capacity of mimo channels with antenna selection this correspondence studies the capacity of multiple input multiple output mimo channels in the presence of antenna selection antenna selection reduces the complexity of the radio devices and requires only a small amount of channel state feedback for high signal to noise ratio snr we define excess rate as the constant term in the expansion of the ergodic capacity in terms of snr it is shown that this value is representative of the channel state information csi at the transmitter the asymptotic behavior of the excess rate is then analyzed for three cases complete csi no csi and partial csi at transmitter antenna selection while water filling provides a excess rate that increases logarithmically in m the number of transmit antennas the excess rate of transmit antenna selection behaves only like log log m for the low snr case we use the concept of channel gain a measure introduced by verdu we show that channel gain for antenna selection increases only logarithmically in m as opposed to water filling channel gain which increases linearly in m the same techniques are also applied to the receive selection and corresponding results are noted in high and low snr regimes the methodology developed in this correspondence although motivated by antenna selection is fairly general and can be used for any system where partial csi is available at the mimo transmitter

performance bounds for polynomial phase parameter estimation with nonuniform and random sampling schemes estimating the parameters of a cisoid with an unknown amplitude and polynomial phase using uniformly spaced samples can result in ambiguous estimates due to nyquist sampling limitations it has been shown previously that nonuniform sampling has the advantage of unambiguous estimates beyond the nyquist frequency however the effect of sampling on the cramer rao bounds is not well known this paper first derives the maximum likelihood estimators and cramer rao bounds for the parameters with known arbitrary sampling times it then outlines two methods for incorporating random sampling times into the lower variance bounds describing one in detail it is then shown that for a signal with additive white gaussian noise the bounds for the estimation with nonuniform sampling tend toward those of uniform sampling thus nonuniform sampling overcomes the ambiguity problems of uniform sampling without incurring the penalty of an increased variance in parameter estimation

generalized selection combining based on the log likelihood ratio we propose a generalized selection combining gsc scheme for binary signaling in which a subset of diversity branches providing the largest magnitude of log likelihood ratio llr are selected and combined it is shown that the bit error probability with maximum ratio combining mrc or square law combining of l branches is identical to that with llr based gsc of l 2 branches we also propose a simple but suboptimal gsc based on a noncoherent envelope detection and discuss its potential advantages over the conventional signal to noise ratio based gsc and mrc

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

analysis of hybrid selection maximal ratio combining in correlated nakagami fading we present an analysis of a hybrid selection maximal ratio combining diversity system over an evenly correlated slow frequency nonselective nakagami fading channel where the correlation coefficient between any pair of the diversity branch gain amplitudes is the same and all average branch signal to noise ratios snrs are equal in this system the l branches with the largest instantaneous snr out of n available branches are selected and combined using maximal ratio combining from the joint characteristic function cf of the instantaneous branch snrs we obtain an expression for the cf of the combiner output snr as a series of elementary cfs the expression can be conveniently used to obtain the symbol error probability of coherent detection of different m ary modulation schemes we illustrate our methodology using m ary phase shift keying as an example

scale space view of curve estimation scale space theory from computer vision leads to an interesting and novel approach to nonparametric curve estimation the family of smooth curve estimates indexed by the smoothing parameter can be represented as a surface called the scale space surface the smoothing parameter here plays the same role as that played by the scale of resolution in a visual system in this paper we study in detail various features of that surface from a statistical viewpoint weak convergence of the empirical scale space surface to its theoretical counterpart and some related asymptotic results have been established under appropriate regularity conditions our theoretical analysis provides new insights into nonparametric smoothing procedures and yields useful techniques for statistical exploration of features in the data in particular we have used the scale space approach for the development of an effective exploratory data analytic tool called sizer

on the snr penalty of mpsk with hybrid selection maximal ratio combining over i i d rayleigh fading channels closed form expressions that lower and upper bound the penalty of hybrid selection maximal ratio combining relative to maximal ratio combining mrc for m ary phase shift keying mpsk modulation are proved the bounds offer simple to evaluate explicit expressions and are typically within 0 6 db for hybrid systems with diversity order up to eight that use at least two branches yet are independent of signal to noise ratio snr contrary to conclusions conjectured in a previously published paper it is proved that the snr penalty is not a constant independent of snr it is also shown that previous estimates of the performance losses of selection diversity relative to mrc underestimate or lower bound the losses for mpsk modulation systems and that the true loss can be significantly larger than previously believed an upper bound to this loss is also obtained

rate of channel hardening of antenna selection diversity schemes and its implication on scheduling for a multiple antenna system we find a simple and accurate expression for the asymptotic distribution of the antenna selection gain when the transmitter selects the transmit antenna with the strongest channel we use this to estimate the underlying channel capacity distributions and obtain the approximate ergodic capacity this estimate is compared with upper and lower bounds this analysis demonstrates that unlike multiple input multiple output mimo systems the channel for antenna selection systems hardens at a slower rate and thus a significant multiuser scheduling gain can exist theta 1 logm for channel selection as opposed to theta 1 radicm for mimo where m is the number of transmit antennas

an adaptation theory for nonparametric confidence intervals a nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals a between class modulus of continuity captures the expected length of adaptive confidence intervals sharp lower bounds are given for the expected length and an ordered modulus of continuity is used to construct adaptive confidence procedures which are within a constant factor of the lower bounds in addition minimax theory over nonconvex parameter spaces is developed

average level crossing rate and average outage duration of generalized selection combining the paper presents an analytical methodology for the evaluation of the average level crossing rate and the average outage duration of generalized selection combining more specifically it presents a general approach when this scheme is employed over independent but not necessarily identically distributed fading channels the general approach is then specialized to independent identically distributed rayleigh fading paths selected numerical examples and plots are also provided and discussed

analysis of hybrid selection maximal ratio combining in rayleigh fading we use a novel virtual branch technique to succinctly derive the mean and variance of the combiner output signal to noise ratio for hybrid selection maximal ratio combining in a multipath fading environment

wavelet shrinkage using cross validation summary wavelets are orthonormal basis functions with special properties that show potential in many areas of mathematics and statistics this paper concentrates on the estimation of functions and images from noisy data by using wavelet shrinkage a modified form of twofold cross validation is introduced to choose a threshold for wavelet shrinkage estimators operating on data sets of length a power of 2 the cross validation algorithm is then extended to data sets of any length and to multidimensional data sets the algorithms are compared with established threshold choosers by using simulation an application to a real data set arising from anaesthesia is presented

confidence sets for split points in decision trees we investigate the problem of finding confidence sets for split points in decision trees cart our main results establish the asymptotic distribution of the least squares estimators and some associated residual sum of squares statistics in a binary decision tree approximation to a smooth regression curve cube root asymptotics with nonnormal limit distributions are involved we study various confidence sets for the split point one calibrated using the subsampling bootstrap and others calibrated using plug in estimates of some nuisance parameters the performance of the confidence sets is assessed in a simulation study a motivation for developing such confidence sets comes from the problem of phosphorus pollution in the everglades ecologists have suggested that split points provide a phosphorus threshold at which biological imbalance occurs and the lower endpoint of the confidence set may be interpreted as a level that is protective of the ecosystem this is illustrated using data from a duke university wetlands center phosphorus dosing study in the everglades

optimal signaling and selection verification for single transmit antenna selection in marked contrast with the ideal error free feedback assumption that is common in the literature practical systems are likely to have severely bandwidth limited error prone feedback channels we consider the scenario where feedback from the receiver is used by the transmitter to select the best antenna out of many available antennas for data transmission feedback errors cause the transmitter to select an antenna different from the one signaled by the receiver we show that optimizing the signaling assignment which maps the antenna indices to the feedback codewords improves performance without introducing any additional redundancy for a system that uses error prone feedback to transmit quadrature phase shift keying modulated data from a single antenna selected from many available spatially correlated antennas we derive closed form approximations for the data symbol error probability for an arbitrary number of receive antennas we use these to systematically find the optimal signaling assignments using a low complexity algorithm the optimal signaling is intimately coupled to how the receiver performs selection verification i e how it decodes the data signal when due to feedback errors it does not always know which antenna was used for data transmission we show that ignoring feedback errors at the receiver can lead to an unacceptable performance degradation and develop optimal and suboptimal blind and nonblind selection verification methods with a small side information overhead nonblind verification approaches the ideal perfect selection verification performance

a unified approach to computing error probabilities of diversity combining schemes over correlated fading channels the average bit error rate performance of one stage and two stage diversity combining schemes operating over correlated fading channels is investigated two channel models that can significantly simplify the performance analysis are considered in particular a linear correlation channel model having equal branch variances can be decorrelated at the receiver so that the branches become independent it is shown that in general employing diversity combining schemes for decorrelated or orthogonalized branches can recover some of the diversity gain lost due to the branch correlations this is observed for example for the case of hybrid selection maximum ratio combining operating over decorrelated and orthogonalized non zero mean gaussian fading channels furthermore a fading amplitude channel model is proposed assuming vector norm superposition of the impinging plane waves this channel model is well suited for the performance analysis of maximum ratio and equal gain combining schemes operating over correlated fading channels finally the average bit error rates of several diversity combining schemes are evaluated analytically using the prony approximation method as well as using computer simulation

analysis of minimum selection h s mrc in rayleigh fading we analyze the error performance of an improved hybrid selection maximal ratio combining h s mrc technique called minimum selection h s mrc in flat rayleigh fading for coherent digital modulation schemes here the minimum number of diversity branches are selected such that their combined signal to noise ratio is above a given threshold we derive a closed form expression for the distribution of the number of selected branches this distribution is used to obtain the symbol error probability

asymptotic performance of hybrid selection maximal ratio combining over fading channels in this letter we study the asymptotic performance of hybrid selection maximal ratio combining hs mrc and postdetection hs equal gain combining hs egc over generalized fading channels for large average signal to noise ratios asnrs by evaluating the asymptotic moment generating function of the hs mrc output snr at high asnr we derive the diversity and coding gains for hs mrc for a large class of modulation formats and versatile fading conditions including different types of fading channels and nonidentical snr statistics across diversity branches our analytical results reveal that the diversity gains of hs mrc and hs egc are equivalent to that of mrc and the difference in the coding gains for different modulation formats is manifested in terms of a modulation factor defined in this letter some new analytical results about effects of the number of combined branches for hs mrc and noncoherent combining loss of hs egc are also provided

quasi linear wavelet estimation abstract the main paradigm of the modern wavelet theory of spatial adaptation formulated by donoho and johnstone is that there is a divergence between the linear minimax adaptation theory and the heuristic guiding algorithm development that leads to the necessity of using strongly nonlinear adaptive thresholded methods on the other hand it is well known that linear adaptive estimates are the best whenever an estimated function is smooth is it possible to suggest a quasi linear wavelet estimate by adding to a linear adaptive estimate a minimal number of nonlinear terms on finest scales that offers advantages of linear adaptive estimates and at the same time matches asymptotic properties of strongly nonlinear procedures like the benchmark sureshrink the answer is yes and we discuss quasi linear estimation both theoretically and via a monte carlo study in particular i show that asymptotically a quasi linear procedure not only matches properties of sureshrink over the besov scale but also allows

nonquadratic estimators of a quadratic functional estimation of a quadratic functional over parameter spaces that are not quadratically convex is considered it is shown in contrast to the theory for quadratically convex parameter spaces that optimal quadratic rules are often rate suboptimal in such cases minimax rate optimal procedures are constructed based on local thresholding these nonquadratic procedures are sometimes fully efficient even when optimal quadratic rules have slow rates of convergence moreover it is shown that when estimating a quadratic functional nonquadratic procedures may exhibit different elbow phenomena than quadratic procedures

performance analysis of generalized selection combining in generalized correlated nakagami m fading the exact performance of selection combining hybrid selection maximal ratio combining h s mrc and threshold based h s mrc in correlated nakagami m fading for positive integer values of fading parameter m is analyzed for a particular correlation structure this correlation model though not general is much more general than the equal correlation case and includes equal correlation as a special case the symbol error rate and outage probability of the three combining schemes are obtained by transforming the correlated branch gains into a set of conditionally independent branch gains numerical and simulation results show excellent agreement with theoretical results

adaptive mimo antenna selection via discrete stochastic optimization recently it has been shown that it is possible to improve the performance of multiple input multiple output mimo systems by employing a larger number of antennas than actually used and selecting the optimal subset based on the channel state information existing antenna selection algorithms assume perfect channel knowledge and optimize criteria such as shannon capacity or various bounds on error rate this paper examines mimo antenna selection algorithms where the set of possible solutions is large and only a noisy estimate of the channel is available in the same spirit as traditional adaptive filtering algorithms we propose simulation based discrete stochastic optimization algorithms to adaptively select a better antenna subset using criteria such as maximum mutual information bounds on error rate etc these discrete stochastic approximation algorithms are ideally suited to minimize the error rate since computing a closed form expression for the error rate is intractable we also consider scenarios of time varying channels for which the antenna selection algorithms can track the time varying optimal antenna configuration we present several numerical examples to show the fast convergence of these algorithms under various performance criteria and also demonstrate their tracking capabilities

kernel estimation of the instantaneous frequency considers kernel estimators of the instantaneous frequency of a slowly evolving sinusoid in white noise the expected estimation error consists of two terms the systematic bias error grows as the kernel halfwidth increases while the random error decreases for a nonmodulated signal g t the kernel halfwidth that minimizes the expected error is proportional to h spl sim spl sigma sup 2 n spl part sub t sup 2 g 2 sup 1 5 where spl sigma sup 2 is the noise variance and n is the number of measurements per unit time the author shows that estimating the instantaneous frequency corresponds to estimating the first derivative of a modulated signal a t exp i spl phi t for instantaneous frequency estimation the halfwidth which minimizes the expected error is larger h sub 1 3 spl sim spl sigma sup 2 a sup 2 n spl part sub t sup 3 e sup i spl phi t sup 2 sup 1 u7 since the optimal halfwidths depend on derivatives of the unknown function the authors initially estimate these derivatives prior to estimating the actual signal

performance analysis of generalized sort switch and examine combining examples of low complexity diversity combining schemes are among others the generalized selection combining gsc scheme and the generalized switch and examine combining gsec in this paper we propose a new low complexity combining scheme termed generalized sort switch and examine combining gssec that in a sense can be considered as a hybrid gsc gsec scheme a generic expression for the moment generating function of the gssec output snr in general independent identically distributed fading channels is derived and is then applied to the analysis of its error performance

adaptive confidence interval for pointwise curve estimation we present a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around f x 0 in either a white noise model or a regression setting a suitable modification in the truncation rule for wavelets allows construction of confidence intervals that achieve optimal coverage accuracy up to a logarithmic factor the procedure does not require knowledge of the regularity of the unknown function f it is also efficient for functions with a low degree of regularity

approximate ser of h s mrc in nakagami fading with arbitrary branch power correlation an accurate approximation to the average symbol error rate of hybrid selection maximal ratio combining h s mrc in correlated nakagami m fading with positive integer values of m is obtained by using a green s matrix approximation this approach is valid for different m ary linear modulation schemes we illustrate our methodology using m ary phase shift keying as an example

adaptive wavelet estimation a block thresholding and oracle inequality approach we study wavelet function estimation via the approach of block thresh olding and ideal adaptation with oracle oracle inequalities are derived and serve as guides for the selection of smoothing parameters based on an oracle inequality and motivated by the data compression and localization properties of wavelets an adaptive wavelet estimator for nonparametric re gression is proposed and the optimality of the procedure is investigated we show that the estimator achieves simultaneously three objectives adaptiv ity spatial adaptivity and computational efficiency specifically it is proved that the estimator attains the exact optimal rates of convergence over a range of besov classes and the estimator achieves adaptive local minimax rate for estimating functions at a point the estimator is easy to imple ment at the computational cost of on simulation shows that the es timator has excellent numerical performance relative to more traditional wavelet estimators 1 introduction wavelet methods have demonstrated considerable suc cess in nonparametric function estimation in terms of spatial adaptivity com putational efficiency and asymptotic optimality in contrast to the traditional linear procedures wavelet methods achieve near optimal convergence rates over large function classes such as besov classes and enjoy excellent mean squared error properties when used to estimate functions that are spatially inhomogeneous for example as shown by donoho and johnstone 1998 wavelet methods can outperform optimal linear methods even at the level of convergence rate over certain besov classes standard wavelet methods achieve adaptivity through term by term thresholding of the empirical wavelet coefficients there each individual empirical wavelet coefficient is compared with a predetermined threshold a wavelet coefficient is retained if its magnitude is above the threshold level and is discarded otherwise a well known example of term by term thresholding is donoho and johnstone s visushrink donoho and johnstone 1994 visushrink is spatially adaptive and the estimator is within a log arithmic factor of the optimal convergence rate over a wide range of besov classes visushrink achieves a degree of tradeoff between variance and bias contributions to the mean squared error however the tradeoff is not optimal visushrink reconstruction is often over smoothed hall kerkyacharian and picard 1999 considered block thresholding for wavelet function estimation which thresholds empirical wavelet coefficients in

statistical inference for the optimal approximating model in the setting of high dimensional linear models with gaussian noise we investigate the possibility of confidence statements connected to model selection although there exist numerous procedures for adaptive point estimation the construction of adaptive confidence regions is severely limited cf li in ann stat 17 1001 1008 1989 the present paper sheds new light on this gap we develop exact and adaptive confidence regions for the best approximating model in terms of risk one of our constructions is based on a multiscale procedure and a particular coupling argument utilizing exponential inequalities for noncentral 2 distributions we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one

confidence sets for nonparametric wavelet regression we construct nonparametric confidence sets for regression functions using wavelets that are uniform over besov balls we consider both thresholding and modulation estimators for the wavelet coefficients the confidence set is obtained by showing that a pivot process constructed from the loss function converges uniformly to a mean zero gaussian process inverting this pivot yields a confidence set for the wavelet coefficients and from this we obtain confidence sets on functionals of the regression curve

analysis of long period variable stars with nonparametric tests for trend detection in astronomy the study of variable stars that is stars characterized by showing significant variation in their brightness over time has made crucial contributions to our understanding of many phenomena from stellar birth and evolution to the calibration of the extragalactic distance scale in this article we develop a method for analyzing multiple pseudo periodic time series with the goal of detecting temporal trends in their periods we allow for nonstationary noise and for clustering among the various time series we apply this method to the long standing astronomical problem of identifying variable stars whose regular brightness fluctuations have periods that change over time the results of our analysis show that such changes can be substantial raising the possibility that astronomers estimates of galactic distances can be refined two significant contributions of our approach relative to existing methods for this problem are as follows 1 the method is nonparametric making minimal assumpt

adaptive nonparametric confidence sets we construct honest confidence regions for a hilbert space valued parameter in various statistical models the confidence sets can be centered at arbitrary adaptive estimators and have diameter which adapts optimally to a given selection of models the latter adaptation is necessarily limited in scope we review the notion of adaptive confidence regions and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation applications include the finite normal mean model the white noise model density estimation and regression with random design institute of mathematical statistics 2006

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

minimax estimation via wavelet shrinkage we attempt to recover an unknown function from noisy sampled data using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients the shrinkage can be tuned to be nearly minimax over any member of a wide range of triebel and besov type smoothness constraints and asymptotically minimax over besov bodies with p q linear estimates cannot achieve even the minimax rates over triebel and besov classes with p 2 so the method can significantly outperform every linear method e g kernel smoothing spline sieve in a minimax sense variants of our method based on simple threshold nonlinear estimators are nearly minimax our method possesses the interpretation of spatial adaptivity it reconstructs using a kernel which may vary in shape and bandwidth from point to point depending on the data least favorable distributions for certain of the triebel and besov scales generate objects with sparse wavelet transforms many real objects have similarly sparse transforms which suggests that these minimax results are relevant for practical problems sequels to this paper which was first drafted in november 1990 discuss practical implementation spatial adaptation properties universal near minimaxity and applications to inverse problems

ser and outage of threshold based hybrid selection maximal ratio combining over generalized fading channels the average symbol error rate and outage probability of threshold based hybrid selection maximal ratio combining t hs mrc in generalized fading environments are analyzed a t hs mrc combiner chooses the combined branches according to a predetermined normalized threshold and the strength of the instantaneous signal to noise ratio snr of each branch therefore the number of combined branches is a random variable rather than a fixed number as in conventional hybrid selection maximal ratio combining h s mrc using the moment generating function method a unified analysis of t hs mrc over various slow and frequency nonselective fading channels is presented both independent identically distributed and independent nonidentically distributed diversity branches are considered the derivation allows different m ary linear modulation schemes the theory is illustrated using coherent m ary phase shift keying in nakagami m fading as an example it is shown that previous published results are incorrect

comments on exact error rate analysis of diversity 16 qam with channel estimation error recently cao and beaulieu presented an insightful analysis on the bit error performance of 16 quadrature amplitude modulation qam scheme on rayleigh fading channels with maximal ratio combining diversity and channel estimation errors unfortunately although exact the results presented in that paper are based on a complicated parabolic cylinder function and a two dimensional numerical integration has to be performed to evaluate the average probability of bit error in this letter we present a surprisingly simple expression for the average probability of error in a well known closed form we point out that the error rates for any n ary square rectangular qam constellation with gray mapping can also be expressed in this form furthermore we show that the presented results can also be modified in a simple fashion for a generalized selection combining scheme in the presence of channel estimation errors

on the snr penalties of ideal and non ideal subset diversity systems subset diversity ssd techniques which select and combine the signals from a subset of the available diversity branches are important for practical wireless systems this paper characterizes the performance loss or signal to noise ratio snr penalty of one ssd system with respect to another both ideal and non ideal channel estimation are considered and the analysis is valid for the important case of arbitrary two dimensional signal constellations expressions are given for the asymptotic snr penalty for both small and large snr for all the comparisons considered additionally we develop bounds and approximations to quantify the performance of one system in terms of another for all snrs of interest furthermore for some signal constellations we derive the exact snr penalty of a non ideal system with respect to an ideal system as well as the exact penalty associated with two non ideal systems with varying degrees of estimation energy the snr penalty enables the assessment of system sensitivity to channel estimation energy combining architecture and signal constellation

adaptive confidence balls adaptive confidence balls are constructed for individual resolution levels as well as the entire mean vector in a multiresolution framework finite sample lower bounds are given for the minimum expected squared radius for confidence balls with a prespecified confidence level the confidence balls are centered on adaptive estimators based on special local block thresholding rules the radius is derived from an analysis of the loss of this adaptive estimator in addition adaptive honest confidence balls are constructed which have guaranteed coverage probability over all of r n and expected squared radius adapting over a maximum range of besov bodies

adaptive confidence bands we show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions we propose instead to construct adaptive bands that cover a surrogate function f which is close to but simpler than f the surrogate captures the significant features in f we establish lower bounds on the width for any confidence band for f and construct a procedure that comes within a small constant factor of attaining the lower bound for finite samples

performance analysis of linear modulation schemes with generalized diversity combining on rayleigh fading channels with noisy channel estimates generalized diversity combining gdc also known as hybrid selection maximal ratio combining or generalized selection combining is a low complexity diversity combining technique by which a fixed subset of a large number of available diversity channels is chosen and then combined using the rules of maximal ratio combining in this paper we analyze the performance of gdc on time correlated rayleigh fading channels with noisy channel estimates we derive expressions for the probability of error for various linear modulation schemes with coherent detection and discuss the conditions under which the analysis can be extended to noncoherent and differentially coherent receiver structures throughout the paper using a fundamental approach to obtain the decision statistic at the combiner output a number of new expressions for the error probabilities are obtained in a rigorous way along with a presentation of their performance with channel estimation errors the final expressions have roughly the same complexity of evaluation as that for the channel with only additive gaussian noise our results correct various inaccuracies in the literature and show that coherent receivers based on imperfectly estimated channel knowledge incur a significant performance loss

dual diversity over correlated log normal fading channels a great deal of attention has been devoted in the literature to studying the bit error rate ber performance of diversity combining systems in the presence of rayleigh rice and nagakami m fading by comparison the literature is relatively sparse in comparable analyses over log normal channels which typically characterize shadowing from indoor obstacles and moving human bodies one reason for this disparity stems from the difficulty in evaluating the exact average ber when log normal variates are involved using for example the moment generating function mgf approach due to the inability of expressing the mgf itself in a simple closed form since it is possible to evaluate the marginal and joint statistical moments as well as the cumulative distribution function cdf associated with a log normal distribution in closed form we rather focus here on other performance measures namely average combined output signal to noise ratio amount of fading and outage probability the first two performance measures depend only on the moments whereas the outage probability depends solely on the cdf closed form expressions in terms of known functions single integral representations or upper and lower bounds are obtained for these measures corresponding to maximal ratio combining selection combining and switch and stay combining schemes allowing for the possibility of correlation between the two branches numerical evaluations of these expressions illustrating the performances of each individual diversity type as well as comparisons among them are also presented

characterization of the optimum transmitter correlation matrix for mimo with antenna subset selection we give a simple and complete characterization of the optimum transmitter correlation matrix for multiple input multiple output mimo systems when antenna subset selection is used it is assumed that the receiver feeds back to the transmitter only the selected set of antennas without providing any kind of rank ordering of the selected antennas it turns out that the optimal correlation matrix in this case must be a convex combination of an identity matrix and a matrix whose elements are all ones this reduces the problem of finding the actual optimum to a one dimensional search in any given scenario

joint probability mass function estimation from asynchronous samples a common approach to study the relationship between different signals is to model them as random processes and estimate their joint probability distribution from the observed data when synchronous samples of the random processes are available then the empirical distribution gives a reliable estimate however in several situations such as sensors spread over a vast region or a software probing smart phone sensors for readings synchronous samples are either not available or are difficult costly to obtain in such cases we have to depend on non periodic asynchronous samples to obtain good estimates of the joint distribution in this paper we consider independent poisson sampling of the individual random processes and we propose a kernel based estimate of the joint probability mass function we prove that our estimate is consistent in the mean square sense for strong mixing processes which is a wide class of random processes including markov processes we also provide expressions for the asymptotic mean square error mse study the bias variance tradeoff and discuss the choice of the kernel bandwidth by appropriately choosing the kernel we show that we can obtain an asymptotic rate of t 4 5 for the mse where t is the interval of observation we also present several numerical results to discuss the accuracy of our asymptotic approximations for finite t

error rate of quadrature subbranch hybrid selection maximal ratio combining in rayleigh fading the symbol error rate ser of a quadrature subbranch hybrid selection maximal ratio combining qbhs mrc scheme for 1 d modulations in rayleigh fading is examined at the receiver n diversity branches are split into 2n in phase and quadrature subbranches traditional hybrid selection maximal ratio combining h s mrc is then applied over the 2n subbranches m ary pulse amplitude modulation including coherent binary phase shift keying with qbhs mrc is studied the ser performances of qbhs mrc and h s mrc are compared results show that qbhs mrc systems outperform traditional h s mrc systems

posterior probability intervals for wavelet thresholding summary we use cumulants to derive bayesian credible intervals for wavelet regression estimates the first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions these powers are closely approximated by linear combinations of wavelet scaling functions at an appropriate finer scale hence a suitable modification of the discrete wavelet transform allows the posterior cumulants to be found efficiently for any given data set johnson transformations then yield the credible intervals themselves simulations show that these intervals have good coverage rates even when the underlying function is inhomogeneous where standard methods fail in the case where the curve is smooth the performance of our intervals remains competitive with established nonparametric regression methods

asymptotic equivalence and adaptive estimation for robust nonparametric regression asymptotic equivalence theory developed in the literature so far are only for bounded loss functions this limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded in this paper we develop asymptotic equivalence results for robust nonparametric regression with unbounded loss functions the results imply that all the gaussian nonparametric regression procedures can be robustified in a unified way a key step in our equivalence argument is to bin the data and then take the median of each bin the asymptotic equivalence results have significant practical implications to illustrate the general principles of the equivalence argument we consider two important nonparametric inference problems robust estimation of the regression function and the estimation of a quadratic functional in both cases easily implementable procedures are constructed and are shown to enjoy simultaneously a high degree of robustness and adaptivity other problems such as construction of confidence sets and nonparametric hypothesis testing can be handled in a similar fashion

generalized fiducial inference for wavelet regression we apply fisher s fiducial idea to conduct statistical inference for wavelet regression we first develop a general methodology for handling model selection problems within the fiducial framework with this new methodology we then propose fiduical based methods for performing wavelet curve estimation as well as constructing both pointwise and curvewise confidence intervals it is shown that under some mild regularity conditions both the new fiducial based pointwise and curvewise confidence intervals have asymptotically correct coverage furthermore simulation results show that these new fiducial based methods especially for constructing pointwise confidence intervals also possess promising empirical properties to the best of our knowledge this is the first time that the fiducial idea has been applied to a nonparametric estimation problem

the root unroot algorithm for density estimation as implemented via wavelet block thresholding we propose and implement a density estimation procedure which begins by turning density estimation into a nonparametric regression problem this regression problem is created by binning the original observations into many small size bins and by then applying a suitable form of root transformation to the binned data counts in principle many common nonparametric regression estimators could then be applied to the transformed data we propose use of a wavelet block thresholding estimator in this paper finally the estimated regression function is un rooted by squaring and normalizing the density estimation procedure achieves simultaneously three objectives computational efficiency adaptivity and spatial adaptivity a numerical example and a practical data example are discussed to illustrate and explain the use of this procedure theoretically it is shown that the estimator simultaneously attains the optimal rate of convergence over a wide range of the besov classes the estimator also automatically adapts to the local smoothness of the underlying function and attains the local adaptive minimax rate for estimating functions at a point there are three key steps in the technical argument poissonization quantile coupling and oracle risk bound for block thresholding in the non gaussian setting some of the technical results may be of independent interest

receive antenna selection under discrete inputs approximation and applications to analyze the achievable performance of antenna selection as in practical multi antenna systems this paper studies the receive antenna selection ras in single input multiple output as simo systems under discrete inputs we first propose an approximate expression to evaluate the instantaneous mutual information mi of m ary quadrature amplitude modulation m qam signaling over additive white gaussian noise awgn channels then by exploiting this approximate formula we develop a closed form formula for the ergodic mi in as simo systems with m qam signaling additionally we also analyze the asymptotic mi for a large number of receive antennas n mathrm r this asymptotic analysis suggests that the scaling rate of the mi with n mathrm r becomes zero rate in contrast to the double logarithmic rate under gaussian inputs besides our result is also extended to discuss the mutual information of multiple input multiple output mimo systems having discrete inputs with receive antenna selection and an upper bound for the mi is derived finally the derived result is applied to analyze several performance measures of the discrete inputs driven as simo systems specifically it is first used to discuss the relationship between the ergodic mi and the number of active antennas our investigation shows that this relationship follows pareto principle i e 80 of the mi of full antenna selection can be achieved via 20 of the total antennas then our proposed approximation is employed to analytically study the effective mi which takes channel estimation ce into consideration indicating that ce is a main limit of large scale systems moreover the energy efficiency ee is explored on the basis of our results and we find there exists an optimal number of active antennas to maximize the energy efficiency in addition to theoretical derivations all the analytical results are validated by numerical simulations