throughput maximization in poisson fading channels with limited feedback a shot noise limited single user single input single output siso poisson fading channel with partial channel state information csi at the transmitter and perfect csi at the receiver is considered we address an optimal transmit power allocation problem that maximizes the ergodic capacity of the siso poisson fading channel subject to peak and average power constraints with only quantized csi available at the transmitter acquired via a no delay and error free feedback link with finite rate from the receiver to the transmitter due to the non convexity of the proposed optimization problem a globally optimum solution is difficult to obtain however we manage to obtain a locally optimal quantized power allocation qpa scheme by solving its dual lagrangian optimization problem we develop two efficient optimal qpa algorithms for solving the dual optimization problem and show that both of these algorithms converge to the globally optimal solution of the dual problem a low complexity near optimal qpa algorithm is also derived for the case of large number of feedback bits the results are then extended to the high peak signal to noise ratio snr regime and an explicit expression for the approximate asymptotic ergodic capacity behavior in the high snr regime with high rate quantization as the number of feedback bits goes to infinity is also provided it is seen via numerical simulations that this asymptotic capacity expression correctly approaches the capacity of the corresponding full csi case as the number of feedback bits becomes large finally the effectiveness of the derived algorithms is examined through numerical simulations

the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

feedback subsampling in temporally correlated slowly fading channels using quantized csi this paper studies the problem of feedback subsampling in temporally correlated wireless networks utilizing quantized channel state information csi under both peak and average power constraints the system data transmission efficiency is studied in two scenarios first we focus on the case where the codewords span one fading block in the second scenario the throughput is determined for piecewise slowly fading channels where the codewords are so long that a finite number of correlated gain realizations are experienced during each codeword transmission considering different temporal correlation conditions in both scenarios substantial throughput increment is observed with feedback rates well below 1 bit per slot

on the performance of music with toeplitz rectification in the context of large arrays when using subspace methods for doa estimation such as music it is well known that a performance loss occurs when the number of available samples n is not large compared to the number of sensors m this degradation is mainly due to the use of the sample correlation matrix scm which is a poor estimator of the true correlation matrix of the observations in this situation when the latter exhibits a toeplitz structure a standard trick consists in correcting the structure of the scm by averaging its entries along the subdiagonals this procedure known as toeplitz rectification is widely known to improve the estimation of the true correlation matrix hence the performance of the corresponding subspace methods in this paper we propose a statistical analysis of the music method using toeplitz rectified scm refered to as r music in the context where m n are of the same order of magnitude more precisely considering the asymptotic regime in which m n converge to infinity at the same rate we prove the consistency and asymptotic normality of the r music doa estimates numerical simulations show the accurate prediction provided by the proposed theoretical analysis

covariance matrix estimation for stationary time series we obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes a precise order of magnitude is derived for spectral radius of sample covariance matrices we also consider thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse as our main tool we implement toeplitz 1911 s idea and relate eigenvalues of covariance matrices to the spectral densities or fourier transforms of the covariances we develop a large deviation result for quadratic forms of stationary processes using m dependence approximation under the framework of causal representation and physical dependence measures

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

bit allocation law for multiantenna channel feedback quantization single user case this paper studies the design and optimization of a limited feedback single user system with multiple antenna transmitter and single antenna receiver the design problem is cast in form of the minimizing the average transmission power at the base station subject to the user s outage probability constraint the optimization is over the user s channel quantization codebook and the transmission power control function at the base station our approach is based on fixing the outage scenarios in advance and transforming the design problem into a robust system design problem we start by showing that uniformly quantizing the channel magnitude in db scale is asymptotically optimal regardless of the magnitude distribution function we derive the optimal uniform in db channel magnitude codebook and combine it with a spatially uniform channel direction codebook to arrive at a product channel quantization codebook we then optimize such a product structure in the asymptotic regime of b where b is the total number of quantization feedback bits the paper shows that for channels in the real space the asymptotically optimal number of direction quantization bits should be m 1 2 times the number of magnitude quantization bits where m is the number of base station antennas we also show that the performance of the designed system approaches the performance of the perfect channel state information system as 2 2b m 1 for complex channels the number of magnitude and direction quantization bits are related by a factor of m 1 and the system performance scales as 2 b m as b

linear dispersion codes for mimo systems based on frame theory multiple input multiple output mimo wireless communication systems provide high capacity due to the plurality of modes available in the channel existing signaling techniques for mimo systems have focused primarily on multiplexing for high data rate or diversity for high link reliability in this paper we present a new linear dispersion code design for mimo rayleigh fading channels the proposed design bridges the gap between multiplexing and diversity and yields codes that typically perform well both in terms of ergodic capacity as well as error probability this is important because as we show designs performing well from an ergodic capacity point of view do not necessarily perform well from an error probability point of view various techniques are presented for finding codes with good error probability performance monte carlo simulations illustrate performance of some example code designs in terms of ergodic capacity codeword error probability and bit error probability

adaptive coded modulation for fading channels we apply coset codes to adaptive modulation in fading channels adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable therefore trellis and lattice codes designed for additive white gaussian noise awgn channels can be superimposed on adaptive modulation for fading channels with the same approximate coding gains we first describe the methodology for combining coset codes with a general class of adaptive modulation techniques we then apply this methodology to a spectrally efficient adaptive m ary quadrature amplitude modulation mqam to obtain trellis coded adaptive mqam we present analytical and simulation results for this design which show an effective coding gain of 3 db relative to uncoded adaptive mqam for a simple four state trellis code and an effective 3 6 db coding gain for an eight state trellis code more complex trellis codes are shown to achieve higher gains we also compare the performance of trellis coded adaptive mqam to that of coded modulation with built in time diversity and fixed rate modulation the adaptive method exhibits a power savings of up to 20 db

optimum power control at finite blocklength this paper investigates the maximal channel coding rate achievable at a given blocklength n and error probability epsilon when the codewords are subjected to a long term i e averaged over all codeword power constraint the second order term in the large n expansion of the maximal channel coding rate is characterized both for additive white gaussian noise awgn channels and for quasi static fading channels with perfect channel state information available at both the transmitter and the receiver it is shown that in both the cases the second order term is proportional to n 1 ln n 1 2 for the quasi static fading case this second order term is achieved by truncated channel inversion namely by concatenating a dispersion optimal code for an awgn channel subject to a short term power constraint with a power controller that inverts the channel whenever the fading gain is above a certain threshold easy to evaluate approximations of the maximal channel coding rate are developed for both the awgn and the quasi static fading case

limiting performance of block fading channels with multiple antennas we derive the performance limits of a radio system consisting of a transmitter with t antennas and a receiver with r antennas a block fading channel with additive white gaussian noise awgn delay and transmit power constraints and perfect channel state information available at both the transmitter and the receiver because of a delay constraint the transmission of a codeword is assumed to span a finite and typically small number m of independent channel realizations therefore the relevant performance limits are the information outage probability and the delay limited or nonergodic capacity we derive the coding scheme that minimizes the information outage probability this scheme can be interpreted as the concatenation of an optimal code for the awgn channel without fading to an optimal beamformer for this optimal scheme we evaluate minimum outage probability and delay limited capacity among other results we prove that for the fairly general class of regular fading channels the asymptotic delay limited capacity slope expressed in bits per second per hertz b s hz per decibel of transmit signal to noise ratio snr is proportional to min t r and independent of the number of fading blocks m since m is a measure of the time diversity induced by interleaving or of the frequency diversity of the system this result shows that if channel state information is available also to the transmitter very high rates with asymptotically small error probabilities are achievable without the need of deep interleaving or high frequency diversity moreover for a large number of antennas delay limited capacity approaches ergodic capacity

quantized feedback information in orthogonal space time block coding this work considers how the presence of quantized channel information obtained from a feedback link may be utilized for determining a transmit weighting matrix that improves the performance of a predetermined orthogonal space time block ostb code to reduce the effects of feedback delay quantization errors and feedback channel bit errors methods based on vector quantization for noisy channels are used in the design of the feedback link the resulting transmission scheme and feedback link take the imperfect nature of the channel information into account while combining the benefits of conventional beamforming with those provided by ostb coding

maximum expected rates of block fading channels with entropy constrained channel state feedback we obtain the maximum average data rates achievable over block fading channels when the receiver has perfect channel state information csi and only an entropy constrained quantized approximation of this csi is available at the transmitter we assume channel gains in consecutive blocks are independent and identically distributed and consider a short term power constraint our analysis is valid for a wide variety of channel fading statistics including rician and nakagami m fading for this situation the problem translates into designing an optimal entropy constrained quantizer to convey approximated csi to the transmitter and to define a rate adaptation policy for the latter so as to maximize average downlink data rate a numerical procedure is presented which yields the thresholds and reconstruction points of the optimal quantizer together with the associated maximum average downlink rates by finding the roots of a small set of scalar functions of two scalar arguments utilizing this procedure it is found that achieving the maximum downlink average capacity c requires in some cases time sharing between two regimes in addition it is found that for an uplink entropy constraint h log2 l a quantizer with more than l cells provides only a small capacity increase especially at high snrs

estimation of toeplitz covariance matrices in large dimensional regime with application to source detection in this paper we derive concentration inequalities for the spectral norm of two classical sample estimators of large dimensional toeplitz covariance matrices demonstrating in particular their asymptotic almost sure consistence the consistency is then extended to the case where the aggregated matrix of time samples is corrupted by a rank one or more generally low rank matrix as an application of the latter the problem of source detection in the context of large dimensional sensor networks within a temporally correlated noise environment is studied as opposed to standard procedures this application is performed online i e without the need to possess a learning set of pure noise samples

regularized estimation of large covariance matrices this paper considers estimating a covariance matrix of p variables from n observations by either banding the sample covariance matrix or estimating a banded version of the inverse of the covariance we show that these estimates are consistent in the operator norm as long as logp 2 n 0 and obtain explicit rates the results are uniform over some fairly natural well conditioned families of covariance matrices we also introduce an analogue of the gaussian white noise model and show that if the population covariance is embeddable in that model and well conditioned then the banded approximations produce consistent estimates of the eigenvalues and associated eigenvectors of the covariance matrix the results can be extended to smooth versions of banding and to non gaussian distributions with su ciently short tails a resampling approach is proposed for choosing the banding parameter in practice this approach is illustrated numerically on both simulated and real data

robust kronecker product pca for spatio temporal covariance estimation kronecker pca involves the use of a space versus time kronecker product decomposition to estimate spatio temporal covariances in this paper the addition of a sparse correction factor is considered which corresponds to a model of the covariance as a sum of kronecker products of low separation rank and a sparse matrix this sparse correction extends the diagonally corrected kronecker pca of greenewald and hero 2014 to allow for sparse unstructured outliers anywhere in the covariance matrix e g arising from variables or correlations that do not fit the kronecker model well or from sources such as sensor noise or sensor failure we introduce a robust pca based algorithm to estimate the covariance under this model an extension to toeplitz temporal factors is also provided producing a parameter reduction for temporally stationary measurement modeling high dimensional mse performance bounds are given for these extensions finally the proposed extension of kronpca is evaluated on both simulated and real data coming from yeast cell cycle experiments this establishes the practical utility of robust kronecker pca in biological and other applications

link adaptation schemes based on parametric estimation of snr distribution over nakagami m fading channels link adaptation la schemes maximize average spectral efficiency ase using accurate channel state information csi and knowledge of signal to noise ratio snr distribution in practical systems partial csi is available at the transmitter through feedback of modulation and coding scheme index often known as channel quality indicator cqi however parameters of snr distribution theta are not known or only assumed to be known we propose two la schemes for execution at the receiver and transmitter respectively each without prior knowledge about theta in the receiver centric schemes parametric estimation of snr distribution is performed using unquantized snr samples in the transmitter centric scheme we estimate theta from cqi samples using an iterative joint quantization estimation algorithm these parametric estimates form long term snr distribution which is used to compute snr switching thresholds using these thresholds rate and power adaptation decisions are made based on instantaneous snr we have derived the maximum likelihood estimator and cramer rao lower bound for the proposed estimator using cqi feedback for nakagami m fading channels and demonstrate that near optimal ase can be achieved while using the proposed schemes as in an ideal scenario where perfect knowledge about csi and snr distribution are available a priori

combining beamforming and orthogonal space time block coding multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication efficient space time codes have been developed that utilize a large portion of the available capacity these codes are designed under the assumption that the transmitter has no knowledge about the channel in this work on the other hand we consider the case when the transmitter has partial but not perfect knowledge about the channel and how to improve a predetermined code so that this fact is taken into account a performance criterion is derived for a frequency nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code the resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods in addition a particularly efficient solution method is developed for the special case of independently fading channel coefficients the proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space time block coding simulation results for a narrow band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge

on the average rate performance of hybrid arq in quasi static fading channels the problem of efficient communication over a scalar quasi static fading channel is considered the single layer transmission slt and multi layer transmission mlt schemes do not require any knowledge of the channel state information csi at the transmitter but their performance is also limited it is shown that using hybrid arq harq can significantly improve the average rate performance provided that the rate assignment between different arq rounds is carefully chosen the average rate performance of several harq schemes is optimized and compared in addition optimal power allocation among retransmissions is derived and shown to further increase the average rate this power allocation gain is remarkable at low signal to noise ratio snr but becomes negligible at high snr comparison of two different types of limited feedback sequential feedback arq and one shot feedback quantized csi is made from several perspectives although the optimization problem is formed with respect to the average rate simulation results give a comprehensive comparison under different metrics including average rate outage probability and the combination of both substantial performance improvement is observed with even one arq retransmission in all simulations more importantly this gain appears to be robust with respect to the fading distributions

line soliton interactions of a nonisospectral and variable coefficient kadomtsev petviashvili equation an extension of the dressing method is developed to solve a nonisospectral and variable coefficient generalization of the kadomtsev petviashvili equation nonstandard dynamics of the one soliton solutions are presented decomposition of the two solitons and their interactions are studied in detail

delay constrained capacity with causal feedback a block fading channel model is considered and a k block delay constraint is imposed on data transmission the key consideration is that the channel state information is fed back to the transmitter in a causal manner a general cost function spl mu x is considered in solving the delay constrained transmission problem under the short term and the long term power constraints a causal power adaptation strategy is needed to maximize the cost function hence dynamic programming is found to give the optimum solution the general cost function is then specialized to the cases of expected and outage capacities in the case of expected capacity it is observed that optimizing the transmitted power does not give much benefit at high signal to noise ratio snr but provides a substantial gain at low snr at low snr it is proved that the capacity increases by a factor of approximately log k m due to power adaptation when the channel fades according to the spl chi sub 2m sup 2 statistics in the case of outage capacity it is shown that the optimum power adaptation solution to the long term constraint problem provides a substantial snr gain at both low and high values of snr random coding bounds are derived for the outage capacity algorithms

rate diversity tradeoff of space time codes with fixed alphabet and optimal constructions for psk modulation we show that for any q spl times m space time code s having a fixed finite signal constellation there is a tradeoff between the transmission rate r and the transmit diversity gain spl nu achieved by the code the tradeoff is characterized by r spl les q spl nu 1 where q is the number of transmit antennas when either binary phase shift keying bpsk or quaternary phase shift keying qpsk is used as the signal constellation a systematic construction is presented to achieve the maximum possible rate for every possible value of transmit diversity gain

on the expected rate of slowly fading channels with quantized side information we study a multiple layer variable rate system employing quantized feedback to maximize the expected rate over a single input single output slowly fading gaussian channel the transmitter uses partial channel state information which is obtained via an optimized resolution constrained feedback link to adapt the power and to assign code layer rates subject to different power constraints to systematically design the system parameters we develop a simple iterative algorithm that successfully exploits results in the study of parallel broadcast channels we present the necessary and sufficient conditions for single layer coding to be optimal irrespective of the number of code layers that the system can afford unlike in the ergodic case even coarsely quantized feedback is shown to improve the expected rate considerably our results also indicate that with as little as one bit of feedback information the role of multilayer coding reduces significantly

multi source signal detection with arbitrary noise covariance detecting the presence of signals in noise from multiple sources is a fundamental problem in statistical signal processing in this paper we consider multi antenna signal detection when the noise covariance matrix is assumed to be arbitrary and unknown we address this problem in the context of cognitive radio where a multiple primary user detector is analyzed this detector is known as wilks detector in statistics literature which was derived under the generalized likelihood ratio criterion we calculate the moments of wilks detector which lead to simple and accurate approximate analytical formulae for the false alarm probability the detection probability and the receiver operating characteristic from the considered simulation settings performance gain over existing detection algorithms is observed in scenarios with arbitrary and unknown noise correlation and multiple primary users

pfaffianization of the generalized variable coefficient kadomtsev petviashvili equation abstract in this paper the pfaffianization procedure is applied to the generalized variable coefficient kadomtsev petviashvili vckp equation which can describe the realistic nonlinear phenomena in the fluid dynamics and plasmas using the pfaffianization procedure the coupled system for the generalized vckp equation is derived together with the wronski type pfaffian solution for this generalized coupled vckp system under certain coefficient constraint furthermore the gramm type pfaffian solution for such a coupled system is presented and verified by virtue of the pfaffian identities

performance of statistical tests for single source detection using random matrix theory this paper introduces a unified framework for the detection of a single source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver the generalized maximum likelihood test is studied and yields the analysis of the ratio between the maximum eigenvalue of the sampled covariance matrix and its normalized trace using recent results from random matrix theory a practical way to evaluate the threshold and the p value of the test is provided in the asymptotic regime where the number k of sensors and the number n of observations per sensor are large but have the same order of magnitude the theoretical performance of the test is then analyzed in terms of receiver operating characteristic roc curve it is in particular proved that both type i and type ii error probabilities converge to zero exponentially as the dimensions increase at the same rate and closed form expressions are provided for the error exponents these theoretical results rely on a precise description of the large deviations of the largest eigenvalue of spiked random matrix models and establish that the presented test asymptotically outperforms the popular test based on the condition number of the sampled covariance matrix

bounds on packings of spheres in the grassmann manifold we derive the gilbert varshamov and hamming bounds for packings of spheres codes in the grassmann manifolds over r and c asymptotic expressions are obtained for the geodesic metric and projection frobenius chordal metric on the manifold

optimal rates of convergence for covariance matrix estimation covariance matrix plays a central role in multivariate statistical analysis significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices however a minimax theory has yet been developed in this paper we establish the optimal rates of convergence for estimating the covariance matrix under both the operator norm and frobenius norm it is shown that optimal procedures under the two norms are different and consequently matrix estimation under the operator norm is fundamentally different from vector estimation the minimax upper bound is obtained by constructing a special class of tapering estimators and by studying their risk properties a key step in obtaining the optimal rate of convergence is the derivation of the minimax lower bound the technical analysis requires new ideas that are quite different from those used in the more conventional function sequence estimation problems

painleve property auto backlund transformation lax pairs and reduction to the standard form for the korteweg de vries equation with nonuniformities it is demonstrated that the kdv equation with nonuniformities ut a t u b x t u x c t uux d t uxxx e x t 0 has the painleve property if the compatibility condition among the coefficients of it holds bt a lc b bbx dbxxx 2ah hl d c2 dh dt ce x 2a2 al d3 c4 da dt l d c l d c2 d dt l d c where l d dt lg and h t is an arbitrary function of t the auto backlund transformation and lax pairs for this equation are obtained by truncating the laurent expansion furthermore assuming the compatibility condition then the kdv equation with nonuniformities is transformable via suitable variable transformations to the standard kdv

painleve analysis and reducibility to the canonical form for the generalized kadomtsev petviashvili equation the most general kadomtsev petviashvili kp type equation ut a t x y u b t x y ux c t x y uux d t x y uxxx x k t x y uyy e t x y is studied and the conditions for the coefficients in order that it owns complete integrability are determined via a painleve test finally it is proved that the above conditions are the same as those requested for reducing the equation to the canonical form via suitable transformations

grassmannian beamforming for multiple input multiple output wireless systems transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple input multiple output mimo wireless systems unfortunately optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector both are hard to realize in this article a quantized maximum signal to noise ratio snr beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter by using the distribution of the optimal beamforming vector in independent and identically distributed rayleigh fading matrix channels the codebook design problem is solved and related to the problem of grassmannian line packing the proposed design criterion is flexible enough to allow for side constraints on the codebook vectors bounds on the codebook size are derived to guarantee full diversity order results on the density of grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or snr loss monte carlo simulations are presented that compare the probability of error for different quantization strategies

solutions of a variable coefficient kadomtsev petviashvili equation via computer algebra we apply the truncated painleve expansion and computer algebra to a type of the variable coefficient kadomtsev petviashvilli equations and find a class of the analytical solutions along with the corresponding constraints on the variable coefficients shown in this class are the physically meaningful solutions which possess the usual soliton profile

sparsistency and rates of convergence in large covariance matrix estimation this paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions here sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one depending on the case of applications sparsity priori may occur on the covariance matrix its inverse or its cholesky decomposition we study these three sparsity exploration problems under a unified framework with a general penalty function we show that the rates of convergence for these problems under the frobenius norm are of order s n log p n n 1 2 where s n is the number of nonzero elements p n is the size of the covariance matrix and n is the sample size this explicitly spells out the contribution of high dimensionality is merely of a logarithmic factor the conditions on the rate with which the tuning parameter n goes to 0 have been made explicit and compared under different penalties as a result for the l 1 penalty to guarantee the sparsistency and optimal rate of convergence the number of nonzero elements should be small sn o pn at most among o pn2 parameters for estimating sparse covariance or correlation matrix sparse precision or inverse correlation matrix or sparse cholesky factor where sn is the number of the nonzero elements on the off diagonal entries on the other hand using the scad or hard thresholding penalty functions there is no such a restriction

a broadcast approach for a single user slowly fading mimo channel a broadcast transmission strategy for the slowly fading gaussian multiple input multiple output mimo channel is introduced this broadcast strategy is an extension of the single input single output siso broadcast approach perfect channel state information csi is assumed known at the receiver end only this strategy facilitates to adapt the reliably decoded rate to the actual channel state without having any feedback link to the transmitter transmission of layered coded information is motivated by the theory of majorization we derive the basic equations characterizing achievable rates of the strategy several ad hoc approximations to the achievable region are considered and their performance is compared with the siso setting and the ergodic capacity it has been demonstrated that a single layer outage approach is reasonably efficient in the mimo setting in terms of the average reliably decoded rate a multiple access channel mac broadcast approach is also applied for the mimo case and demonstrated to be relatively efficient

optimal rates of convergence for estimating toeplitz covariance matrices toeplitz covariance matrices are used in the analysis of stationary stochastic processes and a wide range of applications including radar imaging target detection speech recognition and communications systems in this paper we consider optimal estimation of large toeplitz covariance matrices and establish the minimax rate of convergence for two commonly used parameter spaces under the spectral norm the properties of the tapering and banding estimators are studied in detail and are used to obtain the minimax upper bound the results also reveal a fundamental difference between the tapering and banding estimators over certain parameter spaces the minimax lower bound is derived through a novel construction of a more informative experiment for which the minimax lower bound is obtained through an equivalent gaussian scale model and through a careful selection of a finite collection of least favorable parameters in addition optimal rate of convergence for estimating the inverse of a toeplitz covariance matrix is also established

on the multicast capacity of the wireless broadcast channel for a multicast network in which a common source is transmitted to n users the problem of maximizing the average rate subject to a coverage constraint minimum quality of service is studied considering such a network with single antenna nodes and assuming that the channel state information is available only at the receiver side the highest expected rate achievable by a random user in the network called the expected typical rate is derived in two scenarios hard coverage constraint and soft coverage constraint in the first case the coverage is expressed in terms of the outage probability while in the second case the expected rate should satisfy a certain minimum requirement it is shown that the optimum solution achieving the highest expected typical rate for given coverage requirements in both cases is achieved by an infinite layer superposition code for which the optimal power allocation among different layers is derived the analysis is extended to a scenario with multiple transmit antennas for the miso case a suboptimal coding scheme is proposed which is shown to be asymptotically optimal when the number of transmit antennas grows at least logarithmically with the number of users in the network

communication on the grassmann manifold a geometric approach to the noncoherent multiple antenna channel we study the capacity of multiple antenna fading channels we focus on the scenario where the fading coefficients vary quickly thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver we use a noncoherent block fading model proposed by marzetta and hochwald see ibid vol 45 p 139 57 1999 the model does not assume any channel side information at the receiver or at the transmitter but assumes that the coefficients remain constant for a coherence interval of length t symbol periods we compute the asymptotic capacity of this channel at high signal to noise ratio snr in terms of the coherence time t the number of transmit antennas m and the number of receive antennas n while the capacity gain of the coherent multiple antenna channel is min m n bits per second per hertz for every 3 db increase in snr the corresponding gain for the noncoherent channel turns out to be m 1 m t bits per second per hertz where m min m n t 2 the capacity expression has a geometric interpretation as sphere packing in the grassmann manifold

on beamforming with finite rate feedback in multiple antenna systems we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations assuming that the transmitter uses the quantized information for beamforming we derive a universal lower bound on the outage probability for any finite set of beamformers the universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel using the bound it is shown that finite information systems approach the perfect information case as t 1 2 sup b t 1 where b is the number of feedback bits and t is the number of transmit antennas the geometrical bounding technique used in the proof of the lower bound also leads to a design criterion for good beamformers whose outage performance approaches the lower bound the design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook and is equivalent to the problem of designing unitary space time codes under certain conditions finally we show that good beamformers are good packings of two dimensional subspaces in a 2t dimensional real grassmannian manifold with chordal distance as the metric