percolation in strongly correlated systems abstract we investigate the threshold percolation density pc in strongly correlated lattice systems the probability distribution of the system is the stationary state for a combined kawasaki and glauber dynamics the voter model with flips when the glauber rate goes to zero the pair correlation function of the system at any density decays in three dimensions as r 1 and does not decay at all in two dimensions using monte carlo calculations and finite size scaling we obtain information about pc as a function of the glauber rate percolation in gaussian fields on a lattice which have similar slow decay is also discussed

bit error rate of binary and quaternary dpsk signals with multiple differential feedback detection a differentially coherent detection scheme with improved bit error rate ber performance is presented for differentially encoded binary and quaternary phase shift keying psk modulation the improvement is based on using l symbol detectors with delays of 1 2 l symbol periods and on feeding back detected psk symbols exact formulas for the bit error probability are derived for the case that correct symbols are fed back the effect of symbol errors in the feedback path on the ber is determined by computer simulations

delayed decision feedback sequence estimation the authors delayed decision feedback sequence estimation ddfse for uncoded pam signals is considered estimates on the performance of the algorithm are given and simulation results are provided for several examples a more general form of ddfse applicable to coded modulation systems is also presented as an example detection of trellis coded qpsk quadrature phase shift keyed signals over intersymbol interference channels is discussed

a note on linear transformations which leave controllable multiinput descriptor systems controllable abstract consider a generalized linear dynamical system e x ax bu where x cn u cm and e a b are matrices of appropriate sizes with entries in c this system or the matrix triple e a b is called controllable if det e a is not a zero polynomial in and e a b is of full rank for all c 0 0 letf be a linear transformation on cn n cn m the linear space of all matrix pairs a b in an earlier paper mehrmann and krause attempted to prove that if f is of the form x at uxv and rank f e a b n for all c2 0 0 and all controllable systems e a b then u v are nonsingular matrix with v in some lower block triangular form in this paper we correct an error contained in this result and discuss whether the corrected result can be generalized in such a way that no restrictions are placed on the form of f

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

linear operators preserving certain equivalence relations originating in system theory abstract let f be c or r a finite dimensional linear time invariant system is described in state space form by xdot ax bu y cx du and is identified with the matrix 4 tuple a b c d where x f n u f m y f p and a b c d are matrices of appropriate sizes and with entries in f for fixed n m p let m be the linear space of all systems a b c d equivalence relations can be defined on m based on the possibility of changes of basis inthe state space the input space or the output space and the possibility of state feedback and or output feedback we characterize those nonsingular linear operators on m that satisfy x y whenever x y

linear preserver problems a brief introduction and some special techniques abstract linear preserver problems concern the characterization of linear operators on matrix spaces that leave certain functions subsets relations etc invariant the earliest papers on linear preserver problems date back to 1897 and a great deal of effort has been devoted to the study of this type of question since then we present a brief picture of the subject aiming at giving a gentle introduction to the reader then we describe some techniques used in our recent papers on this type of problem

closed form solutions to the nonhomogeneous yakubovich transpose matrix equation abstract the nonhomogeneous yakubovich transpose matrix equation x a x t b c y r which contains the well known kalman yakubovich transpose matrix equation and general discrete lyapunov transpose matrix equation as special cases has many important applications in control system theory this study presents two methods to obtain the closed form solutions of the nonhomogeneous yakubovich transpose matrix equation moreover the equivalent forms of the solutions are provided and one of the solutions is established with the controllability matrix the observability matrix and symmetric operator matrix

percolation in the harmonic crystal and voter model in three dimensions we investigate the site percolation transition in two strongly correlated systems in three dimensions the massless harmonic crystal and the voter model in the first case we start with a gibbs measure for the potential u j2 summation operatorx y phi x phi y 2 x y z3 j 0 and phi x r a scalar height variable and define occupation variables rhoh x 1 0 for phi x h h the probability p of a site being occupied is then a function of h in the voter model we consider a stationary measure in which each site is either occupied or empty with probability p in both cases the truncated pair correlation of the occupation variables g x y decays asymptotically as mid x y 1 using some monte carlo simulation methods and finite size scaling we find accurate values of pc as well as the critical exponents for these systems the latter are different from that of independent percolation in d 3 as expected from the work of weinrib and halperin wh for the percolation transition of systems with g r approximately r a phys rev b 27 413 1983 in particular the correlation length exponent nu is very close to the predicted value of 2 supporting the conjecture by wh that nu 2 a is exact

the phase of a vector perturbed by gaussian noise and differentially coherent receivers some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by gaussian noise it is shown that for large signal to noise ratio the asymptotic distribution of the phase is of the tikhonov type this framework is then used for the synthesis of differentially coherent receiver structures one for m ary phase shift keying mpsk and the other for minimum shift keying msk the first structure bridges the performance gap between coherent and differentially coherent demodulation of mpsk the msk receiver uses matched filtering with differential demodulation

reduced state sequence estimation with set partitioning and decision feedback a reduced state sequence estimator for linear intersymbol interference channels is described the estimator uses a conventional viterbi algorithm with decision feedback to search a reduced state subset trellis that is constructed using set partitioning principles the complexity of maximum likelihood sequence estimation mlse due to the length of the channel memory and the size of the signal set is systematically reduced an error probability analysis shows that a good performance complexity tradeoff can be obtained in particular the results indicate that the required complexity to achieve the performance of mlse is independent of the size of the signal set for large enough signal sets simulation results are provided for two partial response systems a simple technique for quadrature partial response signaling qprs is described that eliminates the quasicatastrophic nature of the ml trellis

a unified framework for tree search decoding rediscovering the sequential decoder we consider receiver design for coded transmission over linear gaussian channels we restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search clps here a tree search framework for solving the clps is adopted in our framework the clps algorithm is decomposed into the preprocessing and tree search stages the role of the preprocessing stage is to expose the tree structure in a form matched to the search stage we argue that the forward and feedback matrix filters of the minimum mean square error decision feedback equalizer mmse dfe are instrumental for solving the joint detection and decoding problem in a single search stage it is further shown that mmse dfe filtering allows for solving underdetermined linear systems and using lattice reduction methods to diminish complexity at the expense of a marginal performance loss for the search stage we present a generic method based on the branch and bound bb algorithm and show that it encompasses all existing sphere decoders as special cases the proposed generic algorithm further allows for an interesting classification of tree search decoders sheds more light on the structural properties of all known sphere decoders and inspires the design of more efficient decoders in particular an efficient decoding algorithm that resembles the well known fano sequential decoder is identified the excellent performance complexity tradeoff achieved by the proposed mmse dfe fano decoder is established via simulation results and analytical arguments in several multiple input multiple output mimo and intersymbol interference isi scenarios

a complete characterization of orbit closures of controllable singular systems under restricted system equivalence in this paper properties of the orbit space of controllable generalized state space systems modulo restricted system equivalence are derived in particular it is shown that this space is a smooth quasiprojective variety of dimension nm then the possible degenerations of controllable systems under transformations of restricted system equivalence are characterized and it is proved that every noncontrollable system can be approximated by a family of controllable systems that belong to a single equivalence class in the single input case this class is uniquely determined whereas in the multivariable case a noncontrollable system may lie in the boundary of finitely or even infinitely many equivalence classes

linear preservers of controllability and or observability abstract consider a linear control differential equations system x ax bu y cx du where x c n u c m y c p and a b c d are matrices of appropriate sizes with entries in c this system or the matrix pair a b or the matrix 4 tuple a b c d is called controllable if rank a i b n for all 0 let be a linear transformation on c n n m the linear space of all matrix pairs a b then is said to preserve controllability if it maps controllable matrix pairs to controllable matrix pairs we prove that preserves controllability if and only if a b sas 1 sbf sbr f a b i 0 where is a nonzero scalar s r are nonsingular and f is a linear functional based on this result we also find all linear mappings on the linear space of all matrix 4 tuples a b c d which preserve controllability characterizations of linear preservers of observability a concept dual to controllability hence follow some variations of the above problems are also discussed

toward solution of matrix equation x af x b c abstract this paper studies the solvability existence of unique solution closed form solution and numerical solution of matrix equation x af x b c with f x x t f x x and f x x h where x is the unknown it is proven that the solvability of these equations is equivalent to the solvability of some auxiliary standard stein equations in the form of w a w b c where the dimensions of the coefficient matrices a b and c are the same as those of the original equation closed form solutions of equation x af x b c can then be obtained by utilizing standard results on the standard stein equation on the other hand some generalized stein iterations and accelerated stein iterations are proposed to obtain numerical solutions of equation x af x b c necessary and sufficient conditions are established to guarantee the convergence of the iterations

a canonical form for controllable singular systems abstract a new canonical form for the action of restricted system equivalence on controllable singular systems is given the construction of this form is based on the weierstrass decomposition of the singular system into a slow and a fast subsystem both subsystems are transformed into hermite canonical form the resulting hermite canonical form for singular systems has a particularly simple structure and is expected to be useful for e g identification purposes continuity properties of the hermite form are investigated and the nonexistence of a globally defined continuous canonical form for controllable singular systems is shown

decision feedback differential detection of mdpsk for flat rayleigh fading channels in this paper decision feedback differential detection df dd of m ary differential phase shift keying mdpsk signals which has been introduced previously for the additive white gaussian noise awgn channel by leib et al 1988 and edbauer 1992 is extended to flat rayleigh fading channels the corresponding df dd metric is derived from the multiple symbol detection msd metric and for genie aided df dd an exact expression for the bit error rate ber of qdpsk m 4 is calculated furthermore the dependence of ber on the power spectrum of the fading process is investigated for feedback filters of infinite order it is shown that in this case for ideally bandlimited fading processes the error floor of conventional differential detection dd can be removed entirely simulation results confirm that both msd and df dd with feedback filters of finite order can reduce the error floor of conventional dd significantly df dd thereby causes considerably less computational load

similarity preserving linear maps on matrices abstract we determine all similarity preserving linear maps on the space of n x n complex matrices and all unitary equivalence preserving linear maps on the space of n x n hermitian matrices sub majorization preserving linear maps on hermitian matrices are also determined

on noncoherent receivers for dstm in spatially correlated fading in this letter we derive a multiple symbol differential detection msdd and a novel msdd based decision feedback differential detection ms dfdd receiver for differential space time modulation transmitted over spatially correlated multiple input multiple output fading channels we show that ms dfdd outperforms previously proposed dfdd schemes that are based on scalar and vector prediction sp dfdd and vp dfdd in addition we prove that at high signal to noise ratio snr vp dfdd is equivalent to sp dfdd and thus fails to properly exploit the spatial fading correlations

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

designing low complexity near optimal multiple symbol detectors for impulse radio uwb systems multiple symbol detection has recently caught attention in ultrawideband uwb communications because of its high performance without requiring explicit channel estimation in this context the generalized likelihood ratio test glrt for multiple symbol detection problem is developed to jointly detect multiple symbols which exhibits considerable error performance improvement over transmitted reference transmissions methods unfortunately the glrt is a boolean quadratic programming bqp problem which is generally nondeterministic polynomial hard np hard in this paper we propose two near optimal detectors with polynomial complexity the first detector performs semidefinite relaxation to approximately solve the bqp problem called sdp msd the second detector is based on a sphere based relaxation of the bqp problem we refer to this as modified unconstrained relaxation multiple symbol detector mur msd both detectors achieve near optimal performance while the sdp msd performs slightly better than the mur msd at the price of higher computational complexity furthermore the mur msd can be treated as a further nontight relaxation of sdp msd simulations are utilized to validate our findings and to demonstrate performance robustness to multiaccess interference

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

decision feedback differential detection in impulse radio ultra wideband systems in this paper we present decision feedback differential detection df dd schemes for autocorrelation based detection in impulse radio ultra wideband ir uwb systems a signaling scheme regarded as a promising candidate in particular for low complexity wireless sensor networks to this end we first discuss ideal noncoherent sequence estimation and approximations thereof based on block wise multiple symbol differential detection msdd and the viterbi algorithm va from the perspective of tree search trellis decoding exploiting relations well known from tree search decoding we are able to derive the novel decision feedback differential detection df dd schemes a comprehensive comparison with respect to performance and complexity of the presented schemes in a typical ir uwb scenario reveals along with novel insights in techniques for complexity reduction of the sphere decoder applied for msdd that sorted df dd achieves close to optimum performance at very low and in particular constant receiver complexity

linear transformations which leave controllable multiinput descriptor systems controllable abstract a general linear descriptor system e itx ax bu where e a c n n b c n m x c n u c m e singular is called controllable if rank e a b n for all 0 0 c let f c n n m c n n m be a linear transformation form f x cxd we characterize all such linear transformations that leave the set c e a b rank e a b n 0 0 c invariant and show that only the well known transformations that leave controllability invariant can occur

scaling corrections site percolation and ising model in three dimensions using finite size scaling techniques we obtain accurate results for critical quantities of the ising model and the site percolation in three dimensions we pay special attention to parametrizing the corrections to scaling which is necessary to bring the systematic errors below the statistical ones

linear operators preserving t congruence on matrices abstract two complex or real square matrices a and b are said to be t congruent if there exists a nonsingular matrix s such that a sbs t if a and b are complex respectively real and s is unitary respectively real orthogonal we say that they are unitarily t congruent respectively real orthogonally congruent in this note we obtain characterizations of linear operators on various matrix spaces that preserve t congruence results and problems concerning unitary t congruence or orthogonal t congruence are discussed

similarity and block similarity we present some equivalent characterizations of the block similarity of matrix pairs with an application to a characterization of the similarity of two square matrices also a survey of some generalizations of properties of the invariants of similarity to the invariants of block similarity is presented