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

shift full rank matrices and applications in space time trellis codes for relay networks with asynchronous cooperative diversity to achieve full cooperative diversity in a relay network most of the existing space time coding schemes require the synchronization between terminals a family of space time trellis codes that achieve full cooperative diversity order without the assumption of synchronization has been recently proposed the family is based on the stack construction by hammons and el gamal and its generalizations by lu and kumar it has been shown that the construction of such a family is equivalent to the construction of binary matrices that have full row rank no matter how their rows are shifted where a row corresponds to a terminal or transmit antenna and its length corresponds to the memory size of the trellis code on that terminal we call such matrices as shift full rank sfr matrices a family of sfr matrices has been also constructed but the memory sizes of the corresponding space time trellis codes the number of columns of sfr matrices grow exponentially in terms of the number of terminals the number of rows of sfr matrices which may cause a high decoding complexity when the number of terminals is not small in this paper we systematically study and construct sfr matrices of any sizes for any number of terminals furthermore we construct shortest square sfr ssfr matrices that correspond to space time trellis codes with the smallest memory sizes and asynchronous full cooperative diversity we also present some simulation results to illustrate the performances of the space time trellis codes associated with sfr matrices in asynchronous cooperative communications

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

high rate single symbol ml decodable precoded dstbcs for cooperative networks distributed orthogonal space time block codes dostbcs achieving full diversity order and single symbol maximum likelihood ml decodability have been introduced recently by yi and kim for cooperative networks and an upper bound on the maximal rate of such codes along with code constructions has been presented in this paper a new class of single symbol ml decodable precoded distributed space time block codes ssd pdstbcs called semiorthogonal ssd pdstbcs semi ssd pdstbcs is introduced wherein the source performs linear precoding of information symbols appropriately before transmitting it to all the relays it is shown that dostbcs are a special case of semi ssd pdstbcs a special class of semi ssd pdstbcs having diagonal covariance matrix at the destination is studied and an upper bound on the maximal rate of such codes is derived the bounds obtained are approximately twice larger than that of the dostbcs a systematic construction of semi ssd pdstbcs is presented when the number of relays k ges 4 the constructed codes are shown to achieve the upper bound on the rate when k is of the form 0 or 3 modulo 4 for the rest of the values of k the constructed codes are shown to have rates higher than that of dostbcs it is shown that semi ssd pdstbcs cannot be constructed with any form of linear processing at the relays when the source does not perform linear precoding of the information symbols

fast decodable asymmetric space time codes from division algebras multiple input double output mido codes are important in the near future wireless communications where the portable end user device is physically small and will typically contain at most two receive antennas especially tempting is the 4 2 channel due to its immediate applicability in the digital video broadcasting dvb such channels optimally employ rate two space time st codes consisting of 4 4 matrices unfortunately such codes are in general very complex to decode hence setting forth a call for constructions with reduced complexity recently some reduced complexity constructions have been proposed but they have mainly been based on different ad hoc methods and have resulted in isolated examples rather than in a more general class of codes in this paper it will be shown that a family of division algebra based mido codes will always result in at least 37 5 worst case complexity reduction while maintaining full diversity and for the first time the nonvanishing determinant nvd property the reduction follows from the fact that similarly to the alamouti code the codes will be subsets of matrix rings of the hamiltonian quaternions hence allowing simplified decoding at the moment such reductions are among the best known for rate two mido codes 5 6 several explicit constructions are presented and shown to have excellent performance through computer simulations simulations

generalized silver codes for an nt transmit nr receive antenna system nt nr system a full rate space time block code stbc transmits at least nmin min nt nr complex symbols per channel use the well known golden code is an example of a full rate full diversity stbc for two transmit antennas its ml decoding complexity is of the order of m2 5 for square m qam the silver code for two transmit antennas has all the desirable properties of the golden code except its coding gain but offers lower ml decoding complexity of the order of m2 importantly the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ml decoding complexity for higher number of transmit antennas the best known codes are the perfect codes which are full rate full diversity information lossless codes for nr nt but have a high ml decoding complexity of the order of mntnmin for nr nt the punctured perfect codes are considered in this paper a scheme to obtain full rate stbcs for 2a transmit antennas and any nr with reduced ml decoding complexity of the order of mnt nmin 3 4 0 5 is presented the codes constructed are also information lossless for nr nt like the perfect codes and allow higher mutual information than the comparable punctured perfect codes for nr nt these codes are referred to as the generalized silver codes since they enjoy the same desirable properties as the comparable perfect codes except possibly the coding gain with lower ml decoding complexity analogous to the silver code and the golden code for two transmit antennas simulation results of the symbol error rates for four and eight transmit antennas show that the generalized silver codes match the punctured perfect codes in error performance while offering lower ml decoding complexity

a direct formulation for sparse pca using semidefinite programming given a covariance matrix we consider the problem of maximizing the variance explained by a particular linear combination of the input variables while constraining the number of nonzero coefficients in this combination this problem arises in the decomposition of a covariance matrix into sparse factors or sparse principal component analysis pca and has wide applications ranging from biology to finance we use a modification of the classical variational representation of the largest eigenvalue of a symmetric matrix where cardinality is constrained and derive a semidefinite programming based relaxation for our problem we also discuss nesterov s smooth minimization technique applied to the semidefinite program arising in the semidefinite relaxation of the sparse pca problem the method has complexity o n 4 sqrt log n epsilon where n is the size of the underlying covariance matrix and epsilon is the desired absolute accuracy on the optimal value of the problem

high dimensional semiparametric scale invariant principal component analysis we propose a new high dimensional semiparametric principal component analysis pca method named copula component analysis coca the semiparametric model assumes that after unspecified marginally monotone transformations the distributions are multivariate gaussian coca improves upon pca and sparse pca in three aspects i it is robust to modeling assumptions ii it is robust to outliers and data contamination iii it is scale invariant and yields more interpretable results we prove that the coca estimators obtain fast estimation rates and are feature selection consistent when the dimension is nearly exponentially large relative to the sample size careful experiments confirm that coca outperforms sparse pca on both synthetic and real world data sets

truncated power method for sparse eigenvalue problems this paper considers the sparse eigenvalue problem which is to extract dominant largest sparse eigenvectors with at most k non zero components we propose a simple yet effective solution called truncated power method that can approximately solve the underlying nonconvex optimization problem a strong sparse recovery result is proved for the truncated power method and this theory is our key motivation for developing the new algorithm the proposed method is tested on applications such as sparse principal component analysis and the densest k subgraph problem extensive experiments on several synthetic and real world data sets demonstrate the competitive empirical performance of our method

square matrix embeddable space time block codes for complex signal constellations space time block codes for providing transmit diversity in wireless communication systems are considered based on the principles of linearity and unitarity a complete classification of linear codes is given in the case when the symbol constellations are complex and the code is based on a square matrix or restriction of such by deleting columns antennas maximal rate delay optimal codes are constructed within this category the maximal rates allowed by linearity and unitarity fall off exponentially with the number of transmit antennas

on the sphere decoding complexity of high rate multigroup decodable stbcs in asymmetric mimo systems a space time block code stbc is said to be multigroup decodable if the information symbols encoded by it can be partitioned into two or more groups such that each group of symbols can be maximum likelihood ml decoded independently of the other symbol groups in this paper we show that the upper triangular matrix r encountered during the sphere decoding of a linear dispersion stbc can be rank deficient even when the rate of the code is less than the minimum of the number of transmit and receive antennas we then show that all known families of high rate rate greater than 1 multigroup decodable codes have rank deficient r matrix even when the rate is less than the number of transmit and receive antennas and this rank deficiency problem arises only in asymmetric mimo systems when the number of receive antennas is strictly less than the number of transmit antennas unlike the codes with full rank r matrix the complexity of the sphere decoding based ml decoder for stbcs with rank deficient r matrix is polynomial in the constellation size and hence is high we derive the ml sphere decoding complexity of most of the known high rate multigroup decodable codes and show that for each code the complexity is a decreasing function of the number of receive antennas

sparse principal component analysis via rotation and truncation sparse principal component analysis sparse pca aims at finding a sparse basis to improve the interpretability over the dense basis of pca while still covering the data subspace as much as possible in contrast to most existing work that addresses the problem by adding sparsity penalties on various objectives of pca we propose a new method sparse pca via rotation and truncation spcart which finds a rotation matrix and a sparse basis such that the sparse basis approximates the basis of pca after the rotation the algorithm of spcart consists of three alternating steps 1 rotating the pca basis 2 truncating small entries and 3 updating the rotation matrix its performance bounds are also given the spcart is efficient with each iteration scaling linearly with the data dimension parameter choice is simple due to explicit physical explanations we give a unified view to several existing sparse pca methods and discuss the connections with spcart some ideas from spcart are extended to gpower a popular sparse pca algorithm to address its limitations experimental results demonstrate that spcart achieves the state of the art performance along with a good tradeoff among various criteria including sparsity explained variance orthogonality balance of sparsity among loadings and computational speed

full diversity high rate space time block codes from division algebras we present some general techniques for constructing full rank minimal delay rate at least one space time block codes stbcs over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras field extensions as well as using noncommutative division algebras of the rational field spl qopf embedded in matrix rings the first half of the paper deals with constructions using field extensions of spl qopf working with cyclotomic field extensions we construct several families of stbcs over a wide range of signal sets that are of full rank minimal delay and rate at least one appropriate for any number of transmit antennas we study the coding gain and capacity of these codes using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas we also present a method of constructing stbcs using noncyclotomic field extensions in the later half of the paper we discuss two ways of embedding noncommutative division algebras into matrices left regular representation and representation over maximal cyclic subfields the 4 spl times 4 real orthogonal design is obtained by the left regular representation of quaternions alamouti s 1998 code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it also we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the stbcs obtained from this construction another family of cyclic division algebras discovered by brauer 1933 is discussed and several examples of stbcs derived from each of these constructions are presented

fast and guaranteed blind multichannel deconvolution under a bilinear system model we consider the multichannel blind deconvolution problem where we observe the output of multiple channels that are all excited with the same unknown input from these observations we wish to estimate the impulse responses of each of the channels we show that this problem is well posed if the channels follow a bilinear model where the ensemble of channel responses is modeled as lying in a low dimensional subspace but with each channel modulated by an independent gain under this model we show how the channel estimates can be found by minimizing a quadratic function over a non convex set we analyze two methods for solving this non convex program and provide performance guarantees for each the first is a method of alternating eigenvectors that breaks the program down into a series of eigenvalue problems the second is a truncated power iteration which can roughly be interpreted as a method for finding the largest eigenvector of a symmetric matrix with the additional constraint that it adheres to our bilinear model as with most non convex optimization algorithms the performance of both of these algorithms is highly dependent on having a good starting point we show how such a starting point can be constructed from the channel measurements our performance guarantees are non asymptotic and provide a sufficient condition on the number of samples observed per channel in order to guarantee channel estimates of certain accuracy our analysis uses a model with a generic subspace that is drawn at random and we show the performance bounds hold with high probability mathematically the key estimates are derived by quantifying how well the eigenvectors of certain random matrices approximate the eigenvectors of their mean we also present a series of numerical results demonstrating that the empirical performance is consistent with the presented theory

convergence of gradient descent for low rank matrix approximation this paper provides a proof of global convergence of gradient search for low rank matrix approximation such approximations have recently been of interest for large scale problems as well as for dictionary learning for sparse signal representations and matrix completion the proof is based on the interpretation of the problem as an optimization on the grassmann manifold and fubiny study distance on this space

near optimal stochastic approximation for online principal component estimation principal component analysis pca has been a prominent tool for high dimensional data analysis online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests despite its rich applications theoretical convergence analysis remains largely open in this paper we cast online pca into a stochastic nonconvex optimization problem and we analyze the online pca algorithm as a stochastic approximation iteration the stochastic approximation iteration processes data points incrementally and maintains a running estimate of the principal component we prove for the first time a nearly optimal finite sample error bound for the online pca algorithm under the subgaussian assumption we show that the finite sample error bound closely matches the minimax information lower bound

distributed differential space time coding for wireless relay networks distributed space time coding is a cooperative transmission scheme for wireless relay networks with this scheme antennas of the distributive relays work as transmit antennas of the sender and generate a space time code at the receiver it achieves the maximum diversity although the scheme needs no channel information at relays it does require full channel information both the channels from the transmitter to relays and the channels from relays to the receiver at the receiver in this paper we propose a differential transmission scheme which requires channel information at neither relays nor the receiver for wireless relay networks as distributed space time coding can be seen as the counterpart of space time coding in the network setting this scheme is the counterpart of differential space time coding compared to coherent distributed space time coding the differential scheme is 3db worse in addition we show that alamouti square real orthogonal and sp 2 codes can be used differentially in networks with corresponding numbers of relays we also propose distributed differential space time codes that work for networks with any number of relays using circulant matrices

on the distribution of the largest eigenvalue in principal components analysis let x 1 denote the square of the largest singular value of an n p matrix x all of whose entries are independent standard gaussian variates equivalently x 1 is the largest principal component variance of the covariance matrix x x or the largest eigenvalue of a p variate wishart distribution on n degrees of freedom with identity covariance consider the limit of large p and n with n p gamma ge 1 when centered by mu p sqrt n 1 sqrt p 2 and scaled by sigma p sqrt n 1 sqrt p 1 sqrt n 1 1 sqrt p 1 3 the distribution of x 1 approaches the tracey widom law of order 1 which is defined in terms of the painleve ii differential equation and can be numerically evaluated and tabulated in software simulations show the approximation to be informative for n and p as small as 5 the limit is derived via a corresponding result for complex wishart matrices using methods from random matrix theory the result suggests that some aspects of large p multivariate distribution theory may be easier to apply in practice than their fixed p counterparts

on the sphere decoding algorithm i expected complexity the problem of finding the least squares solution to a system of linear equations where the unknown vector is comprised of integers but the matrix coefficient and given vector are comprised of real numbers arises in many applications communications cryptography gps to name a few the problem is equivalent to finding the closest lattice point to a given point and is known to be np hard in communications applications however the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known therefore in this paper rather than dwell on the worst case complexity of the integer least squares problem we study its expected complexity averaged over the noise and over the lattice for the sphere decoding algorithm of fincke and pohst we find a closed form expression for the expected complexity both for the infinite and finite lattice it is demonstrated in the second part of this paper that for a wide range of signal to noise ratios snrs and numbers of antennas the expected complexity is polynomial in fact often roughly cubic since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial this suggests that maximum likelihood decoding which was hitherto thought to be computationally intractable can in fact be implemented in real time a result with many practical implications

an enhanced dmt optimality criterion for stbc schemes for asymmetric mimo systems for any nt transmit nr receive antenna nt nr multiple input multiple output mimo system in a quasi static rayleigh fading environment it was shown by elia that linear space time block code schemes lstbc schemes that have the nonvanishing determinant nvd property are diversity multiplexing gain tradeoff dmt optimal for arbitrary values of nr if they have a code rate of nt complex dimensions per channel use however for asymmetric mimo systems where with the exception of a few lstbc schemes it is unknown whether general lstbc schemes with nvd and a code rate of nr complex dimensions per channel use are dmt optimal in this paper an enhanced sufficient criterion for any stbc scheme to be dmt optimal is obtained and using this criterion it is established that any lstbc scheme with nvd and a code rate of min nt nr complex dimensions per channel use is dmt optimal this result settles the dmt optimality of several well known low ml decoding complexity lstbc schemes for certain asymmetric mimo systems

group factor analysis factor analysis fa provides linear factors that describe the relationships between individual variables of a data set we extend this classical formulation into linear factors that describe the relationships between groups of variables where each group represents either a set of related variables or a data set the model also naturally extends canonical correlation analysis to more than two sets in a way that is more flexible than previous extensions our solution is formulated as a variational inference of a latent variable model with structural sparsity and it consists of two hierarchical levels 1 the higher level models the relationships between the groups and 2 the lower models the observed variables given the higher level we show that the resulting solution solves the group factor analysis gfa problem accurately outperforming alternative fa based solutions as well as more straightforward implementations of gfa the method is demonstrated on two life science data sets one on brain activation and the other on systems biology illustrating its applicability to the analysis of different types of high dimensional data sources

orthogonal designs with maximal rates orthogonal designs have been used as space time block codes for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have a very simple decoupled maximum likelihood decoding algorithm the rate of an orthogonal design is defined as the ratio of the number of transmitted information symbols in a block of channel uses to the length of the given block which reflects the bandwidth efficiency of the employed space time block code constructed from the orthogonal design this paper focuses on the analysis and synthesis of orthogonal designs with the maximum possible rates which may be real or complex and square or rectangular matrices we first provide several representations of orthogonal designs and their characterizations in terms of hurwitz radon matrix equations next we observe that the real orthogonal designs square or rectangular and the complex square orthogonal designs with maximal rates have been well understood from the existing results in the mathematics literature which can be dated back to 1890s however unfortunately it is not the case for the complex rectangular orthogonal designs with rates as high as possible we then construct a class of complex orthogonal designs for any number of transmit antennas the proposed complex orthogonal designs for the number of transmit antennas n 2m 1 and 2m have the same rate m 1 and 2m where m is any natural number finally we demonstrate that for n 2m 1 and 2m with any given natural number m the value m 1 and 2m is the maximum possible rate that the complex orthogonal designs square or rectangular with n transmit antennas can achieve

orthogonal sparse pca and covariance estimation via procrustes reformulation the problem of estimating sparse eigenvectors of a symmetric matrix has attracted a lot of attention in many applications especially those with a high dimensional dataset while classical eigenvectors can be obtained as the solution of a maximization problem existing approaches formulate this problem by adding a penalty term into the objective function that encourages a sparse solution however the vast majority of the resulting methods achieve sparsity at the expense of sacrificing the orthogonality property in this paper we develop a new method to estimate dominant sparse eigenvectors without trading off their orthogonality the problem is highly nonconvex and hard to handle we apply the minorization maximization framework wherein we iteratively maximize a tight lower bound surrogate function of the objective function over the stiefel manifold the inner maximization problem turns out to be a rectangular procrustes problem which has a closed form solution in addition we propose a method to improve the covariance estimation problem when its underlying eigenvectors are known to be sparse we use the eigenvalue decomposition of the covariance matrix to formulate an optimization problem wherein we impose sparsity on the corresponding eigenvectors numerical experiments show that the proposed eigenvector extraction algorithm outperforms existing algorithms in terms of support recovery and explained variance whereas the covariance estimation algorithms improve the sample covariance estimator significantly

sparse pca optimal rates and adaptive estimation principal component analysis pca is one of the most commonly used statistical procedures with a wide range of applications this paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional setting under mild technical conditions we first establish the optimal rates of convergence for estimating the principal subspace which are sharp with respect to all the parameters thus providing a complete characterization of the difficulty of the estimation problem in term of the convergence rate the lower bound is obtained by calculating the local metric entropy and an application of fano s lemma the rate optimal estimator is constructed using aggregation which however might not be computationally feasible we then introduce an adaptive procedure for estimating the principal subspace which is fully data driven and can be computed efficiently it is shown that the estimator attains the optimal rates of convergence simultaneously over a large collection of the parameter spaces a key idea in our construction is a reduction scheme which reduces the sparse pca problem to a high dimensional multivariate regression problem this method is potentially also useful for other related problems

single symbol ml decodable distributed stbcs for cooperative networks in this correspondence the distributed orthogonal space time block codes dostbcs which achieve the single symbol maximum likelihood ml decodability and full diversity order are first considered however systematic construction of the dostbcs is very hard since the noise covariance matrix is not diagonal in general thus some special dostbcs which have diagonal noise covariance matrices at the destination terminal are investigated these codes are referred to as the row monomial dostbcs an upper bound of the data rate of the row monomial dostbc is derived and it is approximately twice higher than that of the repetition based cooperative strategy furthermore systematic construction methods of the row monomial dostbcs achieving the upper bound of the data rate are developed when the number of relays and or the number of information bearing symbols are even

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

eca high dimensional elliptical component analysis in non gaussian distributions abstractwe present a robust alternative to principal component analysis pca called elliptical component analysis eca for analyzing high dimensional elliptically distributed data eca estimates the eigenspace of the covariance matrix of the elliptical data to cope with heavy tailed elliptical distributions a multivariate rank statistic is exploited at the model level we consider two settings either that the leading eigenvectors of the covariance matrix are nonsparse or that they are sparse methodologically we propose eca procedures for both nonsparse and sparse settings theoretically we provide both nonasymptotic and asymptotic analyses quantifying the theoretical performances of eca in the nonsparse setting we show that eca s performance is highly related to the effective rank of the covariance matrix in the sparse setting the results are twofold i we show that the sparse eca estimator based on a combinatoric program attains the optimal rate of convergence ii based on some recent d

new algebraic constructions of rotated z sup n lattice constellations for the rayleigh fading channel in this correspondence we present various families of full diversity rotated z sup n lattice constellations based on algebraic number theory constructions we are able to give closed form expressions of their minimum product distance using the corresponding algebraic properties

approximately universal codes over slow fading channels performance of reliable communication over a coherent slow fading multiple input multiple output mimo channel at high signal to noise ratio snr is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains this paper studies the problem of designing codes that optimally tradeoff the diversity and multiplexing gains the main contribution is a precise characterization of codes that are universally tradeoff optimal i e they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel this characterization is referred to as approximate universality the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains respectively the characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space time coding literature

on fast decodable space time block codes we focus on full rate fast decodable space time block codes stbcs for 2 times 2 and 4times2 multiple input multiple output mimo transmission we first derive conditions and design criteria for reduced complexity maximum likelihood ml decodable 2times2 stbcs and we apply them to two families of codes that were recently discovered next we derive a novel reduced complexity 4times2 stbc and show that it outperforms all previously known codes with certain constellations

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

single symbol maximum likelihood decodable linear stbcs space time block codes stbcs from orthogonal designs ods and coordinate interleaved orthogonal designs ciod have been attracting wider attention due to their amenability for fast single symbol maximum likelihood ml decoding and full rate with full rank over quasi static fading channels however these codes are instances of single symbol decodable codes and it is natural to ask if there exist codes other than stbcs form ods and ciods that allow single symbol decoding in this paper the above question is answered in the affirmative by characterizing all linear stbcs that allow single symbol ml decoding not necessarily full diversity over quasi static fading channels calling them single symbol decodable designs sdd the class sdd includes ods and ciods as proper subclasses further among the sdd a class of those that offer full diversity called full rank sdd fsdd are characterized and classified we then concentrate on square designs and derive the maximal rate for square fsdds using a constructional proof it follows that 1 except for n 2 square complex ods are not maximal rate and 2 a rate one square fsdd exist only for two and four transmit antennas for nonsquare designs generalized coordinate interleaved orthogonal designs a superset of ciods are presented and analyzed finally for rapid fading channels an equivalent matrix channel representation is developed which allows the results of quasi static fading channels to be applied to rapid fading channels using this representation we show that for rapid fading channels the rate of single symbol decodable stbcs are independent of the number of transmit antennas and inversely proportional to the block length of the code significantly the ciod for two transmit antennas is the only stbc that is single symbol decodable over both quasi static and rapid fading channels

fast decodable mido codes with large coding gain in this paper a new method is proposed to obtain full diversity rate 2 rate of two complex symbols per channel use space time block codes stbcs that are full rate for multiple input double output mido systems using this method rate 2 stbcs for 4 2 6 2 8 2 and 12 2 systems are constructed and these stbcs are fast ml decodable have large coding gains and stbc schemes consisting of these stbcs have a non vanishing determinant nvd so that they are dmt optimal for their respective mido systems it is also shown that the srinath rajan code for the 4 2 system which has the lowest ml decoding complexity among known rate 2 stbcs for the 4 2 mido system with a large coding gain for 4 16 qam has the same algebraic structure as the stbc constructed in this paper for the 4 2 system this also settles in positive a previous conjecture that the stbc scheme that is based on the srinath rajan code has the nvd property and hence is dmt optimal for the 4 2 system

multichannel sparse blind deconvolution on the sphere multichannel blind deconvolution is the problem of recovering an unknown signal f and multiple unknown channels x i from their circular convolution y i x i circledast f i 1 2 dots n we consider the case where the x i s are sparse and convolution with f is invertible our nonconvex optimization formulation solves for a filter h on the unit sphere that produces sparse output y i circledast h under some technical assumptions we show that all local minima of the objective function correspond to the inverse filter of f up to an inherent sign and shift ambiguity and all saddle points have strictly negative curvatures this geometric structure allows successful recovery of f and x i using a simple manifold gradient descent mgd algorithm the same approach is also applicable to blind gain and phase calibration with a fourier sensing matrix our algorithm and analysis require fewer assumptions than previous algorithms for the same problem our theoretical findings are complemented by numerical experiments which demonstrate superior performance of the proposed approach over the previous methods empirically our algorithm has low computation cost converging in a small number of iterations and low memory footprint solving only for the inverse filter of f

statistical and computational trade offs in estimation of sparse principal components in recent years sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high dimensional data the theoretical challenge in the simplest case is to estimate the leading eigenvector of a population covariance matrix under the assumption that this eigenvector is sparse an impressive range of estimators have been proposed some of these are fast to compute while others are known to achieve the minimax optimal rate over certain gaussian or sub gaussian classes in this paper we show that under a widely believed assumption from computational complexity theory there is a fundamental trade off between statistical and computational performance in this problem more precisely working with new larger classes satisfying a restricted covariance concentration condition we show that there is an effective sample size regime in which no randomised polynomial time algorithm can achieve the minimax optimal rate we also study the theoretical performance of a polynomial time variant of the well known semidefinite relaxation estimator revealing a subtle interplay between statistical and computational efficiency

rate optimal denoising of simultaneously sparse and low rank matrices we study minimax rates for denoising simultaneously sparse and low rank matrices in high dimensions we show that an iterative thresholding algorithm achieves near optimal rates adaptively under mild conditions for a large class of loss functions numerical experiments on synthetic datasets also demonstrate the competitive performance of the proposed method

information lossless space time block codes from crossed product algebras it is known that the alamouti code is the only complex orthogonal design cod which achieves capacity and that too for the case of two transmit and one receive antenna only damen proposed a design for two transmit antennas which achieves capacity for any number of receive antennas calling the resulting space time block code stbc when used with a signal set an information lossless stbc in this paper using crossed product central simple algebras we construct stbcs for arbitrary number of transmit antennas over an a priori specified signal set alamouti code and quasi orthogonal designs are the simplest special cases of our constructions we obtain a condition under which these stbcs from crossed product algebras are information lossless we give some classes of crossed product algebras from which the stbcs obtained are information lossless and also of full rank we present some simulation results for two three and four transmit antennas to show that our stbcs perform better than some of the best known stbcs and also that these stbcs are approximately 1 db away from the capacity of the channel with quadrature amplitude modulation qam symbols as input

optimal rates of convergence for noisy sparse phase retrieval via thresholded wirtinger flow this paper considers the noisy sparse phase retrieval problem recovering a sparse signal mathbf x in mathbb r p from noisy quadratic measurements y j mathbf a j mathbf x 2 varepsilon j j 1 ldots m with independent sub exponential noise varepsilon j the goals are to understand the effect of the sparsity of mathbf x on the estimation precision and to construct a computationally feasible estimator to achieve the optimal rates adaptively inspired by the wirtinger flow ieee trans inform theory61 2015 1985 2007 proposed for non sparse and noiseless phase retrieval a novel thresholded gradient descent algorithm is proposed and it is shown to adaptively achieve the minimax optimal rates of convergence over a wide range of sparsity levels when the mathbf a j s are independent standard gaussian random vectors provided that the sample size is sufficiently large compared to the sparsity of mathbf x

non negative principal component analysis message passing algorithms and sharp asymptotics principal component analysis pca aims at estimating the direction of maximal variability of a high dimensional data set a natural question is does this task become easier and estimation more accurate when we exploit additional knowledge on the principal vector we study the case in which the principal vector is known to lie in the positive orthant similar constraints arise in a number of applications ranging from the analysis of gene expression data to spike sorting in neural signal processing in the unconstrained case the estimation performances of pca have been precisely characterized using the random matrix theory under a statistical model known as the spiked model it is known that the estimation error undergoes a phase transition as the signal to noise ratio crosses a certain threshold unfortunately tools from the random matrix theory have no bearing on the constrained problem despite this challenge we develop an analogous characterization in the constrained case within a one spike model in particular 1 we prove that the estimation error undergoes a similar phase transition albeit at a different thresholds in signal to noise ratio that we determine exactly 2 we prove that unlike in the unconstrained case the estimation error depends on the spike vector and characterize the least favorable vectors and 3 we show that a non negative principal component can be approximately computed under the spiked model in nearly linear time this despite the fact that the problem is non convex and in general np hard to solve exactly

sparse principal component analysis based on least trimmed squares sparse principal component analysis pca is used to obtain stable and interpretable principal components pcs from high dimensional data a robust sparse pca method is proposed to handle potentia

stbc schemes with nonvanishing determinant for certain number of transmit antennas a space time block code scheme stbc scheme is a family of stbcs c snr indexed by the signal to noise ratio snr such that the rate of each stbc scales with snr an stbc scheme is said to have a nonvanishing determinant if the coding gain of every stbc in the scheme is lower bounded by a fixed nonzero value the nonvanishing determinant property is important from the perspective of the diversity multiplexing gain dm g tradeoff a concept that characterizes the maximum diversity gain achievable by any stbc scheme transmitting at a particular rate this correspondence presents a systematic technique for constructing stbc schemes with nonvanishing determinant based on cyclic division algebras prior constructions of stbc schemes from cyclic division algebra have either used transcendental elements in which case the scheme may have vanishing determinant or is available with nonvanishing determinant only for two three four and six transmit antennas in this correspondence we construct stbc schemes with nonvanishing determinant for the number of transmit antennas of the form 2 sup k 3 spl middot 2 sup k 2 spl middot 3 sup k and q sup k q 1 2 where q is any prime of the form 4s 3 for cyclic division algebra based stbc schemes in a recent work by elia et al the nonvanishing determinant property has been shown to be sufficient for achieving dm g tradeoff in particular it has been shown that the class of stbc schemes constructed in this correspondence achieve the optimal dm g tradeoff moreover the results presented in this correspondence have been used for constructing optimal stbc schemes for arbitrary number of transmit antennas by elia et al

generalized distributive law for ml decoding of space time block codes the problem of designing good space time block codes stbcs with low maximum likelihood ml decoding complexity has gathered much attention in the literature all the known low ml decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast decodable conditionally multigroup decodable structure of a code we refer to this well known technique of decoding stbcs as conditional ml cml decoding in this paper we introduce a new framework to construct ml decoders for stbcs based on the generalized distributive law gdl and the factor graph based sum product algorithm we say that an stbc is fast gdl decodable if the order of gdl decoding complexity of the code with respect to the constellation size m is strictly less than m where is the number of independent symbols in the stbc we give sufficient conditions for an stbc to admit fast gdl decoding and show that both multigroup and conditionally multigroup decodable codes are fast gdl decodable for any stbc whether fast gdl decodable or not we show that the gdl decoding complexity is strictly less than the cml decoding complexity for instance for any stbc obtained from cyclic division algebras which is not multigroup or conditionally multigroup decodable the gdl decoder provides about 12 times reduction in complexity compared to the cml decoder similarly for the golden code which is conditionally multigroup decodable the gdl decoder is only half as complex as the cml decoder

four group decodable space time block codes two new rate one full diversity space time block codes stbcs are proposed they are characterized by the lowest decoding complexity among the known rate one stbc arising due to the complete separability of the transmitted symbols into four groups for maximum likelihood detection the first and the second codes are delay optimal if the number of transmit antennas is a power of 2 and even respectively the exact pairwise error probability is derived to allow for the performance optimization of the two codes compared with existing low decoding complexity stbc the two new codes offer several advantages such as higher code rate lower encoding decoding delay and complexity lower peak to average power ratio and better performance

majorization minimization algorithms in signal processing communications and machine learning this paper gives an overview of the majorization minimization mm algorithmic framework which can provide guidance in deriving problem driven algorithms with low computational cost a general introduction of mm is presented including a description of the basic principle and its convergence results the extensions acceleration schemes and connection to other algorithmic frameworks are also covered to bridge the gap between theory and practice upperbounds for a large number of basic functions derived based on the taylor expansion convexity and special inequalities are provided as ingredients for constructing surrogate functions with the pre requisites established the way of applying mm to solving specific problems is elaborated by a wide range of applications in signal processing communications and machine learning

perfect space time block codes in this paper we introduce the notion of perfect space time block codes stbcs these codes have full rate full diversity nonvanishing constant minimum determinant for increasing spectral efficiency uniform average transmitted energy per antenna and good shaping we present algebraic constructions of perfect stbcs for 2 3 4 and 6 antennas

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

low ml decoding complexity stbcs via codes over the klein group in this paper we give a new framework for constructing low ml decoding complexity space time block codes stbcs using codes over the klein group k almost all known low ml decoding complexity stbcs can be obtained via this approach new full diversity stbcs with low ml decoding complexity and cubic shaping property are constructed via codes over k for number of transmit antennas n 2m m 1 and rates r 1 complex symbols per channel use when r n the new stbcs are information lossless as well the new class of stbcs have the least known ml decoding complexity among all the codes available in the literature for a large set of n r pairs

multigroup ml decodable collocated and distributed space time block codes in this paper collocated and distributed space time block codes dstbcs which admit multigroup maximum likelihood ml decoding are studied first the collocated case is considered and the problem of constructing space time block codes stbcs which optimally tradeoff rate and ml decoding complexity is posed recently sufficient conditions for multigroup ml decodability have been provided in the literature and codes meeting these sufficient conditions were called clifford unitary weight cuw stbcs an algebraic framework based on extended clifford algebras ecas is proposed to study cuw stbcs and using this framework the optimal tradeoff between rate and ml decoding complexity of cuw stbcs is obtained for few specific cases code constructions meeting this tradeoff optimally are also provided the paper then focuses on multigroup ml decodable dstbcs for application in synchronous wireless relay networks and three constructions of four group ml decodable dstbcs are provided finally the orthogonal frequency division multiplexing ofdm based alamouti space time coded scheme proposed by li xia for a 2 relay asynchronous relay network is extended to a more general transmission scheme that can achieve full asynchronous cooperative diversity for arbitrary number of relays it is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node four group decodable dstbcs applicable in the proposed ofdm based transmission scheme are also given

nordhaus gaddum and other bounds for the sum of squares of the positive eigenvalues of a graph abstract terpai 21 proved the nordhaus gaddum bound that g g 4 n 3 1 where g is the spectral radius of a graph g with n vertices let s denote the sum of the squares of the positive eigenvalues of g we prove that s g s g 2 n and conjecture that s g s g 4 n 3 1 we have used autographix and wolfram mathematica to search for a counter example we also consider nordhaus gaddum bounds for s and bounds for the randic index

explicit space time codes achieving the diversity multiplexing gain tradeoff a recent result of zheng and tse states that over a quasi static channel there exists a fundamental tradeoff referred to as the diversity multiplexing gain d mg tradeoff between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space time st code this tradeoff is precisely known in the case of independent and identically distributed i i d rayleigh fading for tgesnt nr 1 where t is the number of time slots over which coding takes place and nt nr are the number of transmit and receive antennas respectively for t nt case we present two general techniques for building d mg optimal rectangular st codes from their square counterparts a byproduct of our results establishes that the d mg tradeoff for all tgesnt is the same as that previously known to hold for tgesnt n r 1

a novel construction of multi group decodable space time block codes complex orthogonal design cod codes are known to have the lowest detection complexity among space time block codes stbcs however the rate of square cod codes decreases exponentially with the number of transmit antennas the quasi orthogonal design qod codes emerged to provide a compromise between rate and complexity as they offer higher rates compared to cod codes at the expense of an increase of decoding complexity through partially relaxing the orthogonality conditions the qod codes were then generalized with the so called g symbol and g group decodable stbcs where the number of orthogonal groups of symbols is no longer restricted to two as in the qod case however the adopted approach for the construction of such codes is based on sufficient but not necessary conditions which may limit the achievable rates for any number of orthogonal groups in this paper we limit ourselves to the case of unitary weight uw g group decodable stbcs for 2a transmit antennas where the weight matrices are required to be single thread matrices with non zero entries 1 j and address the problem of finding the highest achievable rate for any number of orthogonal groups this special type of weight matrices guarantees full symbol wise diversity and subsumes a wide range of existing codes in the literature we show that in this case an exhaustive search can be applied to find the maximum achievable rates for uw g group decodable stbcs with g 1 for this purpose we extend our previously proposed approach for constructing uw 2 group decodable stbcs based on necessary and sufficient conditions to the case of uw g group decodable stbcs in a recursive manner

sparse principal component analysis and iterative thresholding principal component analysis pca is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix however it behaves poorly when the number of features p is comparable to or even much larger than the sample size n in this paper we propose a new iterative thresholding approach for estimating principal subspaces in the setting where the leading eigenvectors are sparse under a spiked covariance model we find that the new approach recovers the principal subspace and leading eigenvectors consistently and even optimally in a range of high dimensional sparse settings simulated examples also demonstrate its competitive performance

heuristic and special case algorithms for dispersion problems the dispersion problem arises in selecting facilities to maximize some function of the distances between the facilities the problem also arises in selecting nondominated solutions for multiobjective decision making it is known to be np hard under two objectives maximizing the minimum distance max min between any pair of facilities and maximizing the average distance max avg we consider the question of obtaining near optimal solutions for max min we show that if the distances do not satisfy the triangle inequality there is no polynomial time relative approximation algorithm unless p np when the distances satisfy the triangle inequality we analyze an efficient heuristic and show that it provides a performance guarantee of two we also prove that obtaining a performance guarantee of less than two is np hard for max avg we analyze an efficient heuristic and show that it provides a performance guarantee of four when the distances satisfy the triangle inequality we also present a polynomial ti

sparse generalized eigenvalue problem optimal statistical rates via truncated rayleigh flow the sparse generalized eigenvalue problem gep plays a pivotal role in a large family of high dimensional statistical models including sparse fisher s discriminant analysis canonical correlation analysis and sufficient dimension reduction the sparse gep involves solving a non convex optimization problem most existing methods and theory in the context of specific statistical models that are special cases of the sparse gep require restrictive structural assumptions on the input matrices we propose a two stage computational framework to solve the sparse gep at the first stage we solve a convex relaxation of the sparse gep taking the solution as an initial value we then exploit a non convex optimization perspective and propose the truncated rayleigh flow method which we call rifle to estimate the leading generalized eigenvector we show that rifle converges linearly to a solution with the optimal statistical rate of convergence theoretically our method significantly improves on the existing literature by eliminating structural assumptions on the input matrices to achieve this our analysis involves two key ingredients a new analysis of the gradient based method on non convex objective functions and a fine grained characterization of the evolution of sparsity patterns along the solution path thorough numerical studies are provided to validate the theoretical results

optimal permutation recovery in permuted monotone matrix model motivated by recent research on quantifying bacterial growth dynamics based on genome assemblies we consider a permuted monotone matrix model y z where the rows represent different samples th

ruling out ptas for graph min bisection dense k subgraph and bipartite clique assuming that np not subseteq cap epsilon 0 bptime 2 n epsilon we show that graph min bisection dense k subgraph and bipartite clique have no polynomial time approximation scheme ptas we give a reduction from the minimum distance of code mdc problem starting with an instance of mdc we build a quasi random probabilistically checkable proof pcp that suffices to prove the desired inapproximability results in a quasi random pcp the query pattern of the verifier looks random in a certain precise sense among the several new techniques we introduce the most interesting one gives a way of certifying that a given polynomial belongs to a given linear subspace of polynomials as is important for our purpose the certificate itself happens to be another polynomial and it can be checked probabilistically by reading a constant number of its values

on optimal quasi orthogonal space time block codes with minimum decoding complexity orthogonal space time block codes ostbc from orthogonal designs have both advantages of complex symbol wise maximum likelihood ml decoding and full diversity however their symbol rates are upper bounded by 3 4 for more than two antennas for complex symbols to increase the symbol rates they have been generalized to quasi orthogonal space time block codes qostbc in the literature but the diversity order is reduced by half and the complex symbol wise ml decoding is significantly increased to complex symbol pair wise pair of complex symbols ml decoding the qostbc has been modified by rotating half of the complex symbols for achieving the full diversity while maintaining the complex symbol pair wise ml decoding the optimal rotation angles for any signal constellation of any finite symbols located on both square lattices and equal literal triangular lattices have been found by su xia where the optimality means the optimal diversity product or product distance qostbc has also been modified by yuen guan tjhung by rotating information symbols in another way such that it has full diversity and in the meantime it has real symbol pair wise ml decoding the same complexity as complex symbol wise decoding and the optimal rotation angle for square and rectangular qam constellations has been found in this paper we systematically study general linear transformations of information symbols for qostbc to have both full diversity and real symbol pair wise ml decoding we present the optimal transformation matrices among all possible linear transformations not necessarily symbol rotations of information symbols for qostbc with real symbol pair wise ml decoding such that the optimal diversity product is achieved for both general square qam and general rectangular qam signal constellations furthermore our newly proposed optimal linear transformations for qostbc also work for general qam constellations in the sense that qostbc have full diversity with good diversity product property and real symbol pair wise ml decoding interestingly the optimal diversity products for square qam constellations from the optimal linear transformations of information symbols found in this paper coincide with the ones presented by yuen guan tjhung by using their optimal rotations however the optimal diversity products for nonsquare rectangular qam constellations from the optimal linear transformations of information symbols found in this paper are better than the ones presented by yuen guan tjhung by using their optimal rotations in this paper we also present the optimal transformations for the co ordinate interleaved orthogonal designs ciod proposed by khan rajan for rectangular qam constellations

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

dense subgraph partition of positive hypergraphs in this paper we present a novel partition framework called dense subgraph partition dsp to automatically precisely and efficiently decompose a positive hypergraph into dense subgraphs a positive hypergraph is a graph or hypergraph whose edges except self loops have positive weights we first define the concepts of core subgraph conditional core subgraph and disjoint partition of a conditional core subgraph then define dsp based on them the result of dsp is an ordered list of dense subgraphs with decreasing densities which uncovers all underlying clusters as well as outliers a divide and conquer algorithm called min partition evolution is proposed to efficiently compute the partition dsp has many appealing properties first it is a nonparametric partition and it reveals all meaningful clusters in a bottom up way second it has an exact and efficient solution called min partition evolution algorithm the min partition evolution algorithm is a divide and conquer algorithm thus time efficient and memory friendly and suitable for parallel processing third it is a unified partition framework for a broad range of graphs and hypergraphs we also establish its relationship with the densest k subgraph problem d k s an np hard but fundamental problem in graph theory and prove that dsp gives precise solutions to d k s for all k in a graph dependent set called critical k set to our best knowledge this is a strong result which has not been reported before moreover as our experimental results show for sparse graphs especially web graphs the size of critical k set is close to the number of vertices in the graph we test the proposed partition framework on various tasks and the experimental results clearly illustrate its advantages

the sparse principal component of a constant rank matrix the computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue finding this optimal submatrix is what renders the problem np hard in this paper we prove that if the matrix is positive semidefinite and its rank is constant then its sparse principal component is polynomially computable our proof utilizes the auxiliary unit vector technique that has been recently developed to identify problems that are polynomially solvable in addition we use this technique to design an algorithm which for any sparsity value computes the sparse principal component with complexity o nd 1 where n and d are the matrix size and rank respectively our algorithm is fully parallelizable and memory efficient

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