upper bounds on the bit error rate of optimum combining in wireless systems this paper presents upper bounds on the bit error rate ber of optimum combining in wireless systems with multiple cochannel interferers in a rayleigh fading environment we present closed form expressions for the upper bound on the bit error rate with optimum combining for any number of antennas and interferers with coherent detection of bpsk and qam signals and differential detection of dpsk we also present bounds on the performance gain of optimum combining over maximal ratio combining these bounds are asymptotically tight with decreasing ber and results show that the asymptotic gain is within 2 db of the gain as determined by computer simulation for a variety of cases at a 10 sup 3 ber the closed form expressions for the bound permit rapid calculation of the improvement with optimum combining for any number of interferers and antennas as compared with the cpu hours previously required by monte carlo simulation thus these bounds allow calculation of the performance of optimum combining under a variety of conditions where it was not possible previously including analysis of the outage probability with shadow fading and the combined effect of adaptive arrays and dynamic channel assignment in mobile radio systems

sensitivity analysis for antenna near field imaging although imaging and inverse scattering problems have been thoroughly studied during the last century there is only a partial understanding of these complex problems most of the efforts have been placed on the development of efficient inversion algorithms and mathematical uniqueness results in comparison there are very few results and a limited knowledge about the information content in the inversion data in this paper we provide a mathematical framework for sensitivity analysis of antenna near field imaging problems based on the multipole expansion of the electromagnetic field and the fisher information to quantify the quality of data by exploiting this framework a fundamental relation for accuracy and resolution is formulated based on the crameacuter rao bound crb the sensitivity analysis is illustrated using a relevant example with cylindrical measurement data

the beta model maximum likelihood cramer rao bounds and hypothesis testing we study the maximum likelihood estimator in a setting where the dependent variable is a random graph and covariates are available on a graph level the model generalizes the well known beta model for random graphs by replacing the constant model parameters with regression functions cramer rao bounds are derived for special cases of the undirected beta model the directed beta model and the covariate based beta model the corresponding maximum likelihood estimators are compared with the bounds by means of simulations moreover examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance finally the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers

joint estimation of porosity and saturation using stochastic rock physics modeling sediment porosity and saturation affect bulk modulus shearmodulus anddensity consequently estimatinghydrocarbon saturation and reservoir porosity from seismic data is a joint estimation problem uncertainty in porosity will lead toerrorsinsaturationprediction andviceversa porosityand saturation can be jointly estimated using stochastic rockphysicsmodelingandformalbayesianestimationmethodology knowledge of shear impedance reduces the uncertainty inporosityandthusalsoreducesuncertaintyinsaturationestimation this study investigates joint estimation of porosity and saturation by using rock physics stochastic modeling and bayesian estimation theory to derive saturation and porosity maps of expected pay sands in the field example the uncertainty in porosity quantified by the standard deviation stdassociatedwiththeposteriorprobabilitydensityfunctionpdf derivedfrominversionofseismicdataismuchless than the uncertainty in the derived saturation for a typical case the std associated with saturation is 24 while porositystdisabout1 34porosityunitsgivenseismic derived inversionattributeswithreasonableaccuracy comparisonof these numbers with prior estimates showed that inversion of seismic data decreased the uncertainty in porosity to 15 of the prior uncertainty while saturation uncertainty was only reduced to 92 of the prior uncertainty although these resultsmayvaryfromonelocationtoanother themethodology isgeneralandcanbeappliedtootherlocations

on the design of mimo block fading channels with feedback link capacity constraint in this paper we propose a combined adaptive power control and beamforming framework for optimizing multiple input multiple output mimo link capacity in the presence of feedback link capacity constraint the feedback channel is used to carry channel state information only it is assumed to be noiseless and causal with a feedback capacity constraint in terms of maximum number of feedback bits per fading block we show that the hybrid design could achieve the optimal mimo link capacity and we derive a computationally efficient algorithm to search for the optimal design under a specific average power constraint finally we shall illustrate that a minimum mean square error spatial processor with a successive interference canceller at the receiver could be used to realize the optimal capacity we found that feedback effectively enhances the forward channel capacity for all signal to noise ratio snr values when the number of transmit antennas n sub t is larger than the number of receive antennas n sub r the snr gain with feedback is contributed by focusing transmission power on active eigenchannel and temporal power waterfilling the former factor contributed at most 10log sub 10 n sub t n sub r db snr gain when n sub t n sub r while the latter factor s snr gain is significant only for low snr values

limits of sensing temporal concentration changes by single cells berg and purcell biophys j 20 193 1977 calculated how the accuracy of concentration sensing by single celled organisms is limited by noise from the small number of counted molecules here we generalize their results to the sensing of concentration ramps which is often the biologically relevant situation e g during bacterial chemotaxis we calculate lower bounds on the uncertainty of ramp sensing by three measurement devices a single receptor an absorbing sphere and a monitoring sphere we contrast two strategies simple linear regression of the input signal versus maximum likelihood estimation and show that the latter can be twice as accurate as the former finally we consider biological implementations of these two strategies and identify possible signatures that maximum likelihood estimation is implemented by real biological systems

robust linear channel estimation methods for per subcarrier transmit antenna selection the linear minimum mean squared error mse channel estimator for systems employing per subcarrier transmit antenna selection is developed frequency domain correlations after the selection process are shown to be approximated well using a simple function which makes near optimal channel estimation practically possible however the resultant estimators are not robust to errors in the assumed model in terms of the antenna to subcarrier assignment used at transmission as we motivate both analytically and via simulations this is an issue when the channels for conveying this information to the receiver are severely constrained we present windowed channel estimations and new robust estimation algorithms either individually or in combination as solutions to counter this sensitivity the robust estimators are developed based on the principles of 1 minimising the worst case mse over the set of possible models and 2 minimising the expected mse over the set of possible models the latter estimator is preferred due to the lower implementation complexity and better mse performance we also prove theoretical asymptotic in signal to noise ratio performances of the two estimators used with the proposed correlation model simulation results illustrate the performance gains and improved robustness offered by the developed estimators

stimulus selection in adaptive psychophysical procedures in adaptive psychophysical procedures the stimulus should be presented at a relatively high level rather than near the middle of the psychometric function which is often defined as the threshold value for some psychometric functions the optimal stimulus placement level produces 84 to 94 correct responses in a two alternative forced choice task this result is disquieting because the popular two down one up rule tracks a relatively low percentage of correct responses 70 7 computer simulations and a variety of psychometric functions were used to confirm the validity of this analysis these simulations also demonstrate that the precise form of the psychometric function is not critical in achieving the high efficiencies finally data from human listeners indicate that the standard deviation of threshold estimates is indeed larger when the stimulus presented on each trial is at a stimulus level corresponding to 70 7 rather than 94 correct responses

active learning applied to rcs computations with nonuniform sampling using different objective functions an active learning framework is introduced to reduce the number of frequencies and angles one must consider for wideband monostatic scattering computations or measurements this method is used to optimally select those frequencies and angles that would be most informative resulting in nonuniform sampling and often a reduced number of points vis agrave vis uniform sampling in this paper we focus on jointly two dimensional optimal sampling in frequency and incident angle thetas for monostatic scattering the method consists of two basic steps one step involves estimation of model parameters using a least square ls algorithm the next step is to optimally choose the next point frequency and thetas for analysis by the computational model or experiment this new point is selected with the goal of reducing uncertainty in the parametric model quantified via the fisher information matrix iterating these two steps a sequence of numerical computations or measurements are performed each at the most informative point for learning the parameters of the associated simpler parametric model this idea is demonstrated here in the context of reducing the number of points frequencies and orientations at which a computational model must be employed and in order to avoid repeatedly gathering samplings at the edge of the input space an alternative objective function is applied which makes the actively selected points closer to a region of interest

regularity of quasi minimizers of integral functionals with discontinuous p x growth conditions abstract this paper investigates the local boundedness and higher integrability of the gradient of quasi minimizers of integral functionals with discontinuous p x growth conditions

on the effect of receiver estimation error upon channel mutual information our goal in this paper is to study the effect of the receiver structure upon the achievable data rates we consider transmission of linearly precoded data symbols over a frequency selective block fading multiple input multiple output mimo wireless channel to encompass a number of transmission schemes we study this problem utilizing affine precoding which is a unified model of linearly precoded data symbols with superimposed training we focus on bayesian receivers that estimate both the unknown fading coefficients and the data symbols the receiver may adopt either of the following strategies to retrieve the data symbols strategy i the receiver obtains joint bayesian channel and symbol estimates strategy ii the receiver obtains a bayesian channel estimate initially and the channel measurement is utilized to estimate the data symbols for both strategies we provide lower bounds on the mutual information between the data symbols and their corresponding estimates and we relate these bounds to the symbol cramer rao bound crb matrices in contrast to strategy ii for strategy i the lower bound does not depend on either the channel estimate or the covariance of the channel estimation error for strategy ii we show that asymptotically as the size of the transmission block grows there is no loss of information after the maximum a posteriori map estimate of gaussian symbols we also provide guidelines to design affine precoders that maximize the derived lower bounds under the total average transmit power constraint

partial regularity of minimizers of p x growth functionals with p x 1 abstract we prove partial regularity of minimizers u for functionals of the following type a u a i j x u d u i d u j p x 2 g x u d u d x assuming that a i j x u and p x are sufficiently smooth and that p x 1 we prove that u c 0 0 for some 0 1 and an open set 0 with h m 1 0 0 where h s denotes the s dimensional hausdorff measure and 1 inf p x

boundary regularity of minimizers of double phase functionals abstract in this paper we treat the functional of double phase with variable exponents d u g p x a x d u g q x d x where a x is a non negative holder continuous function with 0 1 p x and q x holder continuous functions with 1 p x q x p x and g i j g x i j 1 2 for a continuous positive definite matrix valued function g g we prove that the minimizer of the above functional with suitable dirichlet boundary condition is holder continuous up to the boundary when g is holder continuous we see also that du is locally holder continuous

calculation of the fisher information matrix for multidimensional data sets data sets that are acquired in many practical systems can be described as the output of a multidimensional linear separable denominator system with gaussian measurement noise an important example is nuclear magnetic resonance nmr spectroscopy in nmr spectroscopy high accuracy parameter estimation is of central importance a classical result on the crame spl acute r rao lower bound states that the inverse of the fisher information matrix fim provides a lower bound for the covariance of any unbiased estimator of the parameter vector the calculation of the fim is therefore of central importance for an assessment of the accuracy with which parameters can be estimated it is shown how the fim can be expressed using the matrices that determine the system that generates the data set for uniformly sampled data it is shown how the fim can be expressed through the solutions of lyapunov equations the novel techniques are demonstrated with an example arising from nmr spectroscopy

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

capacity and power allocation for fading mimo channels with channel estimation error in this correspondence we investigate the effect of channel estimation error on the capacity of multiple input multiple output mimo fading channels we study lower and upper bounds of mutual information under channel estimation error and show that the two bounds are tight for gaussian inputs assuming gaussian inputs we also derive tight lower bounds of ergodic and outage capacities and optimal transmitter power allocation strategies that achieve the bounds under perfect feedback for the ergodic capacity the optimal strategy is a modified waterfilling over the spatial antenna and temporal fading domains this strategy is close to optimum under small feedback delays but when the delay is large equal powers should be allocated across spatial dimensions for the outage capacity the optimal scheme is a spatial waterfilling and temporal truncated channel inversion numerical results show that some capacity gain is obtained by spatial power allocation temporal power adaptation on the other hand gives negligible gain in terms of ergodic capacity but greatly enhances outage performance

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

mse balancing in the mimo bc unequal targets and probabilistic interference constraints second order cone soc restrictions have been widely employed in the design of wireless communication systems to recast precoding optimizations in convex form this paper highlights the flexibility of this framework to handle various transmit power and interference limitations also in the multistream multiple input multiple output broadcast channel with imperfect channel state information at the transmitter in particular we propose an iterative solution for mean square error mse balancing with such constraints via the lagrangian dual formulation the mse balancing criteria contrary to signal to interference plus noise ratio and rate criteria exhibit an interesting property when considering different targets for the receivers users with low target values are strictly prioritized in comparison to users with large mse targets that can even be switched off therefore only a subset of the receivers is served at the solution with stringent limitations for the precoders an example of such stringent limitations are small power constraints and probabilistic interference temperature constraints that set a measurable threshold on the generated interference in a cognitive radio system we provide four different approaches to approximate these probabilistic constraints with deterministic soc constraints and compare their accuracy

iterative cdma multiuser receiver with soft decision directed channel estimation we develop an iterative code division multiple access cdma receiver for multipath block fading channels in the uplink the mean square error mse of the channel estimates is reduced iteratively by using soft data estimates as additional pilots the multiuser detector performs parallel interference cancellation pic with subsequent linear filtering we consider a single user matched filter sumf and develop a low complexity linear minimum mse lmmse filter for intersymbol interference isi channels that allows for 33 more users than the sumf we investigate two choices of training sequences for initial channel estimation the first is a random pilot symbol sequence modulated by a short spreading sequence rand and the second is a perfect root of unity sequence prus used as long sounding chip sequence we observe that the rand scheme approaches the single user bound up to 2 db and in case of prus up to 1 db at a target bit error rate ber of 10 3 further several channel estimators are developed that use various combinations of soft decision symbols and statistical a priori knowledge about the channel these are the approximated least squares als approximated linear mmse almmse and linear mmse lmmse estimators the iterative estimators show an improvement of 2 5 and 5 db with prus and rand pilots respectively over estimators that do not exploit soft feedback symbols at a ber of 10 3 the als is sacrificing less than 0 6 db to obtain a ber of 10 3 in a system at load 1 5 when compared with the almmse and lmmse schemes the load is understood as the ratio of the number of users to the spreading factor this paper shows that significant improvements in system capacity can be achieved in multipath scenarios with low complexity choices of multiuser detectors and channel estimators

partial regularity of solutions to p x laplacian pdes with discontinuous coefficients abstract for r n an open and bounded region we consider solutions u w loc 1 p x r n with n 1 of the p x laplacian system a x d u p x 2 d u 0 a e x where concerning the coefficient function x a x we assume only that a w 1 q l where q 1 is essentially arbitrary this implies that the coefficient in the pde can be highly irregular and yet in spite of this we still recover that u c loc 0 0 for each 0 1 where 0 is a set of full measure due to the variational methodology that we employ our results apply to the more general question of the regularity of the integral functional a x d u p x d x

em based recursive estimation of channel parameters recursive online expectation maximization em algorithm along with stochastic approximation is employed in this paper to estimate unknown time invariant variant parameters the impulse response of a linear system channel is modeled as an unknown deterministic vector process and as a gaussian vector process with unknown stochastic characteristics using these models which are embedded in white or colored gaussian noise different types of recursive least squares rls kalman filtering and smoothing and combined rls and kalman type algorithms are derived directly from the recursive em algorithm the estimation of unknown parameters also generates new recursive algorithms for situations such as additive colored noise modeled by an autoregressive process the recursive em algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods

bounds on maximum likelihood ratio part ii application to antenna array detection estimation with imperfect wavefront coherence the multiple hypothesis testing problem of the detection estimation of an unknown number of independent gaussian point sources is adequately addressed by likelihood ratio lr maximization over the set of admissible covariance matrix models we introduce nonasymptotic lower and upper bounds for the maximum lr since lr optimization is generally a nonconvex multiextremal problem any practical solution could now be tested against these bounds enabling a high probability of recognizing nonoptimal solutions we demonstrate that in many applications the lower bound is quite tight with approximate maximum likelihood ml techniques often unable to approach this bound the introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace based direction of arrival doa estimation techniques we also demonstrate that by proper lr maximization we can extend the range of signal to noise ratio snr values and or number of data samples wherein accurate parameter estimates are produced yet when the snr and or sample size falls below a certain limit for a given scenario we show that ml estimation suffers from a discontinuity in the parameter estimates a phenomenon that cannot be eliminated within the ml paradigm

bayesian adaptive estimation of the auditory filter a bayesian adaptive procedure for estimating the auditory filter shape was proposed and evaluated using young normal hearing listeners at moderate stimulus levels the resulting quick auditory filter qaf procedure assumed the power spectrum model of masking with the auditory filter shape being modeled using a spectrally symmetric two parameter rounded exponential roex function during data collection using the qaf procedure listeners detected the presence of a pure tone signal presented in the spectral notch of a noise masker dependent on the listener s response on each trial the posterior probability distributions of the model parameters were updated and the resulting parameter estimates were then used to optimize the choice of stimulus parameters for the subsequent trials results showed that the qaf procedure gave similar parameter estimates to the traditional threshold based procedure in many cases and was able to reasonably predict the masked signal thresholds additional measurements suggested that occasional failures of the qaf procedure to reliably converge could be a consequence of incorrect responses early in a qaf track the addition of a parameter describing lapses of attention reduced the likelihood of such failures

on minimum variance unbiased estimation of clock offset in a two way message exchange mechanism for many applications distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time most of the widely used clock synchronization algorithms in such systems employ the sender receiver protocol based on a two way timing message exchange paradigm maximum likelihood estimator mle of the clock offset based on the timing message exchanges between two clocks was derived in d r jeske on maximum likelihood estimation of clock offset ieee trans commun vol 53 pp 53 54 jan 2005 when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean herein the best linear unbiased estimate using order statistics blue os of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays respectively the rao blackwell lehmann scheffe theorem is then exploited to obtain the minimum variance unbiased estimate mvue for the clock offset which it is shown to coincide with the blue os in addition it is found that the mvue of the clock offset in the presence of symmetric network delays also coincides with the mle finally in the presence of asymmetric network delays although the mle is biased it is shown to achieve lesser mean square error mse than the mvue in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified

partial regularity of p x harmonic maps let g x and hij u be uniformly elliptic symmetric matrices and assume that hij u and p x 2 are sufficiently smooth we prove partial regularity of minimizers for the functional f u z

robust precoding with bayesian error modeling for limited feedback mu miso systems we consider the robust precoder design for multiuser multiple input single output mu miso systems where the channel state information csi is fed back from the single antenna receivers to the centralized transmitter equipped with multiple antennas we propose to compress the feedback data by projecting the channel estimates onto a vector basis known at the receivers and the transmitter and quantizing the resulting coefficients the channel estimator and the basis for the rank reduction are jointly optimized by minimizing the mean square error mse between the true and the rank reduced csi expressions for the conditional mean and the conditional covariance of the channel are derived which are necessary for the robust precoder design these expressions take into account the following sources of error channel estimation truncation for rank reduction quantization and feedback channel delay as an example for the robust problem formulation vector precoding vp is designed based on the expectation of the mse conditioned on the fed back csi our results show that robust precoding based on fed back csi clearly outperforms conventional precoding designs which do not take into account the errors in the csi

representation of mutual information via input estimates a relationship between information theory and estimation theory was recently shown for the gaussian channel relating the derivative of mutual information with the minimum mean square error this paper generalizes the link between information theory and estimation theory to arbitrary channels giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs we illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

improvement of tdoa position fixing using the likelihood curvature a conventional multilateration is a two step process where in the first step the time difference of arrivals tdoa of a signal at multiple sensors are estimated and in the second step these tdoas are used in some position fixing technique to estimate the location of an emitter several estimators have been proposed over the years for the estimation of the tdoas many techniques have been proposed for position fixing as well much of the research on position fixing has been focused on obtaining a simplified closed form solution for the unknown deterministic signal model stein had derived the maximum likelihood estimator mle for the tdoa between two sensors which is the peak location of the cross correlation function since the asymptotic variance of an mle approaches the cramer rao lower bound crlb which is the inverse of the negative of the expected value of the curvature of the log likelihood function using this as a motivation we propose a weighted least squares type position fixing technique where the weights are computed from the curvature of the log likelihood function

the risk unbiased cramer rao bound for non bayesian multivariate parameter estimation how accurately can one estimate a deterministic parameter subject to other unknown deterministic model nuisance parameters the most popular answer to this question is given by the cramer rao bound crb the main assumption behind the derivation of the crb is local unbiased estimation of all model parameters the foundations of this paper rely on doubting this assumption generally in multivariate parameter estimation each parameter in its turn can be treated as a single parameter of interest whereas the other model parameters are treated as nuisance as their misknowledge interferes with the estimation of the parameter of interest this approach is utilized in this paper to provide a fresh look at deterministic parameter estimation a new cramer rao cr type bound is derived without assuming unbiased estimation of the nuisance parameters rather than that we apply lehmann s concept of unbiasedness for a risk that measures the distance between the estimator and the locally best unbiased estimator which assumes perfect knowledge of the nuisance parameters the proposed risk unbiased crb rucrb is proven to be asymptotically attainable by the maximum likelihood estimator while being tighter than the conventional crb furthermore simulations verify the asymptotic achievability of the rucrb by the maximum likelihood estimator for an array processing problem

a signal detection analysis of auditory frequency discrimination in the rat the frequency discrimination behavior of rats in a simple go no go task was analyzed using the theory of signal detection discrimination acuity was studied and the receiver operating characteristic roc was generated in subjects by varying the reinforcement schedule and signal probability the detectability indices d a and sensitivity index si and response bias indices b and responsivity index ri were used to describe behavior a gave the most suitable psychometric functions while ri best described response bias behavior weber ratios were 6 25 0 23 at 5 khz in three subjects the best method to obtain the roc was to vary the probability with which subjects were reinforced the roc in two subjects demonstrated classical forms in another subject the function was asymmetric to the extent that detectability was not independent of response bias subjects altered their decision criterion in reporting a signal from trial to trial depending on previous trial events on any given trial subjects made a decision in one of several decision states variables that influenced decision states included previous reinforcement and timeouts the data indicate that timeouts may not be a useful feature in go no go tasks the identification of multiple decision states within a single behavioral session is a convenient method to generate the roc without expressly manipulating experimental conditions

partial lipschitz regularity of minimizers of asymptotically convex functionals with general growth conditions abstract we consider the partial lipschitz continuity of minimizers of functionals of the form v f x v d v d x where r n is open and bounded the map x u f x u appearing in the above functional is assumed to be holder continuous with respect to its first two arguments of class c 2 in its third argument and asymptotically related to the more regular map x u a x u g as the main novelty is the allowance that even as the map f may retain full dependence on the minimizer u not only its gradient du and the spatial coordinate x

a maximum likelihood procedure for estimating psychometric functions thresholds slopes and lapses of attention green j acoust soc am 87 2662 2674 1990 suggested an efficient maximum likelihood based approach for adaptively estimating thresholds such procedures determine the signal strength on each trial by first identifying the most likely psychometric functions among the pre proposed alternatives based on responses from previous trials and then finding the signal strength at the sweet point on that most likely function the sweet point is the point on the psychometric function that is associated with the minimum expected variance here that procedure is extended to reduce poor estimates that result from lapses in attention the sweet points for the threshold slope and lapse parameters of a transformed logistic psychometric function are derived in addition alternative stimulus placement algorithms are considered the result is a relatively fast and robust estimation of a three parameter psychometric function

partial regularity for subquadratic homogeneity elliptic system with vmo coefficients abstract in this paper we are concerned with subquadratic homogeneity elliptic problems with vmo coefficients in divergence form we obtain that the weak solution u is locally holder continuous besides a singular set by using a harmonic approximation where the holder exponent 0 1 the hausdorff dimension of the singular set is less than n p

robust rls in the presence of correlated noise using outlier sparsity relative to batch alternatives the recursive least squares rls algorithm has well appreciated merits of reduced complexity and storage requirements for online processing of stationary signals and also for tracking slowly varying nonstationary signals however rls is challenged when in addition to noise outliers are also present in the data due to e g impulsive disturbances existing robust rls approaches are resilient to outliers but require the nominal noise to be white an assumption that may not hold in e g sensor networks where neighboring sensors are affected by correlated ambient noise prewhitening with the known noise covariance is not a viable option because it spreads the outliers to noncontaminated measurements which leads to inefficient utilization of the available data and unsatisfactory performance in this correspondence a robust rls algorithm is developed capable of handling outliers and correlated noise simultaneously in the proposed method outliers are treated as nuisance variables and estimated jointly with the wanted parameters identifiability is ensured by exploiting the sparsity of outliers which is effected via regularizing the least squares ls criterion with the l1 norm of the outlier vectors this leads to an optimization problem whose solution yields the robust rls estimates for low complexity real time operation a suboptimal online algorithm is proposed which entails closed form updates per time step in the spirit of rls simulations demonstrate the effectiveness and improved performance of the proposed method in comparison with the nonrobust rls and its state of the art robust renditions

robust precoding with limited feedback design based on precoding mse for mu miso systems for the separation of the signals in the vector broadcast channel bc some information about the channel state is necessary at the transmitter in many cases this channel state information csi must be fed back from the receivers to the transmitter we jointly design the channel estimators and the quantizers at the receivers together with the precoder at the transmitter based on a precoder centric criterion i e the minimization of a mean square error mse metric appropriate for the precoder design this is in contrast to our previous works where the quantizer design was based on a csi mse metric i e based on the minimization of the mse between the true channel and the channel recovered by the transmitter using a feedback channel interestingly the estimators resulting from this joint formulation are independent of the used codebook the codebook entries are the employed precoders therefore each receiver feeds back the index of a set of precoders and the intersection of the sets gives the appropriate precoder since the quantizers of the different receivers have to work separately the metric for the computation of the partition cells cannot be expressed as a simple squared error depending on the quantizer output the proposed system based on a joint optimization clearly outperforms previous designs with separate optimization of feedback and precoding

measurements and calculations on the simple up down adaptive procedure for speech in noise tests the simple up down adaptive procedure is a common method for measuring speech reception thresholds it is used by the dutch speech in noise telephone screening test national hearing test smits and houtgast ear hear 26 89 95 2005 the test uses digit triplets to measure the speech reception threshold in noise by telephone srttn about 66000 people took this test within four months of its introduction and details were stored of all individual measurements analyses of this large volume of data have revealed that the standard deviation of srttn estimates increases with hearing loss this paper presents a calculation model which using an intelligibility function as input can determine the standard deviation of srttn estimates and the bias for the simple up down procedure the effects of variations in the slope of the intelligibility function the guess rate the starting level the heterogeneity of the speech material and the possibilities of optimizing srttn measurements were all explored with this

psychometric functions for pure tone frequency discrimination the form of the psychometric function pf for auditory frequency discrimination is of theoretical interest and practical importance in this study pfs for pure tone frequency discrimination were measured for several standard frequencies 200 8000 hz and levels 35 85 db sound pressure level spl in normal hearing listeners the proportion correct data were fitted using a cumulative gaussian function of the sensitivity index d computed as a power transformation of the frequency difference f the exponent of the power function corresponded to the slope of the pf on log d log f coordinates the influence of attentional lapses on pf slope estimates was investigated when attentional lapses were not taken into account the estimated pf slopes on log d log f coordinates were found to be significantly lower than 1 suggesting a nonlinear relationship between d and f however when lapse rate was included as a free parameter in the fits pf slopes were found not to differ significantly from 1 consistent with a linear relationship between d and f this was the case across the wide ranges of frequencies and levels tested in this study therefore spectral and temporal models of frequency discrimination must account for a linear relationship between d and f across a wide range of frequencies and levels

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

on interior regularity of minimizers of p x energy functionals abstract the aim of the paper is to obtain everywhere c 1 regularity in the interior for a minimizer of the p x energy functional e v g x h i j v d v i x d v j x p x 2 d x defined for maps v r m r n under the so called one sided condition supposing the lipschitz continuity assumption on the exponent p x 2

auditory motivated level crossing approach to instantaneous frequency estimation we address the problem of estimating the instantaneous frequency if of a phase signal using its level crossing lc information based on front end auditory processing motivation we show that the problem of if estimation using lc information can be cast in the framework of estimation from irregularly sampled data the formulation has the generality of estimating different types of if without the need for a quasistationary assumption we consider two types of if polynomial and bandlimited we use polynomial interpolating functions for the former and for the latter we propose a novel line plus sum of sines model the model parameters are estimated by linear regression considering the noisy case lc data for different levels is analyzed and methods for combining different estimators from lcs are discussed theoretical and extensive simulation results show that the performance of the zero crossing zc based if estimator and the level crossing based if estimator with smaller level values is better than those obtained with higher level values or their combinations the new technique reaches the crame spl acute r rao bound crb roughly above 4 db signal to noise ratio snr and its performance does not deteriorate rapidly with mismatch in the if order compared with the other techniques in the literature

subspace partitioning for target detection and identification detection of a given target or set of targets from observed data is a problem countered in many applications regardless of the algorithm selected detection performance can be severely degraded when the subspace defined by the target data set is singular or ill conditioned high correlations between target components and their linear combinations lead to false positives and misidentifications especially for subspace based detectors in this paper we propose a subspace partitioning scheme that allows for detection to be performed in a number of better conditioned subspaces instead of the original subspace the proposed technique is applied to raman spectroscopic data analysis through both simulation and experimental results we demonstrate the improvement in the overall detection performance when using the proposed subspace partitioning scheme in conjunction with several subspace detection methods that are commonly used in practice

transmit beamforming in multiple antenna systems with finite rate feedback a vq based approach this paper investigates quantization methods for feeding back the channel information through a low rate feedback channel in the context of multiple input single output miso systems we propose a new quantizer design criterion for capacity maximization and develop the corresponding iterative vector quantization vq design algorithm the criterion is based on maximizing the mean squared weighted inner product mswip between the optimum and the quantized beamforming vector the performance of systems with quantized beamforming is analyzed for the independent fading case this requires finding the density of the squared inner product between the optimum and the quantized beamforming vector which is obtained by considering a simple approximation of the quantization cell the approximate density function is used to lower bound the capacity loss due to quantization the outage probability and the bit error probability the resulting expressions provide insight into the dependence of the performance of transmit beamforming miso systems on the number of transmit antennas and feedback rate computer simulations support the analytical results and indicate that the lower bounds are quite tight

efficient adaptive procedures for threshold and concurrent slope estimates for psychophysics and speech intelligibility tests the minimum standard deviations achievable for concurrent estimates of thresholds and psychometric function slopes as well as the optimal target values for adaptive procedures are calculated as functions of stimulus level and track length on the basis of the binomial theory the optimum pair of targets for a concurrent estimate is found at the correct response probabilities p1 0 19 and p2 0 81 for the logistic psychometric function an adaptive procedure that converges at these optimal targets is introduced and tested with monte carlo simulations the efficiency increases rapidly when each subject s response consists of more than one statistically independent bernoulli trial sentence intelligibility tests provide more than one bernoulli trial per sentence when each word is scored separately the number of within sentence trials can be quantified by the j factor boothroyd and nittrouer j acoust soc am 84 101 114 1988 the adaptive procedure was evaluated with 10 normal hearing and 11 hearing imp

low complexity lmmse based mimo ofdm channel estimation via angle domain processing in many situations multiple input multiple output with orthogonal frequency division multiplexing mimo ofdm channels tend to be spatially correlated due for example to limited scattering prior knowledge of this channel spatial correlation and the channel frequency correlation can be exploited by using the linear minimum mean square error lmmse technique however the complexity of the 2 d lmmse technique which fully utilizes both the channel spatial and frequency correlation is quite high to solve this problem this paper presents and analyzes several low complexity suboptimal approximated lmmse channel estimation techniques in the angle domain where the channel model lends itself to a physical interpretation the choice of angle domain techniques is largely dependent on the extent of channel stochastic information e g channel correlation or power that is available to the receiver nevertheless all the proposed angle domain techniques have much lower complexity compared to the 2 d lmmse technique further all the angle domain techniques improve over the conventional least square ls technique for all the typical mimo ofdm models under consideration more importantly our simulation results show that the angle domain quasi 1 d ql d lmmse technique can achieve similar performance compared to the 2 d lmmse technique for all typical mimo ofdm models with significantly lower complexity

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

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

calderon zygmund type estimates for a class of obstacle problems with p x growth for local minimizers u wloc1 p of quasiconvex integral functionals of the type f u f x du x dx with p x growth in the class k u wloc1 p u where wloc1 p is a given obstacle function we show estimates of calderon zygmund type i e d p llocq du p llocq for any q 1 provided that the modulus of continuity of the exponent function p satisfies the condition log1 0as 0

mixed morrey spaces and their applications to partial differential equations abstract in this paper new classes of functions are defined these spaces generalize morrey spaces and give a refinement of lebesgue spaces some embeddings between these new classes are also proved finally the authors apply these classes of functions to obtain regularity results for solutions of partial differential equations of parabolic type

loudness adaptation and excitation patterns effects of frequency and level simple loudness adaptation for pure tones was measured at frequencies from 0 125 to 16 khz and at sensation levels from 5 to 60 db sixteen young listeners with normal hearing participated in four experiments most of the loudness measurements were obtained by the method of successive magnitude estimation some were also obtained by loudness matching the two indices of loudness adaptation gave similar results at all frequencies loudness adaptation increased as sensation level decreased after 6 min average loudness declined at most frequencies by about 20 at 40 db sensation level sl and by between 70 and almost 100 at 5 db sl adaptation also increased with increasing frequency and was especially marked at 16 khz where loudness declined more than 60 at a sensation level as high as 40 db most of the adaptation occurred usually within the first 3 min of exposure but loudness continued to diminish at a slower rate up to around 6 min the dependence of loudness adaptation on frequency and level can be largely accounted for by the restricted excitation pattern hypothesis adaptation is assumed to take place when excitation is restricted to a narrow region of the cochlea this hypothesis is supported by a quantitative analysis based on excitation patterns derived from measurements of masking

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

on posterior distributions for signals in gaussian noise with unknown covariance matrix a bayesian approach to estimate parameters of signals embedded in complex gaussian noise with unknown color is presented the study specifically focuses on a bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems by integrating out uncertainties regarding the noise color an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited several noninformative priors for the covariance matrix such as the reference prior the jeffreys prior and modifications to this are considered some of the priors result in analytical solutions whereas others demand numerical approximations in the linear signal model connections are made between the standard adaptive maximum likelihood aml estimate and a bayesian solution using the jeffreys prior with adjustments to the jeffreys prior correspondence to the regularized solution is also established this in turn enables a formal treatment of the regularization parameter simulations indicate that significant improvements compared to the aml estimator can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior the simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged

estimation of flows in flow networks abstract let g be a directed graph with an unknown flow on each edge such that the following flow conservation constraint is maintained except for sources and sinks the sum of flows into a node equals the sum of flows going out of a node given a noisy measurement of the flow on each edge the problem we address which we call the m ost p robable f low e stimation problem mpfe is to estimate the most probable assignment of flow for every edge such that the flow conservation constraint is maintained we provide an algorithm called y mpfe for solving the mpfe problem when the measurement error is gaussian g aussian mpfe the algorithm works in o e v 2 when the underlying undirected graph of g is a 2 connected planar graph and in o e v when it is a 2 connected serial parallel graph or a tree this result is applicable to any m inimum c ost f low problem for which the cost function is e x e e 2 for edge e where e and e are constants and x e is the flow on edge e we show that for all topologies the g aussian mpfe s precision for each edge is analogous to the equivalent resistance measured in series to this edge in an electrical network built by replacing every edge with a resistor reflecting the measurement s precision on that edge

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

a logarithmic improvement of regularity criterion for the mhd equations in terms of the pressure abstract in this paper we prove a logarithmic improvement of regularity criterion only in terms of the pressure in morrey campanato spaces for the cauchy problem to the incompressible mhd equations

quasi ml period estimation from incomplete timing data given a noisy sequence of possibly shifted integer multiples of a certain period it is often of interest to accurately estimate the period with known integer regressors the problem is classical linear regression in many applications however the regressors are unknown integers and only loose bounds on the period are available examples include hop period and timing estimation wherein hops may be missed at the output of the frequency discriminator or the emitter may hop out of band pulse repetition interval pri analysis and passive rotating beam radio scanning we study several pertinent period estimators our emphasis is on a quasi maximum likelihood approach developed herein and an earlier method based on the fourier transform of a dirac delta train representation of the data surprisingly both are capable of attaining the clairvoyant crame spl acute r rao bound at moderate signal to noise ratios snrs even for short e g 10 samples we carefully address parameter identifiability issues and corroborate our findings with extensive simulations

new results on deterministic cramer rao bounds for real and complex parameters the cramer rao bounds crb is a lower bound of great interest for system analysis and design in the asymptotic region high signal to noise ratio snr and or large number of snapshots as it is simple to calculate and it is usually possible to obtain closed form expressions the first part of the paper is a generalization to complex parameters of the barankin rationale for deriving mse lower bounds that is the minimization of a norm under a set of linear constraints with the norm minimization approach the study of fisher information matrix fim singularity constrained crb and regularity conditions become straightforward corollaries of the derivation the second part provides new results useful for system analysis and design a general reparameterization inequality the equivalence between reparameterization and equality constraints and an explicit relationship between parameters unidentifiability and fim singularity

on the evaluation of the polyanskiy poor verdu converse bound for finite block length coding in awgn a tight converse bound to the channel coding rate in the finite block length regime and under additive white gaussian noise conditions was recently proposed by polyanskiy poor verdu ppv the bound is a generalization of a number of other classical results and it was also claimed to be equivalent to shannon s 1959 cone packing bound in this paper we investigate methods for a reliable numerical evaluation of the bound which is troublesome even for not too large values of the block length n by compactly expressing the polyanskiy poor and verdu ppv converse bound in terms of non central chi squared distributions and by evaluating those through an integral expression and a corresponding series expansion which exploit a method proposed by temme as a result a robust evaluation method and new insights on the bound s asymptotics as well as new approximate expressions are obtained