Parameter estimation and equalization techniques for communication channels with multipath and multiple frequency offsets

We consider estimation of frequency offset (FO) and equalization of a wireless communication channel, within a general framework which allows for different frequency offsets for various multipaths. Such a scenario may arise due to different Doppler shifts associated with various multipaths, or in situations where multiple basestations are used to transmit identical information. For this general framework, we propose an approximative maximum-likelihood estimator exploiting the correlation property of the transmitted pilot signal. We further show that the conventional minimum mean-square error equalizer is computationally cumbersome, as the effective channel-convolution matrix changes deterministically between symbols, due to the multiple FOs. Exploiting the structural property of these variations, we propose a computationally efficient recursive algorithm for the equalizer design. Simulation results show that the proposed estimator is statistically efficient, as the mean-square estimation error attains the Crame´r-Rao lower bound. Further, we show via extensive simulations that our proposed scheme significantly outperforms equalizers not employing FO estimation

Fisher Information in Time-Domain Spectroscopy

Spectroscopy detected in the time domain entails many techniques, such as FTIR, pump-probe, FT-Raman, and 2DES, and applications, such as molecule characterization, excited state dynamics studies, or spectra classifications. Surprisingly, all these techniques use sampling schemes that rarely exploit the a priori knowledge the scientist has before the experiment. Indeed, not all the sampling coordinates carry the same amount of information. In this work, we rationalize with examples the various advantages of a smart sampling scheme tailored to the specific experiment characteristics and/or the expected results. The application of a Fisher information approach allows for finding the best sampling scheme to minimize the variance of a desired observable, greatly improving, for example, spectral classifications and multidimensional spectroscopy. In general, we demonstrate how a smart sampling allows reducing by one to two orders of magnitude the acquisition time of an experiment while still providing a similar level of information

Batch-Specific Discrimination Using Nuclear Quadrupole Resonance Spectroscopy

In this paper, we report on the identification of batches of analgesic paracetamol (acetaminophen) tablets using nitrogen-14 nuclear quadrupole resonance spectroscopy (¹⁴N NQR). The high sensitivity of NQR to the electron charge distribution surrounding the quadrupolar nucleus enables the unique characterization of the crystal structure of the material. Two hypothesis were tested on batches of the same brand: the within the same batch variability and the difference between batches that varied in terms of their batch number and expiry date. The multivariate analysis of variance (MANOVA) did not provide any within-batches variations, indicating the natural deviation of a medicine manufactured under the same conditions. Alternatively, the statistical analysis revealed a significant discrimination between the different batches of paracetamol tablets. Therefore, the NQR signal is an indicator of factors that influence the physical and chemical integrity of the material. Those factors might be the aging of the medicine, the manufacturing, or storage conditions. The results of this study illustrate the potential of NQR as promising technique in applications such as detection and authentication of counterfeit medicines

On the Efficient Estimation of Blood Velocities

Pulsed wave (PW) Doppler ultrasound systems are commonly used to examine blood flow dynamics and the technique plays a very important role in numerous diagnostic applications. Commonly, narrow-band PW systems estimate the blood velocity using an autocorrelation-based estimator. Herein, we examine a recently proposed hybrid frequency estimator, and via extensive numerical simulations using simulated blood scatterers show the achievable performance gain of this method as compared to the traditional approach

Data_Sheet_1_Tremor evaluation using smartphone accelerometry in standardized settings.pdf

Tremor can be highly incapacitating in everyday life and typically fluctuates depending on motor state, medication status as well as external factors. For tremor patients being treated with deep-brain stimulation (DBS), adapting the intensity and pattern of stimulation according the current needs therefore has the potential to generate better symptomatic relief. We here describe a procedure for how patients independently could perform self-tests in their home to generate sensor data for on-line adjustments of DBS parameters. Importantly, the inertia sensor technology needed exists in any standard smartphone, making the procedure widely accessible. Applying this procedure, we have characterized detailed features of tremor patterns displayed by both Parkinson’s disease and essential tremor patients and directly compared measured data against both clinical ratings (Fahn-Tolosa-Marin) and finger-attached inertia sensors. Our results suggest that smartphone accelerometry, when used in a standardized testing procedure, can provide tremor descriptors that are sufficiently detailed and reliable to be used for closed-loop control of DBS.</p

Rapid NMR Relaxation Measurements Using Optimal Nonuniform Sampling of Multidimensional Accordion Data Analyzed by a Sparse Reconstruction Method

Nonuniform sampling (NUS) of multidimensional NMR data offers significant time savings while improving spectral resolution or increasing sensitivity per unit time. However, NUS has not been widely used for quantitative analysis because of the nonlinearity of most methods used to model NUS data, which leads to problems in estimating signal intensities, relaxation rate constants, and their error bounds. Here, we present an approach that avoids these limitations by combining accordion spectroscopy and NUS in the indirect dimensions of multidimensional spectra and then applying sparse exponential mode analysis, which is well suited for analyzing accordion-type relaxation data in a NUS context. By evaluating the Cramér-Rao lower bound of the variances of the estimated relaxation rate constants, we achieve a robust benchmark for the underlying reconstruction model. Furthermore, we design NUS schemes optimized with respect to the information theoretical lower bound of the error in the parameters of interest, given a specified number of sampling points. The accordion-NUS method compares favorably with conventional relaxation experiments in that it produces identical results, within error, while shortening the length of the experiment by an order of magnitude. Thus, our approach enables rapid acquisition of NMR relaxation data for optimized use of spectrometer time or accurate measurements on samples of limited lifetime

Compressed Sensing for Reconstructing Coherent Multidimensional Spectra

We apply two sparse reconstruction techniques, the least absolute shrinkage and selection operator (LASSO) and the sparse exponential mode analysis (SEMA), to two-dimensional (2D) spectroscopy. The algorithms are first tested on model data, showing that both are able to reconstruct the spectra using only a fraction of the data required by the traditional Fourier-based estimator. Through the analysis of a sparsely sampled experimental fluorescence detected 2D spectra of LH2 complexes, we conclude that both SEMA and LASSO can be used to significantly reduce the required data, still allowing to reconstruct the multidimensional spectra. Of the two techniques, it is shown that SEMA offers preferable performance, providing more accurate estimation of the spectral line widths and their positions. Furthermore, SEMA allows for off-grid components, enabling the use of a much smaller dictionary than the LASSO, thereby improving both the performance and lowering the computational complexity for reconstructing coherent multidimensional spectra