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

continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions abstract this paper is concerned with singular perturbations in parabolic problems subjected to nonlinear neumann boundary conditions we consider the case for which the diffusion coefficient blows up in a subregion 0 which is interior to the physical domain r n we prove under natural assumptions that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in 0 and converges uniformly to a continuous and positive function in 1 0

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

geometrical relations between space time block code designs and complexity reduction in this work the geometric relation between space time block code design for the coherent channel and its noncoherent counterpart is exploited to get an analog of the information theoretic inequality i x s lesi x h s in terms of diversity it provides a lower bound on the performance of noncoherent codes when used in coherent scenarios this leads in turn to a code design decomposition result splitting coherent code design into two complexity reduced subtasks moreover a geometrical criterion for high performance space time code design is derived

on the multiplicity of equilibrium solutions to a nonlinear diffusion equation on a manifold arising in climatology abstract we analyze the sensitivity of a climatological model with respect to small changes in one of the distinguished parameters the solar constant we start by proving the stabilization of solutions of the evolution model when time tends to infinity later we study the stationary problem and obtain uniqueness or a multiplicity of solutions for different values of the solar constant

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

systems of p laplacian differential inclusions with large diffusion abstract in this paper we consider coupled systems of p laplacian differential inclusions and we prove under suitable conditions that a homogenization process occurs when diffusion parameters become arbitrarily large in fact we obtain that the attractors are continuous at infinity on l 2 l 2 topology with respect to the diffusion coefficients and the limit set is the attractor of an ordinary differential problem

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

mixed q linear space time codes a new modulation method for linear space time codes is proposed based on using constellations of different sizes for different symbols it is shown that the proposed method significantly reduces the complexity of the sphere decoding algorithm the complexity reduction is more pronounced in high rate codes where each code matrix carries a large number of symbols we also show that the choice of constellation size provides a tradeoff between performance and complexity using this some guidelines for choosing constellation size are presented as one introduces more constellation disparity in the code the complexity is further reduced while the performance loss grows typically a complexity reduction of one to two orders of magnitude can be achieved at the expense of about 3 db coding gain we suggest a simple modification in our design to reduce this loss to about 2 db

equivalent piecewise affine models of linear hybrid automata in this technical note we examine the relationship between linear hybrid automata lha and piecewise affine pwa systems while a lha is an autonomous non deterministic model a pwa is a deterministic model with inputs through the key idea of modeling the uncertainty associated with lha transitions as input disturbances in a pwa model by extending continuous time pwa models to include the dynamics of discrete states and resets we show in a constructive way that a lha can be equivalently represented as a pwa system where equivalent means that the two systems generate the same trajectories besides filling in a missing theoretical link between the lha modelling framework and the pwa modelling framework the result has the practical advantage of enabling the use of several existing control theoretical tools developed for pwa models to a wider class of hybrid systems

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

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

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

receive antenna selection for unitary space time modulation over semi correlated ricean channels receive antenna selection for unitary space time modulation ustm over semi correlated ricean fading channels is analyzed this work generalizes that of ma and tepedelenlio glu for the independent and identically distributed i i d rayleigh fading case the antenna selection rule is that the receive antennas with the largest signal powers are chosen for single antenna selection we derive the maximum likelihood decoding for the correlated ricean case we also derive the chernoff bound on the pairwise error probability for the high signal to noise ratio snr region and obtain the coding gain and diversity order our results show that even when there are transmitter side correlations and a line of sight component receive antenna selection with ustm preserves the full diversity order if the ustm constellation is of full rank we also give an approximation to the distribution function of a quadratic form of non zero mean complex gaussian variates from nabar et al at the high snr region based on this approximation a closed form expression for the coding gain is also obtained and compared with that of the i i d rayleigh case we also analyze the case of multiple receive antenna selection and derive the coding gain and diversity order we show that ustm constellations which have been proposed for the i i d rayleigh channel can be used with the correlated ricean channel as well

maximum likelihood detection for differential unitary space time modulation with carrier frequency offset can conventional differential unitary space time modulation dustm be applied when there is an unknown carrier frequency offset cfo this paper answers this question affirmatively and derives the necessary maximum likelihood ml detection rule the asymptotic performance of the proposed ml rule is analyzed leading to a code design criterion for dustm by using the modified diversity product the resulting proposed decision rule is a new differential modulation scheme in both the temporal and spatial domains two sub optimal multiple symbol decision rules with improved performance are also proposed for the efficient implementation of these we derive a modified bound intersection detector bid a generalization of the previously derived optimal bid for the conventional dustm the simulation results show that the proposed differential modulation scheme is more robust against cfo drifting than the existing double temporal differential modulation

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

interaction of localized large diffusion and boundary conditions abstract in this paper we derive the limiting pdes for parabolic problems where localized large diffusion touches the boundary of the domain hence the limit problem reflects the interaction of large diffusion and boundary conditions the limit problem is a pde coupled with a system of odes through some nonlocal terms we study the well posedness and dissipativity of the nonstandard limit problem as well as the continuity of the dynamics as diffusion becomes large

asymptotically dense spherical codes ii laminated spherical codes for pt i see ibid vol 43 no 6 p 1774 85 1997 new spherical codes called laminated spherical codes are constructed in dimensions 2 49 using a technique similar to the construction of laminated lattices each spherical code is recursively constructed from existing spherical codes in one lower dimension laminated spherical codes outperform the best known spherical codes in the minimum distance sense for many code sizes the density of a laminated spherical code approaches the density of the laminated lattice in one lower dimension as the minimum distance approaches zero in particular the three dimensional laminated spherical code is asymptotically optimal in the sense that its density approaches the fejes toth 1959 upper bound as the minimum distance approaches zero laminated spherical codes perform asymptotically as well as wrapped spherical codes in those dimensions where laminated lattices are optimal sphere packings

unitary space time constellation analysis an upper bound for the diversity the diversity product and the diversity sum are two very important parameters for a good performing unitary space time constellation a basic question is what the maximal diversity product or sum is in this correspondence we are going to derive general upper bounds on the diversity sum and the diversity product for unitary constellations of any dimension n and any size m using packing techniques on the compact lie group u n

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

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

geometrical and numerical design of structured unitary space time constellations there exist two important design criteria for unitary space time codes in the situation where the signal to noise ratio snr is large the diversity product dp of a constellation should be as large as possible it is less known that the diversity sum ds is a very important design criterion for codes working in a low snr environment so far no general method to design good performing constellations with large diversity for any number of transmit antennas and any transmission rate exists in this correspondence we propose constellations with suitable structures which allow one to construct codes with excellent diversity using geometrical symmetry and numerical methods the presented design methods work for any dimensional constellation and for any transmission rate

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

upper semicontinuity for attractors of parabolic problems with localized large diffusion and nonlinear boundary conditions the motivations to study the problem considered in this paper come from the theory of composite materials where the heat diffusion properties can change from one part of the domain to another mathematically this leads to a nonlinear second order parabolic equation for which the diffusion coefficient becomes large in a subdomain 0 the equation is supplemented by a nonlinear boundary condition on and an initial condition the authors determine the form of the limit problem the so called shadow system which involves an evolution equation for the averages of the density over 0 the main results include global in time existence of solutions and upper semicontinuity of the associated global attractors when the system approaches the shadow system

dynamical properties of hybrid automata hybrid automata provide a language for modeling and analyzing digital and analogue computations in real time systems hybrid automata are studied here from a dynamical systems perspective necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized the results on existence uniqueness and continuity serve as a starting point for stability analysis lyapunov s theorem on stability via linearization and lasalle s invariance principle are generalized to hybrid automata

continuity properties on p for p laplacian parabolic problems abstract in this work we obtain some continuity properties on the parameter p at p 2 for the takeuchi yamada problem which is a degenerate p laplacian version of the chafee infante problem we prove the continuity of the flows and the equilibrium sets and the upper semicontinuity of the global attractors

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

euclidean and space time block codes relationship optimality performance analysis revisited an equivalent model for a multiple input multiple output communication system with space time block codes stbcs is proposed based on a revealed connection between stbcs and euclidean codes examples of distance spectra signal constellations and signal coordinate diagrams of euclidean codes equivalent to simplest orthogonal stbcs are given a new asymptotic upper bound for the symbol error rate ser of stbcs based on the distance spectra of the equivalent euclidean codes is derived and new general design criteria for signal constellations of the optimal code are proposed some bounds relating distance properties dimensionality and cardinality of stbcs with constituent signals of equal energy are given and new signal constellations with cardinalities of 8 and 16 for alamouti s code are designed a general methodology for performance analysis of stbcs is revisited as an example of the application of this methodology an exact evaluation of the ser of an orthogonal stbc is given namely a new expression for the ser of alamouti s code with binary phase shift keying signals is derived

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

fast slow diffusion and collapsing sandpiles we regard the limit as p of the flow governed by the p laplacian as providing a simplistic model for the collapse of an initially unstable sandpile upon rescaling to stretch out the initial layer we obtain some simple dynamics and provide fairly explicit solutions in certain cases involving nonlocal geometric curvature motion in particular we note that such models entail instantaneous mass transfer governed by monge kantorovich theory

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

efficient conversion of mixed logical dynamical systems into an equivalent piecewise affine form for hybrid systems described by switched linear difference equations linear threshold conditions automata and propositional logic conditions described in mixed logical dynamical form this note describes two algorithms for transforming such systems into an equivalent piecewise affine form where equivalent means that for the same initial conditions and input sequences the trajectories of the system are identical the proposed techniques exploit ideas from mixed integer programming and multiparametric programming

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

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

four inequalities for monotone gradient vector fields we consider vector fields which have realizations as subdifferentials of convex functionals on a hilbert space four inequalities relating the resolvent of the subdifferential to the semigroup flow are known in the literature in this paper the constant appearing in one of these inequalities is improved and the resulting four inequalities are shown to be optimal

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

space time autocoding prior treatments of space time communications in rayleigh flat fading generally assume that channel coding covers either one fading interval in which case there is a nonzero outage capacity or multiple fading intervals in which case there is a nonzero shannon capacity however we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable in short space time signals are their own channel codes we call this phenomenon space time autocoding and the accompanying capacity the space time autocapacity let an m transmitter antenna n receiver antenna rayleigh flat fading channel be characterized by an m spl times n matrix of independent propagation coefficients distributed as zero mean unit variance complex gaussian random variables this propagation matrix is unknown to the transmitter it remains constant during a t symbol coherence interval and there is a fixed total transmit power let the coherence interval and number of transmitter antennas be related as t spl beta m for some constant spl beta a t spl times m matrix valued signal associated with r spl middot t bits of information for some rate r is transmitted during the t symbol coherence interval then there is a positive space time autocapacity c sub a such that for all r c sub a the block probability of error goes to zero as the pair t m spl rarr spl infin such that t m spl beta the autocoding effect occurs whether or not the propagation matrix is known to the receiver and c sub a nlog 1 spl rho in either case independently of spl beta where spl rho is the expected signal to noise ratio snr at each receiver antenna lower bounds on the cutoff rate derived from random unitary space time signals suggest that the autocoding effect manifests itself for relatively small values of t and m for example within a single coherence interval of duration t 16 for m 7 transmitter antennas and n 4 receiver antennas and an 18 db expected snr a total of 80 bits corresponding to rate r 5 can theoretically be transmitted with a block probability of error less than 10 sup 9 all without any training or knowledge of the propagation matrix

from random matrix theory to coding theory volume of a metric ball in unitary group volume estimates of metric balls in manifolds find diverse applications in information and coding theory in this paper new results for the volume of a metric ball in unitary group are derived via tools from random matrix theory the first result is an integral representation of the exact volume which involves a toeplitz determinant of bessel functions a simple but accurate limiting volume formula is then obtained by invoking szeg s strong limit theorem for large toeplitz matrices the derived asymptotic volume formula enables analytical evaluation of some coding theoretic bounds of unitary codes in particular the gilbert varshamov lower bound and the hamming upper bound on the cardinality as well as the resulting bounds on code rate and minimum distance are derived moreover bounds on the scaling law of code rate are found finally a closed form bound on the diversity sum relevant to unitary space time codes is obtained which was only computed numerically in the literature

precoded and vector ofdm robust to channel spectral nulls and with reduced cyclic prefix length in single transmit antenna systems the performance of orthogonal frequency division multiplexing ofdm systems may be degraded when intersymbol interference isi channels have spectral nulls also when isi channels have many taps the data rate overhead due to the insertion of the cyclic prefix is high we first propose a precoded ofdm system that may improve the performance of the ofdm systems for spectral null channels we also propose size k spl times x1 vector ofdm vofdm systems that reduce the cyclic prefix length by k times compared to the conventional ofdm systems the precoding scheme is simply to insert one or more zeros between each two sets of k consecutive information symbols although it can be generalized to a general form this precoding scheme may be able to remove the spectral nulls of an isi channel without knowing the isi channel when no zero is inserted between each two sets of k consecutive information symbols and only each k consecutive symbols are blocked together we obtain vofdm systems both theoretical performance analysis and simulation results are presented finally we compare the combination of the vofdm systems and the unitary matrix modulation with the conventional ofdm systems and the phase shift keying modulation where both differential noncoherent and coherent modulations and demodulations are considered

on the conjectures of su 3 and ab unitary space time codes proofs to the conjectures made by jing and hassibi on having fully diverse 3times3 su 3 and ab unitary space time codes are presented in this correspondence we first prove that the su 3 codes are fully diverse if and only if the design parameters p q r and s are all odd integers and in addition are relatively prime for the type i ab codes it is shown that full diversity can be achieved if and only if the integers p q r and s are relatively prime finally we show that such condition is also sufficient for having fully diverse type ii ab codes

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

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

brief paper event driven optimization based control of hybrid systems with integral continuous time dynamics in this paper we introduce a class of continuous time hybrid dynamical systems called integral continuous time hybrid automata icha for which we propose an event driven optimization based control strategy events include both external actions applied to the system and changes of continuous dynamics mode switches the icha formalism subsumes a number of hybrid dynamical systems with practical interest e g linear hybrid automata different cost functions including minimum time and minimum effort criteria and constraints are examined in the event driven optimal control formulation this is translated into a finite dimensional mixed integer optimization problem in which the event instants and the corresponding values of the control input are the optimization variables as a consequence the proposed approach has the advantage of automatically adjusting the attention of the controller to the frequency of event occurrence in the hybrid process a receding horizon control scheme exploiting the event based optimal control formulation is proposed as a feedback control strategy and proved to ensure either finite time or asymptotic convergence of the closed loop

parameter dependent quasi linear parabolic equations abstract in this work we are concerned with non linear reaction diffusion equations with principal part given by p laplacian and positive diffusion coefficient a l 0 a which has global attractors a we obtain some properties about the convergence of the solutions of these equations and show the upper semicontinuity of the attractors

asymptotic properties in parabolic problems dominated by a p laplacian operator with localized large diffusion abstract this paper is concerned with upper semicontinuity of the family of attractors associated with nonlinear reaction diffusion equations with principal part governed by a degenerate p laplacian in which the diffusion d blows up in localized regions inside the domain

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

a differential space time modulation scheme for correlated rayleigh fading channels performance analysis and design differential space time modulation dstm is an encoding technique for multiantenna systems that allows the receiver to detect the transmitted signals without the knowledge of the fading channels it can be viewed as an extension of the differential phase shift keying scheme in single antenna systems in this paper we investigate the performance of multiantenna systems employing dstm under spatially correlated rayleigh fading channels we present three expressions for calculating the pairwise error probability pep of the dstm scheme the first expression allows us to numerically calculate the exact pep the remaining two are closed form expressions of the exact pep at asymptotically high signal to noise ratios and the pep upper bound it is found that when the distance matrix is proportional to the identity matrix the error probability is determined by the channel correlation matrix and the initial transmitted code matrix based on the new pep upper bound we derive a criterion for optimizing the initial code matrix for this special case simulation results show that the performance of the differential space time coded systems can be significantly improved by designing the initial transmitted code matrix according to the proposed design criterion

signal constellations for quasi orthogonal space time block codes with full diversity space time block codes stbcs from orthogonal designs proposed by alamouti and tarokh jafarkhani calderbank have attracted considerable attention lately due to their fast maximum likelihood ml decoding and full diversity however the maximum symbol transmission rate of an stbc from complex orthogonal designs for complex signals is only 3 4 for three and four transmit antennas and it is difficult to construct complex orthogonal designs with rate higher than 1 2 for more than four transmit antennas recently jafarkhani tirkkonen boariu hottinen and papadias foschini proposed stbcs from quasi orthogonal designs where the orthogonality is relaxed to provide higher symbol transmission rates with the quasi orthogonal structure the quasi orthogonal stbcs still have a fast ml decoding but do not have the full diversity the performance of these codes is better than that of the codes from orthogonal designs at low signal to noise ratio snr but worse at high snr this is due to the fact that the slope of the performance curve depends on the diversity it is desired to have the quasi orthogonal stbcs with full diversity to ensure good performance at high snr in this paper we achieve this goal by properly choosing the signal constellations specifically we propose that half of the symbols in a quasi orthogonal design are chosen from a signal constellation set a and the other half of them are chosen from a rotated constellation e sup j spl phi a the resulting stbcs can guarantee both full diversity and fast ml decoding moreover we obtain the optimum selections of the rotation angles spl phi for some commonly used signal constellations simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high snrs

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

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

unitary space time group codes diversity sums from character tables diversity sum which is calculated from the frobenius norm of the difference of two distinct elements in a signal constellation is the significant parameter to predict a unitary space time constellation having good performance in low signal to noise ratio snr in this correspondence we propose a method to compute the diversity sum of a unitary group constellation using a character table our proposed analysis is simple requiring only a lookup of the character table we illustrate our method for the finite special linear groups sl 2 and compare codes with high diversity sum against fixed point free groups at low snr we also introduce the notion of a faithful group constellation that is one whose diversity sum is greater than 0 faithful group constellations may be obtained from any nontrivial character of a group we describe the method to do so in this correspondence and illustrate it with the example of the finite projective special linear group psl2

sphere packing bounds in the grassmann and stiefel manifolds applying the riemann geometric machinery of volume estimates in terms of curvature bounds for the minimal distance of packings codes in the grassmann and stiefel manifolds will be derived and analyzed in the context of space time block codes this leads to a monotonically increasing minimal distance lower bound as a function of the block length this advocates large block lengths for the code design

antenna selection for unitary space time modulation this correspondence studies receive antenna selection as for multiple antenna systems that employ unitary space time st signals where the channel state information csi is known neither at the transmitter nor at the receiver without csi at the receiver we perform as only at the receiver and the selection is based on a maximum norm criterion i e a subset of receive antennas that have the largest received signal power is chosen using a chernoff bound approach we present theoretical performance analysis based on the pairwise error probability pep and quantify the asymptotic performance at high signal to noise ratio snr by giving the diversity and coding gain expressions we prove that with no csi at the receiver the diversity gain with as is preserved for unitary st codes with full spatial diversity the same as the case with known csi as a concrete example for differential unitary st modulation with m 2 transmit antennas and n 2 receive antennas we have devised new excellent performing parametric codes based on the derived pep bound the new codes which are specifically designed for differential as systems outperform known differential codes when as is employed corroborating simulations validate our analysis and code design

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

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

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

generalized psk in space time coding a wireless communication system using multiple antennas promises reliable transmission under rayleigh flat fading assumptions design criteria and practical schemes have been presented for both coherent and noncoherent communication channels in this paper we generalize one dimensional 1 d phase shift keying psk signals and introduce space time constellations from generalized psk gpsk signals based on the complex and real orthogonal designs the resulting space time constellations reallocate the energy for each transmitting antenna and feature good diversity products consequently their performances are better than some of the existing comparable codes moreover since the maximum likelihood ml decoding of our proposed codes can be decomposed to 1 d psk signal demodulation the ml decoding of our codes can be implemented in a very efficient way

constellation mapping for space time matrix modulation with iterative demodulation decoding the mapping from binary sequences to space time matrices is an important issue in designing space time coded multiple antenna systems where different mapping schemes may lead to different bit error rate ber performance in this letter we use a binary switching algorithm to investigate the mappings of bit interleaved coded modulation with iterative demodulation decoding bicm id for space time modulation both coherent and noncoherent space time modulation in the cases of no a priori information and perfect a priori information of the coded bits for the demodulator are considered

well posed p laplacian problems with large diffusion abstract in this work we study the asymptotic behavior of p laplacian parabolic problems of the form u t d p u u p 2 u b u in a bounded smooth domain in r n and under neumann boundary conditions when the diffusion coefficient d becomes large we prove under suitable assumptions that the family of attractors behaves lower and upper semicontinuously as the diffusion increases to infinity