arXiv subjects

Mario Huemer

Publications and source records attributed to Mario Huemer.

At least 37 records · Page 2Linked to original sources

arXiv2021

VPNet: Variable Projection Networks

We introduce VPNet, a novel model-driven neural network architecture based on variable projection (VP). Applying VP operators to neural networks results in learnable features, interpretable parameters, and compact network structures. This paper discusses the motivation and mathematical background of VPNet and presents experiments. The VPNet approach was evaluated in the context of signal processing, where we classified a synthetic dataset and real electrocardiogram (ECG) signals. Compared to fully connected and one-dimensional convolutional networks, VPNet offers fast learning ability and good accuracy at a low computational cost of both training and inference. Based on these advantages and the promising results obtained, we anticipate a profound impact on the broader field of signal processing, in particular on classification, regression and clustering problems.

cs.LG↗

arXiv2021

ECG Beat Representation and Delineation by means of Variable Projection

The electrocardiogram (ECG) follows a characteristic shape, which has led to the development of several mathematical models for extracting clinically important information. Our main objective is to resolve limitations of previous approaches, that means to simultaneously cope with various noise sources, perform exact beat segmentation, and to retain diagnostically important morphological information. Methods: We therefore propose a model that is based on Hermite and sigmoid functions combined with piecewise polynomial interpolation for exact segmentation and low-dimensional representation of individual ECG beat segments. Hermite and sigmoidal functions enable reliable extraction of important ECG waveform information while the piecewise polynomial interpolation captures noisy signal features like the BLW. For that we use variable projection, which allows the separation of linear and nonlinear morphological variations of the according ECG waveforms. The resulting ECG model simultaneously performs BLW cancellation, beat segmentation, and low-dimensional waveform representation. Results: We demonstrate its BLW denoising and segmentation performance in two experiments, using synthetic and real data (Physionet QT database). Compared to state-of-the-art algorithms, the experiments showed less diagnostic distortion in case of denoising and a more robust delineation for the P and T wave. Conclusion: This work suggests a novel concept for ECG beat representation, easily adaptable to other biomedical signals with similar shape characteristics, such as blood pressure and evoked potentials. Significance: Our method is able to capture linear and nonlinear wave shape changes. Therefore, it provides a novel methodology to understand the origin of morphological variations caused, for instance, by respiration, medication, and abnormalities.

eess.SP↗

arXiv2021

Efficient Majority Voting in Digital Hardware

In recent years, machine learning methods became increasingly important for a manifold number of applications. However, they often suffer from high computational requirements impairing their efficient use in real-time systems, even when employing dedicated hardware accelerators. Ensemble learning methods are especially suitable for hardware acceleration since they can be constructed from individual learners of low complexity and thus offer large parallelization potential. For classification, the outputs of these learners are typically combined by majority voting, which often represents the bottleneck of a hardware accelerator for ensemble inference. In this work, we present a novel architecture that allows obtaining a majority decision in a number of clock cycles that is logarithmic in the number of inputs. We show, that for the example application of handwritten digit recognition a random forest processing engine employing this majority decision architecture implemented on an FPGA allows the classification of more than seven million images per second.

eess.SP↗

arXiv2021

Spline-Based Adaptive Cancellation of Even-Order Intermodulation Distortions in LTE-A/5G RF Transceivers

Radio frequency transceivers operating in in-band full-duplex or frequency-division duplex mode experience strong transmitter leakage. Combined with receiver nonlinearities, this causes intermodulation products in the baseband, possibly with higher power than the desired receive signal. In order to restore the receiver signal-to-noise ratio in such scenarios, we propose two novel digital self-interference cancellation approaches based on spline interpolation. Both employ a Wiener structure, thereby matching the baseband model of the intermodulation effect. Unlike most state-of-the-art spline-based adaptive learning schemes, the proposed concept allows for complex-valued in- and out-put signals. The optimization of the model parameters is based on the stochastic gradient descent concept, where the convergence is supported by an appropriate step-size normalization. Additionally, we provide a gain control scheme and enable pipelining in order to facilitate a hardware implementation. An optional input transform improves the performance consistency for correlated sequences. In a realistic interference scenario, the proposed algorithms clearly outperform a state-of-the-art least mean squares variant with comparable complexity, which is specifically tailored to second-order intermodulation distortions. The high flexibility of the spline interpolation allows the spline-based Wiener models to match the performance of the kernel recursive least squares algorithm at less than 0.6% of the arithmetic operations.

eess.SP↗

arXiv2020

On the Inclusion and Utilization of Pilot Tones in Unique Word OFDM

Unique word-orthogonal frequency division multiplexing (UW-OFDM) is known to provide various performance benefits over conventional OFDM using cyclic prefixes (CP). Most important, UW-OFDM features excellent spectral sidelobe suppression properties and an outstanding bit error ratio performance. Current research has mainly focused on principle performance bounds of UW-OFDM, with less attention on challenges aside from idealized communication scenarios, such as system parameter estimation tasks. In this work we present an approach for including frequency pilots tones into the UW-OFDM signaling scheme, which can then be utilized for these estimation tasks. Suitable optimization criteria are presented and interactions of pilots with data symbols are highlighted. Pilot tone based estimation of a carrier frequency offset (CFO) is conducted as an estimation example, revealing considerable differences to conventional OFDM. Simulation results in a multipath environment demonstrate a significantly increased estimation accuracy in UW-OFDM over CP-OFDM, which becomes even more dominant with an increasing CFO. This performance difference is due to the inherent redundancy present in an UW-OFDM signal.

eess.SP↗

arXiv2018

A Linear State Space Model for Photoacoustic Imaging in an Acoustic Attenuating Media

In photoacoustic imaging, ultrasound waves generated by a temperature rise after illumination of light absorbing structures are measured on the sample surface. These measurements are then used to reconstruct the optical absorption. We develop a method for reconstructing the absorption inside the sample based on a discrete linear state space reformulation of a partial differential equation that describes the propagation of the ultrasound waves. Fundamental properties of the corresponding state space model such as stability, observability and controllability are also analyzed. By using Stokes' equation, the frequency dependent attenuation of the ultrasound waves is incorporated into our model, therefore the proposed method is of general nature. As a consequence, this approach allows for inhomogeneous probes with arbitrary absorption profiles and it accounts for the decrease in laser intensity due to absorption. Furthermore, it provides a method for optimizing the laser modulation signal such that the accuracy of the estimated absorption profile is maximized. Utilizing the optimized laser modulation signal yields an increase in reconstruction accuracy compared to short laser pulses as well as chirp modulation in many scenarios.

physics.app-ph↗

arXiv2018

A Robust Nonlinear RLS Type Adaptive Filter for Second-Order-Intermodulation Distortion Cancellation in FDD LTE and 5G Direct Conversion Transceivers

Transceivers operating in frequency division duplex experience a transmitter leakage (TxL) signal into the receiver due to the limited duplexer stop-band isolation. This TxL signal in combination with the second-order nonlinearity of the receive mixer may lead to a baseband (BB) second-order intermodulation distortion (IMD2) with twice the transmit signal bandwidth. In direct conversion receivers, this nonlinear IMD2 interference may cause a severe signal-to-interference-plus-noise ratio degradation of the wanted receive signal. This contribution presents a nonlinear Wiener model recursive least-squares (RLS) type adaptive filter for the cancellation of the IMD2 interference in the digital BB. The included channel-select-, and DC-notch filter at the output of the proposed adaptive filter ensure that the provided IMD2 replica includes the receiver front-end filtering. A second, robust version of the nonlinear RLS algorithm is derived which provides numerical stability for highly correlated input signals which arise in e.g. LTE-A intra-band multi-cluster transmission scenarios. The performance of the proposed algorithms is evaluated by numerical simulations and by measurement data.

eess.SP↗

arXiv2017

Knowledge-Aided Kaczmarz and LMS Algorithms

The least mean squares (LMS) filter is often derived via the Wiener filter solution. For a system identification scenario, such a derivation makes it hard to incorporate prior information on the system's impulse response. We present an alternative way based on the maximum a posteriori solution, which allows developing a Knowledge-Aided Kaczmarz algorithm. Based on this Knowledge-Aided Kaczmarz we formulate a Knowledge-Aided LMS filter. Both algorithms allow incorporating the prior mean and covariance matrix on the parameter to be estimated. The algorithms use this prior information in addition to the measurement information in the gradient for the iterative update of their estimates. We analyze the convergence of the algorithms and show simulation results on their performance. As expected, reliable prior information allows improving the performance of the algorithms for low signal-to-noise (SNR) scenarios. The results show that the presented algorithms can nearly achieve the optimal maximum a posteriori (MAP) performance.

eess.SP↗

arXiv2017

Parameter Estimation Under Model Uncertainties by Iterative Covariance Approximation

We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the measurement noise and the noise resulting from the model uncertainties. This overall noise term is a function of the true parameter vector, allowing for an iterative algorithm. The proposed algorithm can be applied on structured as well as unstructured models and it outperforms prior art algorithms for a broad range of applications.

math.ST↗

arXiv2017

Constrained Best Linear Unbiased Estimation

The least squares (LS) estimator and the best linear unbiased estimator (BLUE) are two well-studied approaches for the estimation of a deterministic but unknown parameter vector. In many applications it is known that the parameter vector fulfills some constraints, e.g., linear constraints. For such situations the constrained LS estimator, which is a simple extension of the LS estimator, can be employed. In this paper we derive the constrained version of the BLUE. It will turn out that the incorporation of the linear constraints into the derivation of the BLUE is not straight forward as for the constrained LS estimator, but the final expression for the constrained BLUE is closely related to that of the constrained LS estimator.

math.ST↗

arXiv2017

Study of Buffer-aided physical-layer network coding with ML and MMSE linear code designs for cooperative DS-CDMA systems

In this work, we propose buffer-aided physical-layer network coding (PLNC) techniques for cooperative direct-sequence code-division multiple access systems. In the proposed buffer-aided PLNC schemes, a relay pair selection algorithm is employed to obtain the relay pair and the packets in the buffer entries with the best performance and the associated link combinations used for data transmission. We also devise PLNC schemes based on the design of linear network coding matrices using maximum likelihood and minimum mean-square error criteria to generate the network coded symbols that are sent to the destination. Simulation results show that the proposed techniques significantly outperform prior art.

cs.IT↗

arXiv2017

Classical Widely Linear Estimation of Real Valued Parameter Vectors in Complex Valued Environments

This work investigates the task of estimating a real valued parameter vector based on complex valued measurements in a classical set-up. The application of standard estimators in general results in complex valued estimates of the real valued parameter vector. To avoid this systematic error, widely linear classical estimators that produce real valued estimates are investigated. One of these estimators is the widely linear least squares (WLLS) estimator proposed in this work, which does not utilize any noise statistics. Further, we introduce the best widely linear unbiased estimator (BWLUE) for real valued parameter vectors. The proposed estimators in general outperform their standard counterparts LS estimator and BWLUE, respectively, and they only require half as many complex valued measurements. We compare the novel approaches to standard classical estimators in two application scenarios. One of these applications considers the estimation of a real valued impulse response based on noisy measurements of the system's magnitude and phase response. For this problem, we propose a novel two-step approach based on the introduced widely linear concepts that outperforms standard estimators.

math.ST↗

arXiv2016

On the Log-Likelihood Ratio Evaluation of CWCU Linear and Widely Linear MMSE Data Estimators

In soft decoding of data bits, the log-likelihood ratios are evaluated from the estimated data symbols. For proper constellation diagrams such as QPSK or 16-QAM, these data symbols are often estimated using the linear minimum mean square error (LMMSE) estimator. The LMMSE estimator only fulfills the weak Bayesian unbiasedness constraint. Recently, estimators fulfilling the more stringent component-wise conditionally unbiased (CWCU) constraints have been investigated, such as the CWCU LMMSE estimator. In this paper, we prove that the CWCU LMMSE estimates result in the very same log-likelihood ratios as the LMMSE estimates. For improper constellation diagrams such as 8-QAM, widely linear estimators are used. For this case, we show that the widely linear versions of the LMMSE estimator and the CWCU LMMSE estimator also yield identical log-likelihood ratios. Finally, we give a simulation example which illustrates a number of interesting properties of the discussed widely linear estimators.

math.ST↗

arXiv2016

Best Widely Linear Unbiased Estimator for Real Valued Parameter Vectors

For classical estimation with an underlying linear model the best linear unbiased estimator (BLUE) is usually utilized for estimating the deterministic but unknown parameter vector. In the case of real valued parameter vectors but complex valued measurement matrices and noise vectors, the BLUE results in complex valued estimates, introducing a systematic error. In recent years widely linear estimators have been investigated for complex estimation. In this work a novel widely linear classical estimator is derived which incorporates the knowledge that the parameter vector is real valued. The proposed estimator is unbiased in the classical sense and it outperforms the BLUE and the best widely linear unbiased estimator (BWLUE) in terms of the variances of the vector estimator's elements.

math.ST↗

arXiv2014

CWCU LMMSE Estimation: Prerequisites and Properties

The classical unbiasedness condition utilized e.g. by the best linear unbiased estimator (BLUE) is very stringent. By softening the "global" unbiasedness condition and introducing component-wise conditional unbiasedness conditions instead, the number of constraints limiting the estimator's performance can in many cases significantly be reduced. In this work we investigate the component-wise conditionally unbiased linear minimum mean square error (CWCU LMMSE) estimator for different model assumptions. The prerequisites in general differ from the ones of the LMMSE estimator. We first derive the CWCU LMMSE estimator under the jointly Gaussian assumption of the measurements and the parameters. Then we focus on the linear model and discuss the CWCU LMMSE estimator for jointly Gaussian parameters, and for mutually independent (and otherwise arbitrarily distributed) parameters, respectively. In all these cases the CWCU LMMSE estimator incorporates the prior mean and the prior covariance matrix of the parameter vector. For the remaining cases optimum linear CWCU estimators exist, but they may correspond to globally unbiased estimators that do not make use of prior statistical knowledge about the parameters. Finally, the beneficial properties of the CWCU LMMSE estimator are demonstrated with the help of a well-known channel estimation application.

math.ST↗

arXiv2013

Approximate Least Squares

We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical results as well as simulation based performance results. We describe the analysis of its convergence behavior and show that in the noise free case the algorithm converges to the least squares solution.

cs.DS↗

arXiv2012

Non-Systematic Complex Number RS Coded OFDM by Unique Word Prefix

In this paper we expand our recently introduced concept of UW-OFDM (unique word orthogonal frequency division multiplexing). In UW-OFDM the cyclic prefixes (CPs) are replaced by deterministic sequences, the so-called unique words (UWs). The UWs are generated by appropriately loading a set of redundant subcarriers. By that a systematic complex number Reed Solomon (RS) code construction is introduced in a quite natural way, because an RS code may be defined as the set of vectors, for which a block of successive zeros occurs in the other domain w.r.t. a discrete Fourier transform. (For a fixed block different to zero, i.e., a UW, a coset code of an RS code is generated.) A remaining problem in the original systematic coded UW-OFDM concept is the fact that the redundant subcarrier symbols disproportionately contribute to the mean OFDM symbol energy. In this paper we introduce the concept of non-systematic coded UW-OFDM, where the redundancy is no longer allocated to dedicated subcarriers, but distributed over all subcarriers. We derive optimum complex valued code generator matrices matched to the BLUE (best linear unbiased estimator) and to the LMMSE (linear minimum mean square error) data estimator, respectively. With the help of simulations we highlight the advantageous spectral properties and the superior BER (bit error ratio) performance of non-systematic coded UW-OFDM compared to systematic coded UW-OFDM as well as to CP-OFDM in AWGN (additive white Gaussian noise) and in frequency selective environments.

cs.IT↗

arXiv2012

Classical and Bayesian Linear Data Estimators for Unique Word OFDM

Unique word - orthogonal frequency division multiplexing (UW-OFDM) is a novel OFDM signaling concept, where the guard interval is built of a deterministic sequence - the so-called unique word - instead of the conventional random cyclic prefix. In contrast to previous attempts with deterministic sequences in the guard interval the addressed UW-OFDM signaling approach introduces correlations between the subcarrier symbols, which can be exploited by the receiver in order to improve the bit error ratio performance. In this paper we develop several linear data estimators specifically designed for UW-OFDM, some based on classical and some based on Bayesian estimation theory. Furthermore, we derive complexity optimized versions of these estimators, and we study their individual complex multiplication count in detail. Finally, we evaluate the estimators' performance for the additive white Gaussian noise channel as well as for selected indoor multipath channel scenarios.

cs.IT↗