the proposed constellations is reduced to a set of one dimensional closest point problems that we solve using parallel sphere decoder algorithms this decoding strategy can also improve efficiency of existing codes

stochastic linear quadratic regulators with indefinite control weight costs this paper considers optimal minimizing control of stochastic linear quadratic regulators lqrs the assumption that the control weight costs must be positive definite inherited from the determ

stabilization and destabilization of hybrid systems of stochastic differential equations this paper aims to determine whether or not a stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system new methods are developed and sufficient conditions on the stability and instability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization and destabilization

noncoherent sequence detection of differential space time modulation approximate maximum likelihood noncoherent sequence detection nsd for differential space time modulation dstm in time selective fading channels is proposed the starting point is the optimum multiple symbol differential detection for dstm that is characterized by exponential complexity by truncating the memory of the incremental metric a finite state trellis is obtained so that a viterbi algorithm can be implemented to perform sequence detection compared to existing linear predictive receivers a distinguished feature of nsd is that it can accommodate nondiagonal constellations in continuous fading error analysis demonstrates that significant improvement in performance is achievable over linear prediction receivers by incorporating the reduced state sequence detection techniques performance and complexity tradeoffs can be controlled by the branch memory and trellis size numerical results show that most of the performance gain can be achieved by using an l state trellis where l is the size of the dstm constellation

mpsk modulated constellation design for differential space time modulation the constellation design for differential space time modulation usually requires to construct l constellation size unitary matrices making the design complexity increasing rapidly with l in this correspondence we propose a new construction technique which exploits the rotational invariance of unitary matrices and the property of mpsk modulation the proposed constellations are derivable from a smaller set of d l m unitary matrices via rotations defined by an m ary psk symbol which in turn are parameterized by two unitary matrices u1 and u2 they share some good property of group constellations thereby considerably simplifying the optimization of u1 and u2 they also possess other good properties which allow for simplified maximum likelihood ml decoding extensive numerical examples are presented to demonstrate that the proposed constellations in general have larger diversity products than other constellations and thus better error performance

a multiscale finite element method for the helmholtz equation it is well known that when the standard galerkin method is applied to the helmholtz equation it exhibits an error in the wavenumber and the solution does not therefore preserve the phase characteristics of the exact solution improvements on the galerkin method including galerkin least squares gls methods have been proposed however these approaches rely on a dispersion analysis of the underlying difference stencils in order to reduce error in the solution in this paper we propose a multiscale finite element for the helmholtz equation the method employs a multiscale variational formulation which leads to a subgrid model in which subgrid scales are incorporated analytically through appropriate green s functions it is shown that entirely new and accurate methods emerge and that gls methods can be obtained as special cases of the more general subgrid model

differential unitary space time modulation we present a framework for differential modulation with multiple antennas across a continuously fading channel where neither the transmitter nor the receiver knows the fading coefficients the framework can be seen as a natural extension of standard differential phase shift keying commonly used in single antenna unknown channel systems we show how our differential framework links the unknown channel system with a known channel system and we develop performance design criteria as a special ease we introduce a class of diagonal signals where only one antenna is active at any time and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error

design of fully diverse multiple antenna codes based on sp 2 fully diverse constellations i e sets of unitary matrices whose pairwise differences are nonsingular are useful in multiple antenna communications especially in multiple antenna differential modulation since they have good pairwise error properties recently group theoretic ideas especially fixed point free fpf groups have been used to design fully diverse constellations of unitary matrices here we construct four transmit antenna constellations appropriate for differential modulation based on the symplectic group sp 2 they can be regarded as extensions of alamouti s celebrated two transmit antenna orthogonal design which can be constructed from the group sp 1 we further show that the structure of sp 2 codes lends itself to efficient maximum likelihood ml decoding via the sphere decoding algorithm finally the performance of sp 2 codes is compared with that of other existing codes including alamouti s orthogonal design a 4 spl times 4 complex orthogonal design cayley differential unitary space time codes and group based codes

decentralized adaptive output feedback stabilization for large scale stochastic nonlinear systems in this paper the problem of decentralized adaptive output feedback stabilization is investigated for large scale stochastic nonlinear systems with three types of uncertainties including parametric uncertainties nonlinear uncertain interactions and stochastic inverse dynamics under the assumption that the inverse dynamics of the subsystems are stochastic input to state stable an adaptive output feedback controller is constructively designed by the backstepping method it is shown that under some general conditions the closed loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability in addition the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin the contributions of the work are characterized by the following novel features 1 even for centralized single input single output systems this paper presents a first result in stochastic nonlinear adaptive output feedback asymptotic stabilization 2 the methodology previously developed for deterministic large scale systems is generalized to stochastic ones at the same time novel small gain conditions for small signals are identified in the setting of stochastic systems design 3 both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states 4 parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields which may appear nonlinearly 5 the concept of stochastic input to state stability and the method of changing supply functions are adapted for the first time to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control

adaptive continuous time linear quadratic gaussian control the adaptive linear quadratic gaussian control problem where the linear transformation of the state a and the linear transformation of the control b are unknown is solved assuming only that a b is controllable and a q sub 1 sup 1 2 is observable where q sub 1 determines the quadratic form for the state in the integrand of the cost functional a weighted least squares algorithm is modified by using a random regularization to ensure that the family of estimated models is uniformly controllable and observable a diminishing excitation is used with the adaptive control to ensure that the family of estimates is strongly consistent a lagged certainty equivalence control using this family of estimates is shown to be self optimizing for an ergodic quadratic cost functional

spectrally efficient differential space time coding using non full diverse constellations in this paper a method is proposed to construct spectral efficient unitary space time codes for high rate differential communications over multiple antenna channels unlike most of the known methods which are designed to maximize the diversity product the minimum determinant distance our objective is to increase the spectral efficiency the simulation results indicate that for high spectral efficiency and for more than one receive antenna the new method significantly outperforms the existing alternatives in the special case of two transmit antennas which is the main focus of this paper the relation between the proposed code and the alamouti scheme helps us to provide an efficient maximum likelihood decoding algorithm also we demonstrate that similar ideas can be applied for designing codes for more than two transmit antennas as an example we present a construction for a 4 times 4 unitary constellations which has a good performance as compared with the other known codes

full diversity blind space time block codes in this paper the systematic design of a space time block code is considered for a wireless communication system with multiple transmitter receiver antennas and flat fading in which channel state information is completely unknown from the viewpoint of blind signal processing a necessary and sufficient condition is given for the unique identification of the multi input multi output flat fading channel and transmitted signal then some novel unique factorizations for a pair of coprime p ary and q ary phase shift keying psk constellations are established with this and currently available coherent space time block code designs a method is developed to systematically construct full diversity blind nonunitary space time block codes as well as unitary codes by just performing the qr decomposition of the nonunitary codes it is proved that under a noise free environment the code design proposed in this paper can guarantee that the transmitted signals and the channel coefficients are uniquely identified and that under a complex gaussian noise environment in which pth order and q th order statistics p and q are co prime of the received signals are available the channel coefficients can be still uniquely identified in addition a closed form solution to determine the channel coefficients is obtained