arXiv subjects

Franz Hlawatsch

Publications and source records attributed to Franz Hlawatsch.

32 records · Page 2Linked to original sources

arXiv2013

Sigma Point Belief Propagation

The sigma point (SP) filter, also known as unscented Kalman filter, is an attractive alternative to the extended Kalman filter and the particle filter. Here, we extend the SP filter to nonsequential Bayesian inference corresponding to loopy factor graphs. We propose sigma point belief propagation (SPBP) as a low-complexity approximation of the belief propagation (BP) message passing scheme. SPBP achieves approximate marginalizations of posterior distributions corresponding to (generally) loopy factor graphs. It is well suited for decentralized inference because of its low communication requirements. For a decentralized, dynamic sensor localization problem, we demonstrate that SPBP can outperform nonparametric (particle-based) BP while requiring significantly less computations and communications.

cs.AI↗

arXiv2013

Time-Frequency Foundations of Communications

In the tradition of Gabor's 1946 landmark paper [1], we advocate a time-frequency (TF) approach to communications. TF methods for communications have been proposed very early (see the box History). While several tutorial papers and book chapters on the topic are available (see, e.g., [2]-[4] and references therein), the goal of this paper is to present the fundamental aspects in a coherent and easily accessible manner. Specifically, we establish the role of TF methods in communications across a range of subject areas including TF dispersive channels, orthogonal frequency division multiplexing (OFDM), information-theoretic limits, and system identification and channel estimation. Furthermore, we present fundamental results that are stated in the literature for the continuous-time case in simple linear algebra terms.

cs.IT↗

arXiv2013

Generic Correlation Increases Noncoherent MIMO Capacity

We study the high-SNR capacity of MIMO Rayleigh block-fading channels in the noncoherent setting where neither transmitter nor receiver has a priori channel state information. We show that when the number of receive antennas is sufficiently large and the temporal correlation within each block is "generic" (in the sense used in the interference-alignment literature), the capacity pre-log is given by T(1-1/N) for T<N, where T denotes the number of transmit antennas and N denotes the block length. A comparison with the widely used constant block-fading channel (where the fading is constant within each block) shows that for a large block length, generic correlation increases the capacity pre-log by a factor of about four.

cs.IT↗

arXiv2013

Compressive Spectral Estimation for Nonstationary Random Processes

Estimating the spectral characteristics of a nonstationary random process is an important but challenging task, which can be facilitated by exploiting structural properties of the process. In certain applications, the observed processes are underspread, i.e., their time and frequency correlations exhibit a reasonably fast decay, and approximately time-frequency sparse, i.e., a reasonably large percentage of the spectral values is small. For this class of processes, we propose a compressive estimator of the discrete Rihaczek spectrum (RS). This estimator combines a minimum variance unbiased estimator of the RS (which is a smoothed Rihaczek distribution using an appropriately designed smoothing kernel) with a compressed sensing technique that exploits the approximate time-frequency sparsity. As a result of the compression stage, the number of measurements required for good estimation performance can be significantly reduced. The measurements are values of the discrete ambiguity function of the observed signal at randomly chosen time and frequency lag positions. We provide bounds on the mean-square estimation error of both the minimum variance unbiased RS estimator and the compressive RS estimator, and we demonstrate the performance of the compressive estimator by means of simulation results. The proposed compressive RS estimator can also be used for estimating other time-dependent spectra (e.g., the Wigner-Ville spectrum) since for an underspread process most spectra are almost equal.

stat.CO↗

arXiv2013

Minimum Variance Estimation of a Sparse Vector within the Linear Gaussian Model: An RKHS Approach

We consider minimum variance estimation within the sparse linear Gaussian model (SLGM). A sparse vector is to be estimated from a linearly transformed version embedded in Gaussian noise. Our analysis is based on the theory of reproducing kernel Hilbert spaces (RKHS). After a characterization of the RKHS associated with the SLGM, we derive novel lower bounds on the minimum variance achievable by estimators with a prescribed bias function. This includes the important case of unbiased estimation. The variance bounds are obtained via an orthogonal projection of the prescribed mean function onto a subspace of the RKHS associated with the SLGM. Furthermore, we specialize our bounds to compressed sensing measurement matrices and express them in terms of the restricted isometry and coherence parameters. For the special case of the SLGM given by the sparse signal in noise model (SSNM), we derive closed-form expressions of the minimum achievable variance (Barankin bound) and the corresponding locally minimum variance estimator. We also analyze the effects of exact and approximate sparsity information and show that the minimum achievable variance for exact sparsity is not a limiting case of that for approximate sparsity. Finally, we compare our bounds with the variance of three well-known estimators, namely, the maximum-likelihood estimator, the hard-thresholding estimator, and compressive reconstruction using the orthogonal matching pursuit.

cs.IT↗

arXiv2013

A Lower Bound on the Noncoherent Capacity Pre-log for the MIMO Channel with Temporally Correlated Fading

We derive a lower bound on the capacity pre-log of a temporally correlated Rayleigh block-fading multiple-input multiple-output (MIMO) channel with T transmit antennas and R receive antennas in the noncoherent setting (no a priori channel knowledge at the transmitter and the receiver). In this model, the fading process changes independently across blocks of length L and is temporally correlated within each block for each transmit-receive antenna pair, with a given rank Q of the corresponding correlation matrix. Our result implies that for almost all choices of the coloring matrix that models the temporal correlation, the pre-log can be lower-bounded by T(1-1/L) for T <= (L-1)/Q provided that R is sufficiently large. The widely used constant block-fading model is equivalent to the temporally correlated block-fading model with Q = 1 for the special case when the temporal correlation for each transmit-receive antenna pair is the same, which is unlikely to be observed in practice. For the constant block-fading model, the capacity pre-log is given by T(1-T/L), which is smaller than our lower bound for the case Q = 1. Thus, our result suggests that the assumptions underlying the constant block- fading model lead to a pessimistic result for the capacity pre-log.

cs.IT↗

arXiv2012

Simultaneous Distributed Sensor Self-Localization and Target Tracking Using Belief Propagation and Likelihood Consensus

We introduce the framework of cooperative simultaneous localization and tracking (CoSLAT), which provides a consistent combination of cooperative self-localization (CSL) and distributed target tracking (DTT) in sensor networks without a fusion center. CoSLAT extends simultaneous localization and tracking (SLAT) in that it uses also intersensor measurements. Starting from a factor graph formulation of the CoSLAT problem, we develop a particle-based, distributed message passing algorithm for CoSLAT that combines nonparametric belief propagation with the likelihood consensus scheme. The proposed CoSLAT algorithm improves on state-of-the-art CSL and DTT algorithms by exchanging probabilistic information between CSL and DTT. Simulation results demonstrate substantial improvements in both self-localization and tracking performance.

cs.NI↗

arXiv2012

Likelihood Consensus and Its Application to Distributed Particle Filtering

We consider distributed state estimation in a wireless sensor network without a fusion center. Each sensor performs a global estimation task---based on the past and current measurements of all sensors---using only local processing and local communications with its neighbors. In this estimation task, the joint (all-sensors) likelihood function (JLF) plays a central role as it epitomizes the measurements of all sensors. We propose a distributed method for computing, at each sensor, an approximation of the JLF by means of consensus algorithms. This "likelihood consensus" method is applicable if the local likelihood functions of the various sensors (viewed as conditional probability density functions of the local measurements) belong to the exponential family of distributions. We then use the likelihood consensus method to implement a distributed particle filter and a distributed Gaussian particle filter. Each sensor runs a local particle filter, or a local Gaussian particle filter, that computes a global state estimate. The weight update in each local (Gaussian) particle filter employs the JLF, which is obtained through the likelihood consensus scheme. For the distributed Gaussian particle filter, the number of particles can be significantly reduced by means of an additional consensus scheme. Simulation results are presented to assess the performance of the proposed distributed particle filters for a multiple target tracking problem.

stat.AP↗

arXiv2011

Likelihood Consensus-Based Distributed Particle Filtering with Distributed Proposal Density Adaptation

We present a consensus-based distributed particle filter (PF) for wireless sensor networks. Each sensor runs a local PF to compute a global state estimate that takes into account the measurements of all sensors. The local PFs use the joint (all-sensors) likelihood function, which is calculated in a distributed way by a novel generalization of the likelihood consensus scheme. A performance improvement (or a reduction of the required number of particles) is achieved by a novel distributed, consensus-based method for adapting the proposal densities of the local PFs. The performance of the proposed distributed PF is demonstrated for a target tracking problem.

stat.AP↗

arXiv2011

Performance Bounds for Sparse Parametric Covariance Estimation in Gaussian Models

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower bounds on the variance of estimators with a given mean function. This includes unbiased estimation as a special case. We also present a numerical comparison of our lower bounds with the variance of two standard estimators (hard-thresholding estimator and maximum likelihood estimator).

cs.IT↗

arXiv2010

A Lower Bound on the Estimator Variance for the Sparse Linear Model

We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new lower bound on the estimator variance for a given differentiable bias function (including the unbiased case) and an almost arbitrary transformation matrix (including the underdetermined case considered in compressed sensing theory). For the special case of a sparse vector corrupted by white Gaussian noise-i.e., without a linear transformation-and unbiased estimation, our lower bound improves on previously proposed bounds.

math.ST↗

arXiv2010

Unbiased Estimation of a Sparse Vector in White Gaussian Noise

We consider unbiased estimation of a sparse nonrandom vector corrupted by additive white Gaussian noise. We show that while there are infinitely many unbiased estimators for this problem, none of them has uniformly minimum variance. Therefore, we focus on locally minimum variance unbiased (LMVU) estimators. We derive simple closed-form lower and upper bounds on the variance of LMVU estimators or, equivalently, on the Barankin bound (BB). Our bounds allow an estimation of the threshold region separating the low-SNR and high-SNR regimes, and they indicate the asymptotic behavior of the BB at high SNR. We also develop numerical lower and upper bounds which are tighter than the closed-form bounds and thus characterize the BB more accurately. Numerical studies compare our characterization of the BB with established biased estimation schemes, and demonstrate that while unbiased estimators perform poorly at low SNR, they may perform better than biased estimators at high SNR. An interesting conclusion of our analysis is that the high-SNR behavior of the BB depends solely on the value of the smallest nonzero component of the sparse vector, and that this type of dependence is also exhibited by the performance of certain practical estimators.

math.ST↗

arXiv2010

Compressive estimation of doubly selective channels in multicarrier systems: Leakage effects and sparsity-enhancing processing

We consider the application of compressed sensing (CS) to the estimation of doubly selective channels within pulse-shaping multicarrier systems (which include OFDM systems as a special case). By exploiting sparsity in the delay-Doppler domain, CS-based channel estimation allows for an increase in spectral efficiency through a reduction of the number of pilot symbols. For combating leakage effects that limit the delay-Doppler sparsity, we propose a sparsity-enhancing basis expansion and a method for optimizing the basis with or without prior statistical information about the channel. We also present an alternative CS-based channel estimator for (potentially) strongly time-frequency dispersive channels, which is capable of estimating the "off-diagonal" channel coefficients characterizing intersymbol and intercarrier interference (ISI/ICI). For this estimator, we propose a basis construction combining Fourier (exponential) and prolate spheroidal sequences. Simulation results assess the performance gains achieved by the proposed sparsity-enhancing processing techniques and by explicit estimation of ISI/ICI channel coefficients.

cs.IT↗

arXiv2010

On Unbiased Estimation of Sparse Vectors Corrupted by Gaussian Noise

We consider the estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Our focus is on unbiased estimation as a setting under which the difficulty of the problem can be quantified analytically. We show that there are infinitely many unbiased estimators but none of them has uniformly minimum mean-squared error. We then provide lower and upper bounds on the Barankin bound, which describes the performance achievable by unbiased estimators. These bounds are used to predict the threshold region of practical estimators.

cs.IT↗