Weighted subspace methods and spatial smoothing: analysis and comparison

The effect of using a spatially smoothed forward-backward covariance matrix on the performance of weighted eigen-based state space methods/ESPRIT, and weighted MUSIC for direction-of-arrival (DOA) estimation is analyzed. Expressions for the mean-squared error in the estimates of the signal zeros and the DOA estimates, along with some general properties of the estimates and optimal weighting matrices, are derived. A key result is that optimally weighted MUSIC and weighted state-space methods/ESPRIT have identical asymptotic performance. Moreover, by properly choosing the number of subarrays, the performance of unweighted state space methods can be significantly improved. It is also shown that the mean-squared error in the DOA estimates is independent of the exact distribution of the source amplitudes. This results in a unified framework for dealing with DOA estimation using a uniformly spaced linear sensor array and the time series frequency estimation problems.

Receiver-Only Optimized Vector Quantization for Noisy Channels

This paper considers the design and analysis of a filter at the receiver of a source coding system to mitigate the excess Mean-Squared Error (MSE) distortion caused due to channel errors. It is assumed that the source encoder is channel-agnostic, i.e., that a Vector Quantization (VQ) based compression designed for a noiseless channel is employed. The index output by the source encoder is sent over a noisy memoryless discrete symmetric channel, and the possibly incorrect received index is decoded by the corresponding VQ decoder. The output of the VQ decoder is processed by a receive filter to obtain an estimate of the source instantiation. In the sequel, the optimum linear receive filter structure to minimize the overall MSE is derived, and shown to have a minimum-mean squared error receiver type structure. Further, expressions are derived for the resulting high-rate MSE performance. The performance is compared with the MSE obtained using conventional VQ as well as the channel optimized VQ. The accuracy of the expressions is demonstrated through Monte Carlo simulations.

Brownian dynamics simulation of dense binary colloidal mixtures. I. Structural evolution and dynamics

We have carried out Brownian dynamics simulations of binary mixtures of charged colloidal suspensions of two different diameter particles with varying volume fractions phi and charged impurity concentrations n(i). For a given phi, the effective temperature is lowered in many steps by reducing n(i) to see how structure and dynamics evolve. The structural quantities studied are the partial and total pair distribution functions g(tau), the static structure factors, the time average g(<(tau)over bar>), and the Wendt-Abraham parameter. The dynamic quantity is the temporal evolution of the total meansquared displacement (MSD). All these parameters show that by lowering the effective temperature at phi = 0.2, liquid freezes into a body-centered-cubic crystal whereas at phi = 0.3, a glassy state is formed. The MSD at intermediate times shows significant subdiffusive behavior whose time span increases with a reduction in the effective temperature. The mean-squared displacements for the supercooled liquid with phi = 0.3 show staircase behavior indicating a strongly cooperative jump motion of the particles.

Diffusing wave spectroscopy of dense colloids: Liquid, crystal and glassy states

Using intensity autocorrelation of multiply scattered light, we show that the increase in interparticle interaction in dense, binary colloidal fluid mixtures of particle diameters 0.115µm and 0.089µm results in freezing into a crystalline phase at volume fraction? of 0.1 and into a glassy state at?=0.2. The functional form of the field autocorrelation functiong (1)(t) for the binary fluid phase is fitted to exp[??(6k 0 2 D eff t)1/2] wherek 0 is the magnitude of the incident light wavevector and? is a parameter inversely proportional to the photon transport mean free pathl*. TheD eff is thel* weighted average of the individual diffusion coefficients of the pure species. Thel* used in calculatingD eff was computed using the Mie theory. In the solid (crystal or glass) phase, theg (1)(t) is fitted (only with a moderate success) to exp[??(6k 0 2 W(t))1/2] where the mean-squared displacementW(t) is evaluated for a harmonically bound overdamped Brownian oscillator. It is found that the fitted parameter? for both the binary and monodisperse suspensions decreases significantly with the increase of interparticle interactions. This has been justified by showing that the calculated values ofl* in a monodisperse suspension using Mie theory increase very significantly with the interactions incorporated inl* via the static structure factor.

Inverse surface melting in confined clusters: Ar-13 in zeolite L

Monte Carlo and molecular dynamics simulations on an Ar-13 cluster in zeolite L have been carried out at a series of temperatures to understand the rigid-nonrigid transition corresponding to the solid-liquid transition exhibited by the free Ar-13 cluster. The icosahedral geometry of the free cluster is no longer preferred when the cluster is confined in the zeolite. The root-mean-squared pair distance fluctuation, delta, exhibits a sharp, well-defined rigid-nonrigid transition at 17 K as compared to 27 K for the free cluster. Multiple peaks in the distribution of short-time averages of the guest-host interaction energy indicate coexistence of two phases.; It is shown that this transition is associated with the inner atoms becoming mobile at 17 K even while the outer layer atoms, which are in close proximity to the zeolitic wall, continue to be comparatively immobile. This may be contrasted with the melting of large free clusters of 40 or more atoms which exhibit surface melting. Guest-host interactions seem to play a predominant role in determining the properties of confined clusters. We demonstrate that the volume of the cluster increases rather sharply at 17 and 27 K respectively for the confined and the free cluster. Power spectra suggest that the motion of the inner atoms is generally parallel to the atoms which form the cage wall.

Performance analysis of a modified spatial smoothing technique for direction estimation

The statistical performance analysis of ESPRIT, root-MUSIC, minimum-norm methods for direction estimation, due to finite data perturbations, using the modified spatially smoothed covariance matrix, is developed. Expressions for the mean-squared error in the direction estimates are derived based on a common framework. Based on the analysis, the use of the modified smoothed covariance matrix improves the performance of the methods when the sources are fully correlated. Also, the performance is better even when the number of subarrays is large unlike in the case of the conventionally smoothed covariance matrix. However, the performance for uncorrelated sources deteriorates due to an artificial correlation introduced by the modified smoothing. The theoretical expressions are validated using extensive simulations. (C) 1999 Elsevier Science B.V. All rights reserved.

Jointly Optimal MMSE design for non-redundant FIR precoding and equalization

We provide a filterbank precoding framework (FBP) for frequency selective channels using the minimum mean squared error (MMSE) criterion. The design obviates the need for introducing a guard interval between successive blocks, and hence can achieve the maximum possible bandwidth efficiency. This is especially useful in cases where the channel is of a high order. We treat both the presence and the absence of channel knowledge at the transmitter. In the former case, we obtain the jointly optimal precoder-equalizer pair of the specified order. In the latter case, we use a zero padding precoder, and obtain the MMSE equalizer. No restriction on the dimension or nature of the channel matrix is imposed. Simulation results indicate that the filterbank approach outperforms block based methods like OFDM and eigenmode precoding.

Study of translational and rotational mobility and orientational preference of ethane in one-dimensional channels

Structural and dynamical properties of ethane in one-dimensional channels of AlPO4-5 and carbon nanotube have been investigated at dilute concentration with the help of molecular dynamics simulation. Density distributions and orientational structure of ethane have been analyzed. Repulsive interactions seem to play an important role when ethane is located in the narrow part of the AlPO4-5 channel. In AlPO4-5, parallel orientation is predominant over perpendicular orientation except when ethane is located in the broader part of the channel. Unlike in the case of single-file diffusion, our results in carbon nanotube show that at dilute concentrations the mean squared displacement, mu(2)(t) approximate to t(alpha), alpha = 1.8. The autocorrelation function for the z-component of angular velocity of ethane in space-fixed frame of reference shows a pronounced negative correlation. This is attributed to the restriction in the movement of ethane along the x- and y- directions. It is seen that the ratio of reorientational correlation times does not follow the Debye model for confined ethane but it is closer to the predictions of the Debye model for bulk ethane.

High-rate analysis of channel-optimized vector quantization

High-rate analysis of channel-optimized vector quantizationThis paper considers the high-rate performance of channel optimized source coding for noisy discrete symmetric channels with random index assignment. Specifically, with mean squared error (MSE) as the performance metric, an upper bound on the asymptotic (i.e., high-rate) distortion is derived by assuming a general structure on the codebook. This structure enables extension of the analysis of the channel optimized source quantizer to one with a singular point density: for channels with small errors, the point density that minimizes the upper bound is continuous, while as the error rate increases, the point density becomes singular. The extent of the singularity is also characterized. The accuracy of the expressions obtained are verified through Monte Carlo simulations.

Design of MMSE filterbank precoder and equalizer for MIMO frequency selective channels

In this paper, we consider the problem of designing minimum mean squared error (MMSE) filterbank precoder and equalizer for multiple input multiple output (MIMO) frequency selective channels. We derive the conditions to be satisfied by the optimal precoder-equalizer pair, and provide an iterative algorithm for solving them. The optimal design is very general, in that it is not constrained by channel dimensions, channel order, channel rank, or the input constellation. We also discuss some pertinent difierences between the filterbank approach and the space-time approach to the design of optimal precoder and equalizer. Simulation results demonstrate that the proposed design performs better than the space-time systems while supporting a higher data rate.

Dynamic and thermodynamic anomalies of water at low temperatures: from bulk water to reverse micelles and DNA hydration layer

Liquid water is known to exhibit remarkable thermodynamic and dynamic anomalies, ranging from solvation properties in supercritical state to an apparent divergence of the linear response functions at a low temperature. Anomalies in various dynamic properties of water have also been observed in the hydration layer of proteins, DNA grooves and inside the nanocavity, such as reverse micelles and nanotubes. Here we report studies on the molecular origin of these anomalies in supercooled water, in the grooves of DNA double helix and reverse micelles. The anomalies have been discussed in terms of growing correlation length and intermittent population fluctuation of 4- and 5-coordinated species. We establish correlation between thermodynamic response functions and mean squared species number fluctuation. Lifetime analysis of 4- and 5-coordinated species reveals interesting differences between the role of the two species in supercooled and constrained water. The nature and manifestations of the apparent and much discussed liquid-liquid transition under confinement are found to be markedly different from that in the bulk. We find an interesting `faster than bulk' relaxation in reverse micelles which we attribute to frustration effects created by competition between the correlations imposed by surface interactions and that imposed by hydrogen bond network of water.

High-Rate Vector Quantization for Noisy Channels With Applications to Wideband Speech Spectrum Compression

This paper considers the high-rate performance of source coding for noisy discrete symmetric channels with random index assignment (IA). Accurate analytical models are developed to characterize the expected distortion performance of vector quantization (VQ) for a large class of distortion measures. It is shown that when the point density is continuous, the distortion can be approximated as the sum of the source quantization distortion and the channel-error induced distortion. Expressions are also derived for the continuous point density that minimizes the expected distortion. Next, for the case of mean squared error distortion, a more accurate analytical model for the distortion is derived by allowing the point density to have a singular component. The extent of the singularity is also characterized. These results provide analytical models for the expected distortion performance of both conventional VQ as well as for channel-optimized VQ. As a practical example, compression of the linear predictive coding parameters in the wideband speech spectrum is considered, with the log spectral distortion as performance metric. The theory is able to correctly predict the channel error rate that is permissible for operation at a particular level of distortion.

Glassy dynamics in a confined monatomic fluid

Molecular dynamic simulations of a strongly inhomogeneous system reveals that a single-component soft-sphere fluid can behave as a fragile glass former due to confinement. The self-intermediate scattering function, F-s(k,t), of a Lennard-Jones fluid confined in slit-shaped pores, which can accomodate two to four fluid layers, exhibits a two-step relaxation at moderate temperatures. The mean-squared displacement data are found to follow time-temperature superposition and both the self-diffusivity and late a relaxation times exhibit power-law divergences as the fluid is cooled. The system possesses a crossover temperature and follows the scalings of mode coupling theory for the glass transition. The temperature dependence of the self-diffusivity can be expressed using the Vogel-Fulcher-Tammann equation, and estimates of the fragility index of the system indicates a fragile glass former. At lower temperatures, signatures of additional relaxation processes are observed in the various dynamical quantities with a three-step relaxation observed in the F-s(k,t).

SURE-FAST BILATERAL FILTERS

Edge-preserving smoothing is widely used in image processing and bilateral filtering is one way to achieve it. Bilateral filter is a nonlinear combination of domain and range filters. Implementing the classical bilateral filter is computationally intensive, owing to the nonlinearity of the range filter. In the standard form, the domain and range filters are Gaussian functions and the performance depends on the choice of the filter parameters. Recently, a constant time implementation of the bilateral filter has been proposed based on raisedcosine approximation to the Gaussian to facilitate fast implementation of the bilateral filter. We address the problem of determining the optimal parameters for raised-cosine-based constant time implementation of the bilateral filter. To determine the optimal parameters, we propose the use of Stein's unbiased risk estimator (SURE). The fast bilateral filter accelerates the search for optimal parameters by faster optimization of the SURE cost. Experimental results show that the SURE-optimal raised-cosine-based bilateral filter has nearly the same performance as the SURE-optimal standard Gaussian bilateral filter and the Oracle mean squared error (MSE)-based optimal bilateral filter.

On the Selection of Optimum Savitzky-Golay Filters

Savitzky-Golay (S-G) filters are finite impulse response lowpass filters obtained while smoothing data using a local least-squares (LS) polynomial approximation. Savitzky and Golay proved in their hallmark paper that local LS fitting of polynomials and their evaluation at the mid-point of the approximation interval is equivalent to filtering with a fixed impulse response. The problem that we address here is, ``how to choose a pointwise minimum mean squared error (MMSE) S-G filter length or order for smoothing, while preserving the temporal structure of a time-varying signal.'' We solve the bias-variance tradeoff involved in the MMSE optimization using Stein's unbiased risk estimator (SURE). We observe that the 3-dB cutoff frequency of the SURE-optimal S-G filter is higher where the signal varies fast locally, and vice versa, essentially enabling us to suitably trade off the bias and variance, thereby resulting in near-MMSE performance. At low signal-to-noise ratios (SNRs), it is seen that the adaptive filter length algorithm performance improves by incorporating a regularization term in the SURE objective function. We consider the algorithm performance on real-world electrocardiogram (ECG) signals. The results exhibit considerable SNR improvement. Noise performance analysis shows that the proposed algorithms are comparable, and in some cases, better than some standard denoising techniques available in the literature.