asymptotically optimal blind fractionally spaced channel estimation and performance analysis when the received data are fractionally sampled the magnitude and phase of most linear time invariant fir communications channels can be estimated from second order output only statistics we present a general cyclic correlation matching algorithm for known order fir blind channel identification that has closed form expressions for calculating the asymptotic variance of the channel estimates we show that for a particular choice of weights the weighted matching estimator yields at least for large samples the minimum variance channel estimator among all unbiased estimators based on second order statistics furthermore the matching approach unlike existing methods provides a useful estimate even when the channel is not uniquely identifiable from second order statistics

the gaussian assumption in second order estimation problems in digital communications this paper deals with the goodness of the gaussian assumption when designing second order blind estimation methods in the context of digital communications the low and high signal to noise ratio snr asymptotic performance of the maximum likelihood estimator derived assuming gaussian transmitted symbols is compared with the performance of the optimal second order estimator which exploits the actual distribution of the discrete constellation the asymptotic study concludes that the gaussian assumption leads to the optimal second order solution if the snr is very low or if the symbols belong to a multilevel constellation such as quadrature amplitude modulation qam or amplitude phase shift keying apsk on the other hand the gaussian assumption can yield important losses at high snr if the transmitted symbols are drawn from a constant modulus constellation such as phase shift keying psk or continuous phase modulations cpm these conclusions are illustrated for the problem of direction of arrival doa estimation of multiple digitally modulated signals

determining the small solutions to s unit equations in this paper we generalize the method of wildanger for finding small solutions to unit equations to the case of s unit equations the method uses a minor generalization of the lll based techniques used to reduce the bounds derived from transcendence theory followed by an enumeration strategy based on the fincke pohst algorithm the method used reduces the computing time needed from mips years down to minutes

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

biased random walk on the trace of biased random walk on the trace of we study the behaviour of a sequence of biased random walks x scriptscriptstyle i i ge 0 on a sequence of random graphs where the initial graph is mathbb z d and otherwise the graph for the ith walk is the trace of the i 1 st walk the sequence of bias vectors is chosen so that each walk is transient we prove the aforementioned transience and a law of large numbers and provide criteria for ballisticity and sub ballisticity we give examples of sequences of biases for which each x scriptscriptstyle i i ge 1 is transient but not ballistic and the limiting graph is an infinite simple self avoiding path we also give examples for which each x scriptscriptstyle i i ge 1 is ballistic but the limiting graph is not a simple path

a linear programming receiver for blind detection of full rate space time block codes we present a new approach to the blind detection of full rate space time block coded transmissions our method is based on linear programming and is globally convergent we exploit the implicit structure of space time block codes to cast the problem as linear programming to be solved efficiently unlike several known methods the proposed technique is applicable to full rate space time block codes such as the popular alamouti orthogonal code and the quasi orthogonal space time code moreover we utilize the code structure of these full rate codes to achieve simultaneous detection of all coded data streams without relying on successive schemes that are prone to error propagation for orthogonal space time codes our algorithm allows near maximum likelihood detection of orthogonal codes without channel knowledge we also can generalize the application of the proposed receiver to be used with nonorthogonal codes our proposed algorithm can provide performance competitive with existing techniques without imposing any conditions on the number of receive antennas

asymptotically minimum variance second order estimation for noncircular signals with application to doa estimation this paper addresses asymptotically minimum variance amv algorithms within the class of algorithms based on second order statistics for estimating direction of arrival doa parameters of possibly spatially correlated even coherent narrowband noncircular sources impinging on arbitrary array structures to reduce the computational complexity due to the nonlinear minimization required by the matching approach the covariance matching estimation technique comet is included in the algorithm numerical examples illustrate the performance of the amv algorithm

blind channel identifiability for generic linear space time block codes linear space time block codes stbcs have proven their effectiveness in performance improvement of wireless multiple input multiple output communication systems their successful decoding however requires reliable channel knowledge at the receiver in this paper we present a semiblind channel estimation method for linear stbc without the usual code orthogonality condition we provide a set of identification conditions that are mostly verifiable a priori in terms of code parameters and antenna array configuration we also present a simple channel estimation algorithm finally we provide simulation results that illustrate the performance of the proposed scheme

second order parameter estimation this work provides a general framework for the design of second order blind estimators without adopting any approximation about the observation statistics or the a priori distribution of the parameters the proposed solution is obtained minimizing the estimator variance subject to some constraints on the estimator bias the resulting optimal estimator is found to depend on the observation fourth order moments that can be calculated analytically from the known signal model unfortunately in most cases the performance of this estimator is severely limited by the residual bias inherent to nonlinear estimation problems to overcome this limitation the second order minimum variance unbiased estimator is deduced from the general solution by assuming accurate prior information on the vector of parameters this small error approximation is adopted to design iterative estimators or trackers it is shown that the associated variance constitutes the lower bound for the variance of any unbiased estimator based on the sample covariance matrix the paper formulation is then applied to track the angle of arrival aoa of multiple digitally modulated sources by means of a uniform linear array the optimal second order tracker is compared with the classical maximum likelihood ml blind methods that are shown to be quadratic in the observed data as well simulations have confirmed that the discrete nature of the transmitted symbols can be exploited to improve considerably the discrimination of near sources in medium to high snr scenarios

widely linear estimation with complex data mean square estimation of complex and normal data is not linear as in the real case but widely linear the purpose of the paper is to calculate the optimum widely linear mean square estimate and to present its main properties the advantage with respect to the linear procedure is especially analyzed

blind recognition of linear space time block codes a likelihood based approach blind recognition of communication parameters is a research topic of high importance for both military and civilian communication systems numerous studies about carrier frequency estimation modulation recognition as well as channel identification are available in literature this paper deals with the blind recognition of the space time block coding stbc scheme used in multiple input multiple output mimo communication systems assuming there is perfect synchronization at the receiver side this paper proposes three maximum likelihood ml based approaches for stbc classification the optimal classifier the second order statistic sos classifier and the code parameter cp classifier while the optimal and the sos approaches require ideal conditions the cp classifier is well suited for the blind context where the communication parameters are unknown at the receiver side our simulations show that this blind classifier is more easily implemented and yields better performance than those available in literature

blind channel estimation using the second order statistics asymptotic performance and limitations we consider the asymptotic performance and fundamental limitations of the class of blind estimators that use second order statistics an achievable lower bound of the asymptotic normalized mean square error anmse is derived it is shown that the achievable anmse is lower bounded by the condition number of the jacobian matrix of the correlation function with respect to the channel parameters it is shown next that the jacobian matrix is singular if and only if the subchannels share common conjugate reciprocal zeros this condition is different from the existing channel identification conditions asymptotic performance of some existing eigenstructure based algorithms is analyzed closed form expressions of anmse and their lower bounds are derived for the least squares ls and the subspace ss blind channel estimators when there are two subchannels asymptotic efficiency of ls ss algorithms is also evaluated showing that significant performance improvement is possible when the information of the source correlation is exploited

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

dislocation kink chain and multiphase periodic processes in the bounded sine gordon system a finite chain of dislocation kinks in a crystal is considered as a string in the peierls potential its behaviour is discussed in terms of multiphase periodic processes in the sine gordon system under adequate boundary conditions it has been stated that in a particular case dislocation segment containing kinks of the same width the oscillations of the kink chain may be described by the jacobi elliptic functions whereas in a more general case dislocation segment containing kinks of different width the oscillations of the kink chain should be described by the riemann theta functions the presented description is thus a generalisation of that reported by kovalev 1979 for the dynamics of a single frenkel kontorova dislocation in a one dimensional crystal with fixed boundaries a soliton limit of the kink chain behaviour is also briefly discussed

mimo detection for high order qam based on a gaussian tree approximation this paper proposes a new detection algorithm for mimo communication systems employing high order qam constellations the factor graph that corresponds to this problem is very loopy in fact it is a complete graph hence a straightforward application of the belief propagation bp algorithm yields very poor results our algorithm is based on an optimal tree approximation of the gaussian density of the unconstrained linear system the finite set constraint is then applied to obtain a cycle free discrete distribution simulation results show that even though the approximation is not directly applied to the exact discrete distribution applying the bp algorithm to the cycle free factor graph outperforms current methods in terms of both performance and complexity the improved performance of the proposed algorithm is demonstrated on the problem of mimo detection

biased random walk on critical galton watson trees conditioned to survive we consider the biased random walk on a critical galton watson tree conditioned to survive and confirm that this model with trapping belongs to the same universality class as certain one dimensional trapping models with slowly varying tails indeed in each of these two settings we establish closely related functional limit theorems involving an extremal process and also demonstrate extremal aging occurs

the icosian code and the e_8 lattice a new 4 times 4 space time code with nonvanishing determinant this paper introduces a new rate 2 full diversity space time code for four transmit antennas and one receive antenna the 4times4 codeword matrix consists of four 2times2 alamouti blocks with entries from q i radic5 and these blocks can be viewed as quaternions which in turn represent rotations in r 3 the alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron this algebraic structure is different from the golden code but the complex entries are taken from a common underlying field the minimum determinant is bounded below by a constant that is independent of the signal constellation and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the e 8 lattice

blind ml detection of orthogonal space time block codes identifiability and code construction the blind maximum likelihood ml detection of a general space time block code stbc is considered a challenging implementation problem recent work has revealed that for the orthogonal stbcs ostbcs their special code structures can be exploited to formulate highly effective blind ml based algorithms attracted by this realization merit this paper investigates the blind ml identifiability of ostbcs with an emphasis on the binary psk bpsk and quaternary psk qpsk constellations we find a class of ostbcs called the nonrotatable ostbcs that can be uniquely identified up to a sign uiuts almost surely under a few mild assumptions for example for an independently distributed rayleigh channel with any number of receiver antennas a nonrotatable ostbc can be uiuts with probability 1 while this identifiability looks appealing already we further examine a subclass of nonrotatable ostbcs called the nonintersecting subspace nis ostbcs we prove that nis ostbcs are uiuts for any nonzero channel however nis ostbcs are not available in the existing literature to fill this gap we devise a code construction procedure that can convert any bpsk or qpsk ostbc to an nis ostbc

quaternion ica from second order statistics this paper addresses the independent component analysis ica of quaternion random vectors in particular we focus on the gaussian case and therefore only consider the quaternion second order statistics sos which are given by the covariance matrix and three complementary covariance matrices first we derive the necessary and sufficient conditions for the identifiability of the quaternion ica model which are based on the definition of the properness profile of a quaternion random variable and more specifically on the concept of rotationally equivalent properness profiles second we show that the maximum likelihood ml approach to the quaternion ica problem reduces to the approximated joint diagonalization ajd of the sample mean estimates of the covariance and complementary covariance matrices unlike the complex case these four matrices cannot be simultaneously diagonalized in general and we have to resort to a particular ajd algorithm the proposed technique which can be seen as a quasi newton method is based on the local approximation of the nonconvex ml ica cost function a measure of the entropy loss due to the residual correlation among the estimated quaternion sources and it provides a satisfactory solution of the quaternion ica model the performance of the proposed quaternion ml ica algorithm as well as its relationship to the identifiability conditions are illustrated by means of several numerical examples

correlation matching approaches for blind ostbc channel estimation in this paper the problem of blind channel estimation under orthogonal space time block coded ostbc transmissions is solved by minimizing some distance measure between the theoretical and estimated correlation matrices of the observations specifically the minimization of the euclidean distance and the kullback leibler divergence leads respectively to the euclidean correlation matching ecm and kullback correlation matching kcm criteria the proposed techniques exploit the knowledge of the source correlation matrix to unambiguously recover the multiple input multiple output mimo channel furthermore due to the orthogonality properties of ostbcs both the ecm and kcm criteria result in closed form solutions in particular the channel estimate is given by the principal eigenvector of a matrix which is obtained from the estimated correlation matrix of the observations modified by the code matrices and a set of weights in the ecm case the weights are fixed and equal to the eigenvalues of the source correlation matrix whereas the kcm weights depend on both the signal to noise ratio snr and the source eigenvalues additionally we show that the proposed approaches are equivalent in the low snr regime whereas in the high snr regime the kcm criterion is asymptotically equivalent to the relaxed blind maximum likelihood ml decoder finally the performance of the proposed criteria is illustrated by means of some numerical examples

semiblind multiuser mimo channel estimation using capon and music techniques channel state information csi is required at the receiver side of multiple input multiple output mimo systems for decoding space time codes in this paper new semiblind techniques are developed to jointly estimate the receiver csi of multiple multiantenna transmitters that use orthogonal space time block codes ostbcs the proposed techniques are based on the extension of the concepts of the popular capon and music spectral estimators to the problem of multiuser channel estimation our methods blindly estimate the subspace that contains the user channel matrices and then use only a few training symbol blocks to extract the user csi from this subspace it is demonstrated that in addition to improving the bandwidth efficiency the proposed techniques offer better channel estimation accuracy as compared with the standard nonblind least squares ls channel estimation method moreover it is shown that using the proposed capon and music based semiblind channel estimators along with the coherent maximum likelihood ml or the minimum variance mv multiuser mimo receivers results in a substantially better performance as compared with the case when the standard ls channel estimates are used

the speed of biased random walk on percolation clusters we consider biased random walk on supercritical percolation clusters in 2 we show that the random walk is transient and that there are two speed regimes if the bias is large enough the random walk has speed zero while if the bias is small enough the speed of the random walk is positive

detection and estimation of improper complex random signals nonstationary complex random signals are in general improper not circularly symmetric which means that their complementary covariance is nonzero since the karhunen loeve k l expansion in its known form is only valid for proper processes we derive the improper version of this expansion it produces two sets of eigenvalues and improper observable coordinates we then use the k l expansion to solve the problems of detection and estimation of improper complex random signals in additive white gaussian noise we derive a general result comparing the performance of conventional processing which ignores complementary covariances with processing that takes these into account in particular for the detection and estimation problems considered we find that the performance gain as measured by deflection and mean squared error mse respectively can be as large as a factor of 2 in a communications example we show how this finding generalizes the result that coherent processing enjoys a 3 db gain over noncoherent processing

random walk on the range of random walk we study the random walk x on the range of a simple random walk on d in dimensions d 4 when d 5 we establish quenched and annealed scaling limits for the process x which show that the intersections of the original simple random walk path are essentially unimportant for d 4 our results are less precise but we are able to show that any scaling limit for x will require logarithmic corrections to the polynomial scaling factors seen in higher dimensions furthermore we demonstrate that when d 4 similar logarithmic corrections are necessary in describing the asymptotic behavior of the return probability of x to the origin

biased random walks on galton watson trees we consider random walks with a bias toward the root on the family tree t of a supercritical galton watson branching process and show that the speed is positive whenever the walk is transient the corresponding harmonic measures are carried by subsets of the boundary of dimension smaller than that of the whole boundary when the bias is directed away from the root and the extinction probability is positive the speed may be zero even though the walk is transient the critical bias for positive speed is determined

multiple addition theorem for discrete and continuous nonlinear problems the addition relation for the riemann theta functions and for its limits which leads to the appearance of exponential functions in soliton type equations is discussed the form of addition property presented resolves itself to the factorization of the n tuple product of the shifted functions and it seems to be useful for analysis of soliton type continuous and discrete processes in the n 1 space time a close relation with the natural generalization of bi and tri linear operators into multiple linear operators concludes the paper

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

slow movement of a random walk on the range of a random walk in the presence of an external field in this article a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions d ge 5 this demonstrates that unlike in the supercritical percolation setting a slowdown effect occurs as soon as a non trivial bias is introduced the proof applies a decomposition of the underlying simple random walk path at its cut times to relate the associated biased random walk to a one dimensional random walk in a random environment in sinai s regime via this approach a corresponding aging result is also proved

closed form blind mimo channel estimation for orthogonal space time block codes in this paper a new computationally simple approach to blind decoding of orthogonal space time block codes ostbcs is proposed using specific properties of ostbcs the authors approach estimates the channel matrix in a closed form and in a fully blind fashion this channel estimate is then used in the maximum likelihood ml receiver to decode the information symbols the proposed estimation technique provides consistent channel estimates and as a result the performance of the authors blind ml receiver approaches that of the coherent ml receiver which exploits the exact channel state information csi simulation results demonstrate the performance improvements achieved by the proposed blind decoding algorithm relative to the popular differential space time modulation scheme

phase transition for the speed of the biased random walk on the supercritical percolation cluster we prove the sharpness of the phase transition for the speed in biased random walk on the supercritical percolation cluster on d that is for each d 2 and for any supercritical parameter p pc we prove the existence of a critical strength for the bias such that below this value the speed is positive and above the value it is zero we identify the value of the critical bias explicitly and in the subballistic regime we find the polynomial order of the distance moved by the particle each of these conclusions is obtained by investigating the geometry of the traps that are most effective at delaying the walk a key element in proving our results is to understand that on large scales the particle trajectory is essentially one dimensional we prove such a dynamic renormalization statement in a much stronger form than was previously known 2013 wiley periodicals inc

a blind multichannel identification algorithm robust to order overestimation active research in blind single input multiple output simo channel identification has led to a variety of second order statistics based algorithms particularly the subspace ss and the linear prediction lp approaches the ss algorithm shows good performance when the channel output is corrupted by noise and available for a finite time duration however its performance is subject to exact knowledge of the channel order which is not guaranteed by current order detection techniques on the other hand the linear prediction algorithm is sensitive to observation noise whereas its robustness to channel order overestimation is not always verified when the channel statistics are estimated we propose a new second order statistics based blind channel identification algorithm that is truly robust to channel order overestimation i e it is able to accurately estimate the channel impulse response from a finite number of noisy channel measurements when the assumed order is arbitrarily greater than the exact channel order another interesting feature is that the identification performance can be enhanced by increasing a certain smoothing factor moreover the proposed algorithm proves to clearly outperform the lp algorithm these facts are justified theoretically and verified through simulations

blind ml detection of orthogonal space time block codes efficient high performance implementations orthogonal space time block codes ostbcs have attracted much attention owing to their simple code construction maximal diversity gain and low maximum likelihood ml detection complexity when channel state information csi is available at the receiver this paper addresses the problem of ml ostbc detection with unknown csi focusing on the binary and quaternary psk constellations we show that blind ml ostbc detection can be simplified to a boolean quadratic program bqp from an optimization viewpoint the bqp is still a computationally hard problem and we propose two alternatives for dealing with this inherent complexity first we consider the semidefinite relaxation sdr approach which leads to a suboptimal but accurate blind ml detection algorithm with an affordable worst case computational cost we also consider the sphere decoding approach which leads to an exact blind ml detection algorithm that remains computationally expensive in the worst case but generally incurs a reasonable average computational cost for the two algorithms we study implementation methods that can significantly reduce the computational complexity simulation results indicate that the two blind ml detection algorithms are competitive in that the bit error performance of the two algorithms is almost the same and is noticeably better than that of some other existing blind detectors moreover numerical studies show that the sdr algorithm provides better complexity performance than the sphere decoder in the worst case sense and vice versa in the average sense

on the anisotropic walk on the supercritical percolation cluster we investigate in this work the asymptotic behavior of an anisotropic random walk on the supercritical cluster for bond percolation on d d 2 in particular we show that for small anisotropy the walk behaves in a ballistic fashion whereas for strong anisotropy the walk is sub diffusive for arbitrary anisotropy we also prove the directional transience of the walk and construct a renewal structure

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

performance of sphere decoding of block codes a sphere decoder searches for the closest lattice point within a certain search radius the search radius provides a tradeoff between performance and complexity we focus on analyzing the performance of sphere decoding of linear block codes we analyze the performance of soft decision sphere decoding on awgn channels and a variety of modulation schemes a hard decision sphere decoder is a bounded distance decoder with the corresponding decoding radius we analyze the performance of hard decision sphere decoding on binary and q ary symmetric channels an upper bound on the performance of maximum likelihood decoding of linear codes defined over fq e g reed solomon codes and transmitted over q ary symmetric channels is derived and used in the analysis we then discuss sphere decoding of general block codes or lattices with arbitrary modulation schemes the tradeoff between the performance and complexity of a sphere decoder is then discussed

soft quasi maximum likelihood detection for multiple antenna wireless channels the paper addresses soft maximum likelihood ml detection for multiple antenna wireless communication channels we propose a soft quasi ml detector that maximizes the log likelihood function by deploying a semi definite relaxation sdr given perfect channel state information at the receiver the quasi ml sdr detector closely approximates the performance of the optimal ml detector in both coded and uncoded multiple input multiple output mimo channels with quadrature phase shift keying qpsk modulation and frequency flat rayleigh fading the complexity of the quasi ml sdr detector is much less than that of the optimal ml detector thus offering more favorable performance complexity characteristics in contrast to the existing sphere decoder the new quasi ml detector enjoys guaranteed polynomial worst case complexity the two detectors exhibit quite comparable performance in a variety of ergodic qpsk mimo channels but the complexity of the quasi ml detector scales better with increasing number of transmit and receive antennas especially in the region of low signal to noise ratio snr

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

on the blind identifiability of orthogonal space time block codes from second order statistics in this paper the conditions for blind identifiability from second order statistics sos of multiple input multiple output mimo channels under orthogonal space time block coded ostbc transmissions are studied the main contribution of the paper consists in the proof that assuming more than one receive antenna any ostbc with a transmission rate higher than a given threshold which is inversely proportional to the number of transmit antennas permits the blind identification of the mimo channel from sos additionally it has been proven that any real ostbc with an odd number of transmit antennas is identifiable and that any ostbc transmitting an odd number of real symbols permits the blind identification of the mimo channel regardless of the number of receive antennas which extends previous identifiability results and suggests that any nonidentifiable ostbc can be made identifiable by slightly reducing its code rate the implications of these theoretical results include the explanation of previous simulation examples and from a practical point of view they show that the only nonidentifiable ostbcs with practical interest are the alamouti codes and the real square orthogonal design with four transmit antennas simulation examples and further discussion are also provided

reduced and fixed complexity variants of the lll algorithm for communications the lenstra lenstra lovasz lll algorithm is a popular lattice reduction algorithm in communications in this paper variants of the lll algorithm with either reduced or fixed complexity are proposed and analyzed specifically the use of effective lll reduction for lattice decoding is presented where size reduction is only performed for pairs of consecutive basis vectors its average complexity measured by the number of floating point operations and averaged over i i d standard normal lattice bases is shown to be o n 3 log n where n is the lattice dimension this average complexity is an order lower than previously thought to address the issue of variable complexity of the lll algorithm two fixed complexity approximations are proposed one is fixed complexity effective lll for which the first vector of the basis is proven to be bounded in length the other is fixed complexity lll with deep insertion which is shown to be closely related to the well known v blast algorithm such fixed complexity structures are much desirable in hardware implementation since they allow straightforward constant throughput implementation

equalization and semi blind channel estimation for space time block coded signals over a frequency selective fading channel in this paper we investigate the equalization and channel identification for space time block coded signals over a frequency selective multiple input multiple output mimo channel the equalization has been considered by taking into account the cyclostationarity of space time block coded signals the minimum mean square error mmse solutions have been derived for the linear and decision feedback df equalizers the channel estimation is required for the equalization with known symbols as pilot symbols mimo channels can be estimated in addition due to the redundancy induced by space time block code it is possible to identify mimo channels blindly using the subspace method we consider both blind and semi blind channel estimation for mimo channels it is shown that the semi blind channel estimate has fewer estimation errors and it results in less bit error rate performance degradation of the mmse linear and df equalizers

the limit distribution of sinai s random walk in random environment abstract recently sinai proved that if x n is a one dimensional random walk in random environment which is recurrent then log n 2 x n converges in distribution here we calculate the limit distribution explicitly

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

solitons and wavetrains unified approach the direct employment of the t function defined as a limiting transformation of the riemann theta function leading to a system of algebraic dispersion equations yields solutions of some nonlinear partial differential equations in the form of solitons on a background of quasi periodic waves pure solitons and pure quasi periodic solutions appear as particular cases the method is illustrated by the example of the kdv equation and is also compared with the hirota bilinear operator technique

biased random walks on galton watson trees with leaves we consider a biased random walk xn on a galton watson tree with leaves in the sub ballistic regime we prove that there exists an explicit constant 0 1 depending on the bias such that xn is of order n denoting n the hitting time of level n we prove that n n1 is tight moreover we show that n n1 does not converge in law at least for large values of we prove that along the sequences n k k n n1 converges to certain infinitely divisible laws key tools for the proof are the classical harris decomposition for galton watson trees a new variant of regeneration times and the careful analysis of triangular arrays of i i d heavy tailed random variables

on the diversity multiplexing tradeoff under groupwise successive interference cancelation in this paper we study the diversity multiplexing tradeoff assuming groupwise successive interference cancelation gsic gsic with layered codes in multiple input multiple output mimo can vary from the plain sic to the maximum likelihood ml decoding according to the group sizes thus is flexible in both complexity and performance the maximum group size is a dominating factor for the computation complexity of gsic when the processing complexity is polynomially dependent on the group size with a high order in this paper we show the tradeoff among the maximum group size diversity gain and multiplexing gain gdmt under the gsic and under the gsic combined with antenna selection gsicas for a given group size bound c we show that the number of groups achieving the optimal dmt under the gsic with selected transmit antennas is equal to c and a larger group should have a higher priority in decoding order the optimal grouping is obtained in a systematic way based on these results we find a limited set of groupings that contains the grouping achieving the optimal gdmt under gsic and under gsicas the optimal multiplexing gain allocation for the optimal grouping is then found systematically and efficiently within the limited set

eigenvalue based spectrum sensing of orthogonal space time block coded signals we consider spectrum sensing of signals encoded with an orthogonal space time block code ostbc we propose a cfar detector based on knowledge of the eigenvalue multiplicities of the covariance matrix which are inherent owing to the ostbc and derive theoretical performance bounds in addition we show that the proposed detector is robust to a carrier frequency offset and propose a detector that deals with timing synchronization using the detector for the synchronized case as a building block the proposed detectors are shown numerically to perform well

low complexity decoding via reduced dimension maximum likelihood search in this paper we consider a low complexity detection technique referred to as a reduced dimension maximum likelihood search rd mls rd mls is based on a partitioned search which approximates the maximum likelihood ml estimate of symbols by searching a partitioned symbol vector space rather than that spanned by the whole symbol vector the inevitable performance loss due to a reduction in the search space is compensated by 1 the use of a list tree search which is an extension of a single best searching algorithm called sphere decoding and 2 the recomputation of a set of weak symbols i e those ignored in the reduced dimension search for each strong symbol candidate found during the list tree search through simulations on m quadrature amplitude modulation qam transmission in frequency nonselective multi input multioutput mimo channels we demonstrate that the rd mls algorithm shows near constant complexity over a wide range of bit error rate ber 10 1 10 4 while limiting performance loss to within 1 db from ml detection

cryptanalytic attacks on the multiplicative knapsack cryptosystem and on shamir s fast signature scheme the basic merkle hellman additive trapdoor knapsack public key cryptosystem was recently shown to be insecure and attacks have also been developed on stronger variants of it such as the graham shamir system and the iterated knapsack cryptosystem it is shown that some simple variants of another merkle hellman system the multiplicative knapsack cryptosystem are insecure it is also shown that the shamir fast signature scheme can be broken quickly similar attacks can also be used to break the schobi massey authentication scheme these attacks have not been rigorously proved to succeed but heuristic arguments and empirical evidence indicate that they work on systems of practical size

dispersion equations and a comparison of different quasi periodic solutions of the sine gordon equation a system of dispersion equations for quasi periodic solutions of the multidimensional sine gordon equation is discussed this system of algebraical equations determines the parameters appearing in the solution which involves abstract theta functions in the case of the two phase quasi periodic solutions it is shown that the form involving theta functions represents a broader class than the class of solutions given by the expression 4 tan 1 fg the condition for the equivalence of both classes is also reported

maximum likelihood sequence estimation from the lattice viewpoint considers the problem of data detection in multilevel lattice type modulation systems in the presence of intersymbol interference and additive white gaussian noise the conventional maximum likelihood sequence estimator using the viterbi algorithm has a time complexity of o m sup spl nu 1 operations per symbol and a space complexity of o spl delta m sup spl nu storage elements where m is the size of input alphabet spl nu is the length of channel memory and spl delta is the truncation depth by revising the truncation scheme and viewing the channel as a linear transform the authors identify the problem of maximum likelihood sequence estimation with that of finding the nearest lattice point from this lattice viewpoint the lattice sequence estimator for pam systems is developed which has the following desired properties 1 its expected time complexity grows as spl delta sup 2 as snr spl rarr spl infin 2 its space complexity grow as spl delta and 3 its error performance is effectively optimal for sufficiently large m a tight upper bound on the symbol error probability of the new estimator is derived and is confirmed by the simulation results of an example channel it turns out that the estimator is effectively optimal for m spl ges 4 and the loss in signal to noise ratio is less than 0 5 db even for m 2 finally limitations of the proposed estimator are also discussed