an information theoretic framework for deriving canonical decision feedback receivers in gaussian channels a framework is presented that allows a number of known results relating feedback equalization linear prediction and mutual information to be easily understood a lossless additive decomposition of mutual information in a general class of gaussian channels is introduced and shown to produce an information preserving canonical decision feedback receiver the approach is applied to intersymbol interference isi channels to derive the well known minimum mean square error mmse decision feedback equalizer dfe when applied to the synchronous code division multiple access cdma channel the result is the mmse or signal to interference ratio sir maximizing decision feedback detector which is shown to achieve the channel sum capacity at the vertices of the capacity region finally in the case of the asynchronous cdma channel we are able to give new connections between information theory decision feedback receivers and structured factorizations of multivariate spectra

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

optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

zero forcing dfe transceiver design over slowly time varying mimo channels using st gtd this paper considers the optimization of transceivers with decision feedback equalizers dfe for slowly time varying memoryless multi input multi output mimo channels the data vectors are grouped into space time blocks st blocks for the spatial and temporal precoding to take advantage of the diversity offered by time varying channels the space time generalized triangular decomposition st gtd is proposed for application in time varying channels under the assumption that the instantaneous channel state information at the transmitter csit and receiver csir and the channel prediction are available we also propose the space time geometric mean decomposition st gmd system based on st gtd under perfect channel prediction the system minimizes both the arithmetic mse at the feedback detector and the average un coded bit error rate ber in moderate high signal to noise ratio snr region for practical applications a novel st gtd based system which does not require channel prediction but shares the same asymptotic ber performance with the st gmd system is also proposed at the moderate high snr region our analysis and numerical results show that all the proposed systems have better ber performance than the conventional gmd based systems over time varying channels the average bers of the proposed systems are non increasing functions of the st block size

on the general ber expression of one and two dimensional amplitude modulations quadrature amplitude modulation qam is an attractive technique to achieve high rate transmission without increasing the bandwidth a great deal of attention has been devoted to the study of bit error rate ber performance of qam and approximate expressions for the bit error probability of qam have been developed in many places in the literature however the exact and general ber expression of qam with an arbitrary constellation size has not been derived yet we provide an exact and general closed form expression of the ber for one dimensional and two dimensional amplitude modulations i e pam and qam under an additive white gaussian noise awgn channel when gray code bit mapping is employed the provided ber expressions offer a convenient way to evaluate the performance of pam and qam systems for various cases of practical interest moreover simple approximations can be found from our expressions which are the same as the well known approximations if only the dominant terms are considered

block transmission over dispersive channels transmit filter optimization and realization and mmse dfe receiver performance optimal transmit filters for packet based data transmission on dispersive gaussian noise linear time invariant channels are derived by maximizing the mutual information subject to a fixed input power budget a quasi stationary approximation to the optimal nonstationary input covariance process is derived and shown to exhibit negligible mutual information loss from the optimal case for situations of most practical interest moreover this quasi stationary approximation results in efficiently computed lattice or pole zero implementations of the transmit filter by considering the popular finite impulse response minimum mean square error decision feedback equalizer fir mmse dfe as a receiver structure we show that transmitter optimization results in an appreciable improvement in the decision point signal to noise ratio finally we show that as the output blocklength becomes infinite the optimum finite dimensional nonstationary input covariance process converges to a stationary process whose power spectrum obeys the well known water pouring distribution

quantum classical correspondence via a deformed kinetic operator we propose an approach to quantum classical correspondence based on a deformation of the momentum and kinetic operators of quantum mechanics making use of the factorization method we construct classical versions of the momentum and kinetic operators which in addition to the standard quantum expressions contain terms that are functionals of the n particle density we show that this implementation of quantum classical correspondence is related to witten s deformation of the exterior derivative and laplacian introduced in the context of supersymmetric quantum mechanics the corresponding deformed action is also shown to be related to the fisher information finally we briefly consider the possible relevance of our approach to the construction of kinetic energy density functionals

the generalized triangular decomposition given a complex matrix h we consider the decomposition h qrp where r is upper triangular and q and p have orthonormal columns special instances of this decomposition include the singular value decomposition svd and the schur decomposition where r is an upper triangular matrix with the eigenvalues of h on the diagonal we show that any diagonal for r can be achieved that satisfies weyl s multiplicative majorization conditions k k k k i 1 r i i 1 1 k k k i 1 r i i 1 i where k is the rank of h i is the i th largest singular value of h and r i is the i th largest in magnitude diagonal element of r given a vector r which satisfies weyl s conditions we call the decomposition h qrp where r is upper triangular with prescribed diagonal r the generalized triangular decomposition gtd a direct nonrecursive algorithm is developed for computing the gtd this algorithm starts with the svd and applies a series of permutations and givens rotations to obtain the gtd the numerical stability of the gtd update step is established the gtd can be used to optimize the power utilization of a communication channel while taking into account quality of service requirements for subchannels another application of the gtd is to inverse eigenvalue problems where the goal is to construct matrices with prescribed eigenvalues and singular values

a riemannian framework for tensor computing tensors are nowadays a common source of geometric information in this paper we propose to endow the tensor space with an affine invariant riemannian metric we demonstrate that it leads to strong theoretical properties the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries null eigenvalues are at the infinity the geodesic between two tensors and the mean of a set of tensors are uniquely defined etc we have previously shown that the riemannian metric provides a powerful framework for generalizing statistics to manifolds in this paper we show that it is also possible to generalize to tensor fields many important geometric data processing algorithms such as interpolation filtering diffusion and restoration of missing data for instance most interpolation and gaussian filtering schemes can be tackled efficiently through a weighted mean computation linear and anisotropic diffusion schemes can be adapted to our riemannian framework through partial differential evolution equations provided that the metric of the tensor space is taken into account for that purpose we provide intrinsic numerical schemes to compute the gradient and laplace beltrami operators finally to enforce the fidelity to the data either sparsely distributed tensors or complete tensors fields we propose least squares criteria based on our invariant riemannian distance which are particularly simple and efficient to solve

block diagonal gmd for zero padded mimo frequency selective channels in the class of systems with linear precoder and decision feedback equalizers dfe for zero padded zp multiple input multiple output mimo frequency selective channels existing optimal transceiver designs present two drawbacks first the optimal systems require a large number of feedback bits from the receiver to encode the full precoding matrix second the full precoding matrix leads to complex computations these disadvantages become more severe as the bandwidth bw efficiency increases in this paper we propose using block diagonal geometric mean decomposition bd gmd to design the transceiver two new bd gmd transceivers are proposed the zf bd gmd system where the receiver is a zero forcing dfe zf dfe and the mmse bd gmd system where the receiver is a minimum mean square error dfe mmse dfe the bd gmd systems introduced here have the following four properties a they use the block diagonal unitary precoding technique to reduce the required number of encoding bits and simplify the computation b for any block size the bd gmd systems are optimal within the family of systems using block diagonal unitary precoders and dfes as block size gets larger the bd gmd systems produce uncoded bit error rate ber performance similar to the optimal systems using unitary precoders and dfes c for the two zf transceivers zf optimal and zf bd gmd and the two mmse transceivers mmse optimal and mmse bd gmd the average ber degrades as the bw efficiency increases d in the case of single input single output siso channels the bd gmd systems have the same performance as those of the lazy precoder transceivers these properties make the proposed bd gmd systems more favorable designs in practical implementation than the optimal systems

pedestrian detection via classification on riemannian manifolds we present a new algorithm to detect pedestrian in still images utilizing covariance matrices as object descriptors since the descriptors do not form a vector space well known machine learning techniques are not well suited to learn the classifiers the space of d dimensional nonsingular covariance matrices can be represented as a connected riemannian manifold the main contribution of the paper is a novel approach for classifying points lying on a connected riemannian manifold using the geometry of the space the algorithm is tested on inria and daimlerchrysler pedestrian datasets where superior detection rates are observed over the previous approaches

generalized geometric mean decomposition and dfe transceiver design part ii performance analysis in a companion paper the generalized geometric mean decomposition ggmd was proposed and used to design ggmd decision feedback equalizer dfe transceivers for arbitrary multiple input multiple output mimo channels without zero forcing constraint for the application to cyclic prefix cp systems the ggmd dfe transceiver has the most advantage over the gmd dfe mmse transceiver in terms of design and implementation complexity this paper presents the performance analysis for the ggmd dfe transceiver implementation proposed in part i the arithmetic mean square error mse symbol error rate ser and gaussian mutual information of the proposed system are investigated the performance advantages of ggmd dfe transceiver over popular orthogonal frequency division multiplexing ofdm and single carrier cp mmse systems are shown analytically and verified by numerical simulations

the geometric mean decomposition given a complex matrix h we consider the decomposition h qrp where q and p have orthonormal columns and r is a real upper triangular matrix with diagonal elements equal to the geometric mean of the positive singular values of h this decomposition which we call the geometric mean decomposition has application to signal processing and to the design of telecommunication networks the unitary matrices correspond to information lossless filters applied to transmitted and received signals that minimize the maximum error rate of the network another application is to the construction of test matrices with specified singular values

linear mmse multiuser receivers mai conditional weak convergence and network capacity we explore the performance of minimum mean square error mmse multiuser receivers in wireless systems where the signatures are modeled as random and take values in complex space first we study the conditional distribution of the output multiple access interference mai of the mmse receiver by appealing to the notion of conditional weak convergence we find that the conditional distribution of the output mai given the received signatures and received powers converges in probability to a proper complex gaussian distribution that does not depend on the signatures this result indicates that in a large system the output interference of the mmse receiver is approximately gaussian with high probability and that systems with mmse receivers are robust to the randomness of the signatures building on the gaussianity of the output interference we then take the quality of service qos requirements as meeting the signal to interference ratio sir constraints and identify the network capacity of single class systems with random spreading the network capacity is expressed uniquely in terms of the sir requirements and received power distributions compared to the network capacity corresponding to the optimal signature allocation we conclude that at the cost of transmission power the gap between the network capacity corresponding to optimal signatures and that corresponding to random signatures can be made arbitrarily small therefore from the viewpoint of the network capacity systems with mmse receivers are robust to the randomness of signatures

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

asymptotic normality of linear multiuser receiver outputs this paper proves large system asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers this family of receivers encompasses the single user matched filter the decorrelator the minimum mean square error mmse receiver the parallel interference cancelers and many other linear receivers of interest both with and without the assumption of perfect power control we show that the output decision statistic for each user converges to a gaussian random variable in distribution as the number of users and the spreading factor both tend to infinity with their ratio fixed analysis reveals that the distribution conditioned on almost all spreading sequences converges to the same distribution which is also the unconditional distribution this normality principle allows the system performance e g the multiuser efficiency to be completely determined by the output signal to interference ratio sir for large linear systems

asymptotic performance analysis of coded blast architectures with statistical rate and power allocations in this paper we first analyze some mathematical properties of ergodic capacity and outage capacity functions of the layers in bell labs layered space time blast architectures employing successive decoding and interference cancellation we then present statistical rate allocation and power allocation methods that optimize the asymptotic performance of blast architectures since the methods are developed by using ergodic capacity and outage capacity functions of the layers the allocated rates and powers depend only on a given channel statistic finally we prove that the rate allocation yields a better asymptotic performance than the power allocation numerical results show that blast architectures with the rate and power allocation perform better by 4 db and 3 db respectively than a blast architecture with the same rate and power in all layers

improved linear transmit processing for single user and multi user mimo communications systems in this paper we propose a novel linear transmit precoding strategy for multiple input multiple output mimo systems employing improper signal constellations in particular improved zero forcing zf and minimum mean square error mmse precoders are derived based on modified cost functions and are shown to achieve a superior performance without loss of spectrum efficiency compared to the conventional linear and nonlinear precoders the superiority of the proposed precoders over the conventional solutions are verified by both simulation and analytical results the novel approach to precoding design is also applied to the case of an imperfect channel estimate with a known error covariance as well as to the multi user scenario where precoding based on the nullspace of channel transmission matrix is employed to decouple multi user channels in both cases the improved precoding schemes yield significant performance gain compared to the conventional counterparts

equal diagonal qr decomposition and its application to precoder design for successive cancellation detection in multiple input multiple output mimo multiuser detection theory the qr decomposition of the channel matrix h can be used to form the back cancellation detector in this paper we propose an optimal qr decomposition which we call the equal diagonal qr decomposition or briefly the qrs decomposition we apply the decomposition to precoded successive cancellation detection where we assume that both the transmitter and the receiver have perfect channel knowledge we show that for any channel matrix h there exists a unitary precoder matrix s such that hs qr where the nonzero diagonal entries of the upper triangular matrix r in the qr decomposition of hs are all equal to each other the precoder and the resulting successive cancellation detector have the following properties a the minimum euclidean distance between two signal points at the channel output is equal to the minimum euclidean distance between two constellation points at the precoder input up to a multiplicative factor that equals the diagonal entry in the r factor b the superchannel hs naturally exhibits an optimally ordered column permutation i e the optimal detection order for the vertical bell labs layered space time v blast detector is the natural order c the precoder s minimizes the block error probability of the qr successive cancellation detector d a lower and an upper bound for the free distance at the channel output is expressible in terms of the diagonal entries of the r factor in the qr decomposition of a channel matrix e the precoder s maximizes the lower bound of the channel s free distance subject to a power constraint f for the optimal precoder s the performance of the qr detector is asymptotically at large signal to noise ratios snrs equivalent to that of the maximum likelihood detector mld that uses the same precoder further we consider two multiplexing schemes time division multiple access tdma and orthogonal frequency division multiplexing ofdm we d

structure of an optimum linear precoder and its application to ml equalizer the structure of an optimum linear precoder for a rotation invariant performance measure is obtained subject to the constraint of limited input power for a block transmission scheme it is shown that several known performance measures of a communication system are rotation invariant the rotation invariant property provides a unified framework for obtaining the structure of an optimum linear precoder for several criteria such as 1 maximization of minimum distance 2 maximization of channel capacity and 3 optimization of different performance measures such as bit error rate ber mean square error signal to noise ratio of optimum equalizers linear minimum mean square error zero forcing maximum likelihood ml zero forcing block decision feedback minimum mean square error block decision feedback etc this framework provides a method for obtaining the structure of an optimum linear precoder for ber performance measure of the ml equalizer the structure turns out to be a channel diagonalizing structure after a prerotation of the input constellation using this structure the properties of the optimum precoder that minimize the ber of the ml equalizer for two binary phase shift keying symbols transmission under input power constraint are studied

from sample similarity to ensemble similarity probabilistic distance measures in reproducing kernel hilbert space this paper addresses the problem of characterizing ensemble similarity from sample similarity in a principled manner using a reproducing kernel as a characterization of sample similarity we suggest a probabilistic distance measure in the reproducing kernel hilbert space rkhs as the ensemble similarity assuming normality in the rkhs we derive analytic expressions for probabilistic distance measures that are commonly used in many applications such as chernoff distance or the bhattacharyya distance as its special case kullback leibler divergence etc since the reproducing kernel implicitly embeds a nonlinear mapping our approach presents a new way to study these distances whose feasibility and efficiency is demonstrated using experiments with synthetic and real examples further we extend the ensemble similarity to the reproducing kernel for ensemble and study the ensemble similarity for more general data representations

on the relationship between mmse sic and bi gdfe receivers for large multiple input multiple output channels a minimum mean square error mmse based iterative soft interference cancellation mmse sic receiver has been proposed to mitigate the interferences of the multiple input multiple output mimo channels with reduced complexity as compared to maximum likelihood ml detection on the other hand the block iterative generalized decision feedback equalizer bi gdfe attains close to the performance of the mmse sic receivers with further reduced complexity the bi gdfe however requires an accurate estimate of the input decision correlation idc which is a statistical reliability metric of earlier made decisions to date the bi gdfe receiver is applicable only to phase shift keying psk modulations due to the absence of a method to estimate the idc for higher order quadrature amplitude modulations qams in this paper we establish the relationship between the mmse sic and bi gdfe receivers and propose an algorithm to determine the idc for bi gdfe from the unconditional mmse sic u mmse sic we further analyze and compare the asymptotic performances of the two receivers for large random mimo channels and prove that for the limiting case the output signal to interference plus noise ratios sinrs at each iteration for both receivers converge in probability to their respective deterministic limits our simulation results have shown that the bit error rate ber performance of the bi gdfe receiver with the proposed idc selection method achieves close to that of the u mmse sic receiver with similar convergence behavior and reaches the single user matched filter bound mfb with several iterations for high enough signal to noise ratio snr

the optimum combination of block codes and receivers for arbitrary channels a determination is made of the combinations of transmitted block codewords and matching receiver filters that maximize the signal to noise ratio at the detector with arbitrary channel impulse response and arbitrary noise spectrum this permits representing the channel as a set of parallel uncoupled subchannels with uncorrelated noise the representation is used to calculate the capacity of an arbitrary block coded time discrete channel it is shown that substantial coding gains compared to symbol by symbol processing can be achieved the block code used can be concatenated with trellis coded modulation so that the two coding gains are additive

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

space time block codes a maximum snr approach in tarokh et al 1999 space time block codes were introduced to obtain coded diversity for a multiple antenna communication system in this work we cast space time codes in an optimal signal to noise ratio snr framework and show that they achieve the maximum snr and in fact they correspond to a generalized maximal ratio combiner the maximum snr framework also helps in calculating the distribution of the snr and in deriving explicit expressions for bit error rates we bring out the connection between the theory of amicable orthogonal designs and space time codes based on this we give a much simpler proof to one of the main theorems on space time codes for complex symbols we present a rate 1 2 code for complex symbols which has a smaller delay than the code already known we also present another rate 3 4 code which is simpler than the one already known in the sense it does not involve additions or multiplications we also point out the connection between generalized real designs and generalized orthogonal designs

ber minimized ofdm systems with channel independent precoders we consider the minimization of uncoded bit error rate ber for the orthogonal frequency division multiplexing ofdm system with an orthogonal precoder we analyze the ber performance of precoded ofdm systems with zero forcing and minimum mean squared error mmse receivers in the case of mmse receivers we show that for quadrature phase shift keying qpsk there exists a class of optimal precoders that are channel independent examples of this class include the discrete fourier transform dft matrix and the hadamard matrix when the precoder is the dft matrix the resulting optimal transceiver becomes the single carrier system with cyclic prefix sc cp system we also show that the worst solution corresponds to the conventional ofdm system the conventional ofdm system has the largest ber in the case of zero forcing receivers the design of optimal transceiver depends on the signal to noise ratio snr for higher snr solutions of optimal precoders are the same as those of mmse receivers

generalized geometric mean decomposition and dfe transceiver design part i design and complexity this paper considers a new matrix decomposition which decomposes a complex matrix as a product of several sets of semi unitary matrices and upper triangular matrices in an iterative manner the inner most triangular matrix has its diagonal elements equal to the geometric mean of the singular values of the target complex matrix the complexity defined in terms of the number of floating point operations of the new decomposition generalized geometric mean decomposition ggmd depends on its parameters but is always less than or equal to that of geometric mean decomposition gmd the optimal parameters which yield the minimal complexity are derived the paper also shows how to use ggmd to design an optimal decision feedback equalizer dfe transceiver for multiple input multiple output mimo channels without zero forcing constraint a novel iterative receiving detection algorithm for the specific receiver is also proposed for the application to cyclic prefix systems in which the svd of the equivalent channel matrix can be easily computed the proposed ggmd transceiver has k log2 k times complexity advantage over the gmd transceiver where is the number of data symbols per data block and is a power of 2 in a companion paper performance analyses of the proposed ggmd transceiver in terms of arithmetic mean square error mse symbol error rate ser and gaussian mutual information are performed and comparisons with well known transceivers are made the results show that the proposed transceiver reaches the same optimality that a gmd mmse transceiver can possibly achieve

variational approach to dequantization we present a dequantization procedure based on a variational approach whereby quantum fluctuations latent in the quantum momentum are suppressed this is done by adding generic local deformations to the quantum momentum operator which give rise to a deformed kinetic term quantifying the amount of fuzziness caused by such fluctuations considered as a functional of such deformations the deformed kinetic term is shown to possess a unique minimum which is seen to be the classical kinetic energy furthermore we show that extremization of the associated deformed action functional introduces an essential nonlinearity to the resulting field equations which are seen to be the classical hamilton jacobi and continuity equations thus a variational procedure determines the particular deformation that has the effect of suppressing the quantum fluctuations resulting in dequantization of the system

decision feedback multiuser detection a systematic approach a systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of k simultaneously transmitting users of a synchronous correlated waveform multiple access cwma channel with gaussian noise a new performance criterion called symmetric energy is defined which is a low noise indicator of the joint error rate that at least one user is detected erroneously even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum likelihood detector a general class of decision feedback detectors dfds is defined with o k implementational complexity per user the symmetric energy of arbitrary dfd and bounds on their asymptotic effective energy aee performance are obtained along with an exact bit error rate and aee analysis for the decorrelating dfd the optimum dfd that maximizes symmetric energy is obtained each one of the k optimum decorrelating and conventional dfds that correspond to the k orders in which the users can be detected are shown to outperform the linear optimum decorrelating and conventional detectors respectively in terms of symmetric energy moreover algorithms are obtained for determining the choice of order of detection for the three dfds which guarantee that they uniformly user wise outperform their linear counterparts in addition to optimality in symmetric energy it is also shown that under certain conditions the optimum dfd achieves the aee performance of the exponentially complex maximum likelihood detector for all users simultaneously none of the results of this paper make the perfect feedback assumption the implications of our work on power control for multiuser detection are also discussed

error rates of the maximum likelihood detector for arbitrary constellations convex concave behavior and applications motivated by a recent surge of interest in convex optimization techniques convexity concavity properties of error rates of the maximum likelihood detector operating in the awgn channel are studied and extended to frequency flat slow fading channels generic conditions are identified under which the symbol error rate ser is convex concave for arbitrary multidimensional constellations in particular the ser is convex in snr for any one and two dimensional constellation and also in higher dimensions at high snr pairwise error probability and bit error rate are shown to be convex at high snr for arbitrary constellations and bit mapping universal bounds for the ser first and second derivatives are obtained which hold for arbitrary constellations and are tight for some of them applications of the results are discussed which include optimum power allocation in spatial multiplexing systems optimum power time sharing to decrease or increase jamming problem error rate an implication for fading channels fading is never good in low dimensions and optimization of a unitary precoded ofdm system for example the error rate bounds of a unitary precoded ofdm system with qpsk modulation which reveal the best and worst precoding are extended to arbitrary constellations which may also include coding the reported results also apply to the interference channel under gaussian approximation to the bit error rate when it can be expressed or approximated as a nonnegative linear combination of individual symbol error rates and to coded systems

minimum ber block precoders for zero forcing equalization we determine the linear precoder that minimizes the bit error rate ber at moderate to high signal to noise ratios snrs for block transmission systems with zero forcing zf equalization and threshold detection the design is developed for the two standard schemes for eliminating inter block interference viz zero padding zp and cyclic prefix cp we show that both the zp minimum ber precoder and the cp minimum ber precoder provide substantially lower error rates than standard block transmission schemes such as orthogonal frequency division multiplexing ofdm the corresponding snr gains can be on the order of several decibels we also show that the cp minimum ber precoder can be obtained by a two stage modification of the water filling discrete multitone modulation dmt scheme in which the diagonal water filling power loading is replaced by a full matrix consisting of a diagonal minimum mean square error power loading matrix post multiplied by a discrete fourier transform dft matrix

capacity of multiple antenna systems with both receiver and transmitter channel state information the capacity of multiple antenna systems operating in rayleigh flat fading is considered under the assumptions that channel state information csi is available at both transmitter and receiver and that the transmitter is subjected to an average power constraint first the capacity of such systems is derived for the special case of multiple transmit antennas and a single receive antenna the optimal power allocation scheme for such a system is shown to be a water filling algorithm and the corresponding capacity is seen to be the same as that of a system having multiple receive antennas with a single transmitter antenna whose outputs are combined via maximal ratio combining a suboptimal adaptive transmission technique that transmits only over the antenna having the best channel is also proposed for this special case it is shown that the capacity of such a system under the proposed suboptimal adaptive transmission scheme is the same as the capacity of a system having multiple receiver antennas with a single transmitter antenna combined via selection combining next the capacity of a general system of multiple transmitter and receiver antennas is derived together with an equation that determines the cutoff value for such a system the optimal power allocation scheme for such a multiple antenna system is given by a matrix water filling algorithm in order to eliminate the need for cumbersome numerical techniques in solving the cutoff equation approximate expressions for the cutoff transmission value are also provided it is shown that compared to the case in which there is only receiver csi large capacity gains are available with optimal power and rate adaptation schemes the increased capacity is shown to come at the price of channel outage and bounds are derived for this outage probability

output mai distributions of linear mmse multiuser receivers in ds cdma systems multiple access interference mai in a code division multiple access cdma system plays an important role in performance analysis and characterization of fundamental system limits we study the behavior of the output mai of the minimum mean square error mmse receiver employed in the uplink of a direct sequence ds cdma system we focus on imperfect power controlled systems with random spreading and establish that in a synchronous system 1 the output mai of the mmse receiver is asymptotically gaussian and 2 for almost every realization of the signatures and received powers the conditional distribution of the output mai converges weakly to the same gaussian distribution as in the unconditional case we also extend our study to asynchronous systems and establish the gaussian nature of the output interference these results indicate that in a large system the output interference is approximately gaussian and the performance of the mmse receiver is robust to the randomness of the signatures and received powers the gaussianity justifies the use of single user gaussian codes for cdma systems with linear mmse receivers and implies that from the viewpoints of detection and channel capacity signal to interference ratio sir is the key parameter that governs the performance of the mmse receiver in a cdma system

low rank kernel learning with bregman matrix divergences in this paper we study low rank matrix nearness problems with a focus on learning low rank positive semidefinite kernel matrices for machine learning applications we propose efficient algorithms that scale linearly in the number of data points and quadratically in the rank of the input matrix existing algorithms for learning kernel matrices often scale poorly with running times that are cubic in the number of data points we employ bregman matrix divergences as the measures of nearness these divergences are natural for learning low rank kernels since they preserve rank as well as positive semidefiniteness special cases of our framework yield faster algorithms for various existing learning problems and experimental results demonstrate that our algorithms can effectively learn both low rank and full rank kernel matrices

optimal precoder design for correlated mimo communication systems using zero forcing decision feedback equalization we consider the design of the precoder for a multi input multi output mimo communication system equipped with a decision feedback equalizer dfe receiver for such design problems perfect knowledge of the channel state information csi at both the transmitter and the receiver is usually required however in the environment of wireless communications it is often difficult to provide sufficiently timely and accurate feedback of csi from the receiver to the transmitter for such designs to be practically viable in this paper we consider the optimum design of a precoder for a wireless communication link having m transmitter antennas and n receiver antennas m n in which the channels are assumed to be flat fading and may be correlated we assume that full knowledge of csi is available at the receiver at the transmitter however only the first and second order statistics of the channels are available our goal here is to come up with an efficient design of the optimal precoder for such a mimo system by minimizing the average arithmetic mean squared error mse of zero forcing zf decision feedback detection subject to a constraint on the total transmitting power applying some of the properties of the matrix parameters this nonconvex optimization problem can be transformed into a convex geometrical programming problem which can then be efficiently solved using an interior point method the performance of the mimo system equipped with this optimum precoder and a zf dfe has also been found to be comparable and in some cases superior to that of v blast which necessitates optimally ordered successive interference cancellation based on the largest postdetection signal to noise ratio snr in terms of tradeoff between performance and implementation simplicity our new system is certainly an attractive alternative

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

mmse decision feedback equalizers and coding i equalization results the minimum mean squared error decision feedback equalizer mmse dfe has properties that suggest that it is a canonical equalization structure for systems that combine equalization with coded modulation the structure and performance of the mmse dfe are succinctly derived using linear estimation theoretic principles in this first part of this two part paper the front end of the mmse dfe called the mean square whitened matched filter ms wmf is preferable in some ways to a matched filter or a whitened matched filter as a canonical receiver front end in a coded system the feedback filter of the mmse dfe may be implemented in the transmitter using precoding the mmse dfe can perform significantly better than a zero forcing decision feedback equalizer particularly at moderate to low snr s and on severe isi channels the mmse dfe is biased the optimum unbiased mmse dfe is the mmse dfe with the bias removed removing bias improves error probability but reduces the snr to snr sub mmse dfe u snr sub mmse dfe 1 it is shown that this snr relationship is a particular case of a very general result and that snr sub mmse dfe u gives a more realistic estimate of snr the results are extended to partial response equalization and to equalization with correlated inputs in an appendix

jensen bregman logdet divergence with application to efficient similarity search for covariance matrices covariance matrices have found success in several computer vision applications including activity recognition visual surveillance and diffusion tensor imaging this is because they provide an easy platform for fusing multiple features compactly an important task in all of these applications is to compare two covariance matrices using a dis similarity function for which the common choice is the riemannian metric on the manifold inhabited by these matrices as this riemannian manifold is not flat the dissimilarities should take into account the curvature of the manifold as a result such distance computations tend to slow down especially when the matrix dimensions are large or gradients are required further suitability of the metric to enable efficient nearest neighbor retrieval is an important requirement in the contemporary times of big data analytics to alleviate these difficulties this paper proposes a novel dissimilarity measure for covariances the jensen bregman logdet divergence jbld this divergence enjoys several desirable theoretical properties and at the same time is computationally less demanding compared to standard measures utilizing the fact that the square root of jbld is a metric we address the problem of efficient nearest neighbor retrieval on large covariance datasets via a metric tree data structure to this end we propose a k means clustering algorithm on jbld we demonstrate the superior performance of jbld on covariance datasets from several computer vision applications

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

mmse dfe transceiver design over slowly time varying mimo channels using st gtd in a companion paper we have studied the zero forcing zf transceiver with decision feedback equalizer dfe over slowly time varying narrowband multiinput multioutput mimo channels the space time generalized triangular decomposition st gtd was used for the design of zf dfe transceivers the space time geometric mean decomposition st gmd zf transceiver minimizes both the arithmetic mean square error mse at the feedback detector and the average uncoded bit error rate ber in moderate high signal to noise ratio snr this paper addresses the design problem of dfe transceiver without zero forcing constraint in the first part a channel independent temporal precoder is superimposed on the conventional block wise gmd based minimum mean square error mmse dfe transceiver to take advantage of the temporal diversity in the second part st gtd is applied for the design of mmse dfe transceivers with accurate channel prediction and space time powerloading the proposed st gmd mmse transceiver minimizes the arithmetic mse at the feedack detector and maximizes gaussian mutual information for practical applications the st gtd mmse transceiver which does not require channel prediction but shares the same asymptotic ber performance with the st gmd mmse system is also developed in the convex region our analysis shows that the proposed mmse transceivers has better ber performance than the conventional gmd based mmse transceiver the average bers of the proposed systems are nonincreasing functions of the st block size the superior performance of st gmd mmse transceiver over the st gmd zf transceiver is also verified analytically

vector coding for partial response channels a linear technique for combining equalization and coset codes on partial response channels with additive white gaussian noise is developed the technique vector coding uses a set of transmit filters or vectors to partition the channel into an independent set of parallel intersymbol interference isi free channels for any given finite or infinite block length the optimal transmit vectors for such channel partitioning are shown to be the eigenvectors of the channel covariance matrix for the specified block length and the gains of the individual channels are the eigenvalues an optimal bit allocation and energy distribution are derived for the set of parallel channels under an accurate extension of the continuous approximation for power in optimal multidimensional signal sets for constellations with unequal signal spacing in different dimensions examples are presented that demonstrate performance advantages with respect to zero forcing decision feedback methods that use the same coset code on the same partial response channel only resampling the channel at an optimal rate and assuming no errors in the feedback path will bring the performance of the decision feedback methods up to the level of the vector coded system

semigroup kernels on measures we present a family of positive definite kernels on measures characterized by the fact that the value of the kernel between two measures is a function of their sum these kernels can be used to derive kernels on structured objects such as images and texts by representing these objects as sets of components such as pixels or words or more generally as measures on the space of components several kernels studied in this work make use of common quantities defined on measures such as entropy or generalized variance to detect similarities given an a priori kernel on the space of components itself the approach is further extended by restating the previous results in a more efficient and flexible framework using the kernel trick finally a constructive approach to such positive definite kernels through an integral representation theorem is proved before presenting experimental results on a benchmark experiment of handwritten digits classification to illustrate the validity of the approach

mimo transceivers with decision feedback and bit loading theory and optimization this paper considers mimo transceivers with linear precoders and decision feedback equalizers dfes with bit allocation at the transmitter zero forcing zf is assumed considered first is the minimization of transmitted power for a given total bit rate and a specified set of error probabilities for the symbol streams the precoder and dfe matrices are optimized jointly with bit allocation it is shown that the generalized triangular decomposition gtd introduced by jiang li and hager offers an optimal family of solutions the optimal linear transceiver which has a linear equalizer rather than a dfe with optimal bit allocation is a member of this family this shows formally that under optimal bit allocation linear and dfe transceivers achieve the same minimum power the dfe transceiver using the geometric mean decomposition gmd is another member of this optimal family and is such that optimal bit allocation yields identical bits for all symbol streams no bit allocation is necessary when the specified error probabilities are identical for all streams the qr based system used in vblast is yet another member of the optimal family and is particularly well suited when limited feedback is allowed from receiver to transmitter two other optimization problems are then considered a minimization of power for specified set of bit rates and error probabilities the qos problem and b maximization of bit rate for fixed set of error probabilities and power it is shown in both cases that the gtd yields an optimal family of solutions

robust minimax mse equalizer designs for mimo wireless communications with time varying channel uncertainties in this paper we propose robust equalizers based on a minimax mean squares error mse scheme for wireless multi input multi output mimo communications subject to time varying channel uncertainties we consider channel uncertainties within a neighborhood of the estimated channel matrix formed by placing a bound on the spectral matrix norm of channel estimation errors first we derive a linear matrix inequality lmi based solution to the targeted problem next we modify the mse cost function of the targeted problem and derive a guaranteed cost based solution which may save computational cost subsequently channel uncertainty is partitioned into finite markov transitioned channel uncertainty states based on the least upper bound of the set of the tightest upper bounds on the matrix spectral norm of channel uncertainty this leads to a multiple model based minimax mse approach on this basis a feasible equalizer can be obtained from a weighted combination of multiple over guaranteed cost based equalizers each of which is designed with respect to a channel uncertain state simulation results show that a weighted combination of a moderate number of multiple over guaranteed cost based equalizers can achieve robust equalization effectively with superior mse and bit error rate ber performance

infinite dimensional log determinant divergences between positive definite trace class operators abstract this work presents a novel parametrized family of log determinant log det divergences between positive definite unitized trace class operators on a hilbert space this is a generalization of the log det divergences between symmetric positive definite matrices to the infinite dimensional setting for the log det divergences between covariance operators on a reproducing kernel hilbert space rkhs we obtain closed form solutions via the corresponding gram matrices by employing the log det divergences we then generalize the bhattacharyya and hellinger distances and the kullback leibler and renyi divergences between multivariate normal distributions to gaussian measures on an infinite dimensional hilbert space

means of hermitian positive definite matrices based on the log determinant α divergence function the set of hermitian positive definite matrices plays fundamental roles in many disciplines such as mathematics numerical analysis probability and statistics engineering and biological and social sciences in the last few years there has been a renewable interest in developing the theory of means for elements in this set this is due to theoretical and practical implications in this work we present a one parameter family of divergence functions for measuring distances between hermitian positive definite matrices we then study the invariance properties of these divergence functions as well as the matrix means based on them we also give globally convergent algorithms for computing these means

filterbank transceivers optimizing information rate in block transmissions over dispersive channels optimal finite impulse response fir transmit and receive filterbanks are derived for block based data transmissions over frequency selective additive gaussian noise agn channels by maximizing mutual information subject to a fixed transmit power constraint both fir and pole zero channels are considered the inherent flexibility of the proposed transceivers is exploited to derive as special cases zero forcing zf and minimum mean square error receive filterbanks the transmit filterbank converts transmission over a frequency selective fading channel affected by additive colored noise into a set of independent flat fading subchannels with uncorrelated noise samples two loading algorithms are also developed to distribute transmit power and number of bits across the usable subchannels while adhering to an upper bound on the bit error rate ber reduction of the signal to noise ratio snr margin required to satisfy the prescribed ber is achieved by coding each subchannel s bit stream the potential of the proposed transceivers is illustrated and compared to discrete multitone dmt with simulated examples

fisher information and kinetic energy functionals a dequantization approach we strengthen the connection between information theory and quantum mechanical systems using a recently developed dequantization procedure whereby quantum fluctuations latent in the quantum momentum are suppressed the dequantization procedure results in a decomposition of the quantum kinetic energy as the sum of a classical term and a purely quantum term the purely quantum term which results from the quantum fluctuations is essentially identical to the fisher information the classical term is complementary to the fisher information and in this sense it plays a role analogous to that of the shannon entropy we demonstrate the kinetic energy decomposition for both stationary and nonstationary states and employ it to shed light on the nature of kinetic energy functionals

differential feedback of geometrical mean decomposition precoder for time correlated mimo systems for a time correlated channel we consider the differential feedback of the geometrical mean decomposition gmd precoder which is known to be optimal for a number of criteria when the channel varies slowly we can expect the optimal gmd precoders of consecutive channel uses to be close we consider the feedback of the so called differential precoder and show that it lies in a neighborhood of the identity matrix using matrix perturbation theory furthermore the radius of the neighborhood is shown to be proportional to a time correlation parameter such a characterization allows for subsequent efficient quantization of the differential precoder we show how to design codewords for the prescribed radius by perturbing the identity matrix and applying qr decomposition on the perturbed matrix simulations are given to demonstrate that with a small feedback rate the performance of the proposed differential gmd comes close to the case when perfect channel state information is available to the transmitter for slowly time varying channels like those in indoor and microcellular environments

schrodinger equation from an exact uncertainty principle an exact uncertainty principle formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position leads from the classical equations of motion to the schrodinger equation

design of block transceivers with decision feedback detection this paper presents a method for jointly designing the transmitter receiver pair in a block by block communication system that employs intrablock decision feedback detection we provide closed form expressions for transmitter receiver pairs that simultaneously minimize the arithmetic mean squared error mse at the decision point assuming perfect feedback the geometric mse and the bit error rate of a uniformly bit loaded system at moderate to high signal to noise ratios separate expressions apply for the zero forcing and minimum mse mmse decision feedback structures in the mmse case the proposed design also maximizes the gaussian mutual information and suggests that one can approach the capacity of the block transmission system using independent instances of the same gaussian code for each element of the block our simulation studies indicate that the proposed transceivers perform significantly better than standard transceivers and that they retain their performance advantages in the presence of error propagation

joint transmitter receiver optimization for multi input multi output systems with decision feedback the joint transmit receive optimization problem for multiuser communication systems with decision feedback is investigated it is shown that minimization of the geometric mean squared error defined as the determinant of the error covariance matrix leads to a tractable transmitter optimization problem for general multi input multi output decision feedback systems several computational results are included that highlight system performance for a variety of useful transmission scenarios