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  • 51.
    Ciobanu, Alexandru
    et al.
    McGill University, Canada .
    Hemati, Saied
    Linköping University, Department of Electrical Engineering, Electronics System. Linköping University, The Institute of Technology.
    Gross, Warren J.
    McGill University, Canada .
    Adaptive Multiset Stochastic Decoding of Non-Binary LDPC Codes2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 16, p. 4100-4113Article in journal (Refereed)
    Abstract [en]

    We propose a non-binary stochastic decoding algorithm for low-density parity-check (LDPC) codes over GF(q) with degree two variable nodes, called Adaptive Multiset Stochastic Algorithm (AMSA). The algorithm uses multisets, an extension of sets that allows multiple occurrences of an element, to represent probability mass functions that simplifies the structure of the variable nodes. The run-time complexity of one decoding cycle using AMSA is O(q) for conventional memory architectures, and O(1) if a custom memory architecture is used. Two fully-parallel AMSA decoders are implemented on FPGA for two (192,96) (2,4)-regular codes over GF(64) and GF(256), both achieving a maximum clock frequency of 108 MHz. The GF(64) decoder has a coded throughput of 65 Mb/s at E-b/N-0 = 2.4 dB when using conventional memory, while a decoder using the custom memory version can achieve 698 Mb/s at the same E-b/N-0. At a frame error rate (FER) of 2 x 10(-6) the GF(64) version of the algorithm is only 0.04 dB away from the floating-point SPA performance, and for the GF(256) code the difference is 0.2 dB. To the best of our knowledge, this is the first fully parallel non-binary LDPC decoder over GF(256) reported in the literature.

  • 52.
    Cirkic, Mirsad
    et al.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Persson, Daniel
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Larsson, Jan-Åke
    Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, The Institute of Technology.
    Larsson, Erik G.
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, The Institute of Technology.
    Approximating the LLR Distribution for a Class of Soft-Output MIMO Detectors2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 12, p. 6421-6434Article in journal (Refereed)
    Abstract [en]

    We present approximations of the LLR distribution for a class of fixed-complexity soft-output MIMO detectors, such as the optimal soft detector and the soft-output via partial marginalization detector. More specifically, in a MIMO AWGN setting, we approximate the LLR distribution conditioned on the transmitted signal and the channel matrix with a Gaussian mixture model (GMM). Our main results consist of an analytical expression of the GMM model (including the number of modes and their corresponding parameters) and a proof that, in the limit of high SNR, this LLR distribution converges in probability towards a unique Gaussian distribution.

  • 53. Ciuonzo, Domenico
    et al.
    Rossi, Pierluigi Salvo
    Dey, Subhrakanti
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Massive MIMO Channel-Aware Decision Fusion2015In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 3, p. 604-619Article in journal (Refereed)
    Abstract [en]

    In this paper, we provide a study of channel-aware decision fusion (DF) over a "virtual" multiple-input multiple-output (MIMO) channel in the large-array regime at the DF center (DFC). The considered scenario takes into account channel estimation and inhomogeneous large-scale fading between the sensors and the DFC. The aim is the development of (widely) linear fusion rules, as opposed to the unsuitable optimum log-likelihood ratio (LLR). The proposed rules can effectively benefit from performance improvement via a large array, differently from existing suboptimal alternatives. Performance evaluation, along with theoretical achievable performance and complexity analysis, is presented. Simulation results are provided to confirm the findings. Analogies and differences with uplink communication in a multiuser (massive) MIMO scenario are underlined.

  • 54.
    Courts, Jarrad
    et al.
    Univ Newcastle, Fac Engn & Built Environm, Callaghan, NSW 2308, Australia..
    Wills, Adrian
    Univ Newcastle, Fac Engn & Built Environm, Callaghan, NSW 2308, Australia..
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Artificial Intelligence.
    Gaussian Variational State Estimation for Nonlinear State-Space Models2021In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 69, p. 5979-5993Article in journal (Refereed)
    Abstract [en]

    In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable as it involves integrals of general nonlinear functions and the filtered and smoothed state distributions lack closed-form solutions. As such, it is common to approximate the state estimation problem. In this paper, we develop an assumed Gaussian solution based on variational inference, which offers the key advantage of a flexible, but principled, mechanism for approximating the required distributions. Our main contribution lies in a new formulation of the state estimation problem as an optimisation problem, which can then be solved using standard optimisation routines that employ exact first- and second-order derivatives. The resulting state estimation approach involves a minimal number of assumptions and applies directly to nonlinear systems with both Gaussian and non-Gaussian probabilistic models. The performance of our approach is demonstrated on several examples; a challenging scalar system, a model of a simple robotic system, and a target tracking problem using a von Mises-Fisher distribution and outperforms alternative assumed Gaussian approaches to state estimation.

  • 55. Dam, Hai Huyen
    et al.
    Nordebo, Sven
    Svensson, Lars
    Design of Digital Filters as the Sum of Two All--Pass Functions Using the Cepstrum Technique2003In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 51, no 3, p. 726-31Article in journal (Refereed)
  • 56.
    de Araujo, Gilderlan T.
    et al.
    Fed Inst Ceara, BR-62700000 Caninde, Brazil..
    de Almeida, Andre L. F.
    Univ Fed Ceara, Dept Teleinformat, Wireless Telecommun Res Grp GTEL, BR-60455970 Fortaleza, Ceara, Brazil..
    Boyer, Remy
    Univ Lille 1, CRIStAL Lab, F-59655 Villeneuve Dascq, France..
    Fodor, Gabor
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). Ericsson Res, S-16480 Stockholm, Sweden..
    Semi-Blind Joint Channel and Symbol Estimation for IRS-Assisted MIMO Systems2023In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 71, p. 1184-1199Article in journal (Refereed)
    Abstract [en]

    Intelligent reflecting surface (IRS) is a promising technology for the 6$\text{th}$ generation of wireless systems, realizing the smart radio environment concept. This paper presents a novel tensor-based receiver for Intelligent reflecting surface (IRS)-assisted multiple-input multiple-output communications capable of jointly estimating the channels and the transmitted data streams in a semi-blind fashion. Assuming a fully passive IRS architecture and introducing a simple space-time coding scheme at the transmitter, the received signal model can be advantageously built using the PARATUCK tensor model, which can be seen as a hybrid of parallel factor analysis and Tucker models. A semi-blind receiver is derived by exploiting the algebraic structure of the PARATUCK tensor model. We first formulate a semi-blind receiver based on a trilinear alternating least squares method that iteratively estimates the two involved - IRS-base station and user terminal-IRS - communication channels and the transmitted symbol matrix. We discuss identifiability conditions that ensure the joint semi-blind recovery of the involved channel and symbol matrices and propose a joint design of the coding and IRS reflection matrices to optimize the receiver performance. We also formulate an enhanced two-stage semi-blind receiver that efficiently exploits the direct link to refine the channel and symbol estimates iteratively. In particular, we discuss the impact of an imperfect IRS absorption (residual reflection) on the performance of the proposed receiver. Numerical results are proposed for performance evaluation in several system settings in terms of the normalized mean squared error of the estimated channels and the achieved symbol error rate, corroborating the merits of the proposed semi-blind receiver in comparison to competing methods.

  • 57.
    de Fréin, Ruairí
    et al.
    Sparse Signal Processing Group, University College Dublin.
    Rickard, Scott
    Sparse Signal Processing Group, University College Dublin.
    The Synchronized Short-Time-Fourier-Transform: Properties and Definitions for Multichannel Source Separation2011In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, ISSN 1053-587X, Vol. 59, no 1, p. 91-103Article in journal (Refereed)
    Abstract [en]

    This paper proposes the use of a synchronized linear transform, the synchronized short-time-Fourier-transform (sSTFT), for time-frequency analysis of anechoic mixtures. We address the short comings of the commonly used time-frequency linear transform in multichannel settings, namely the classical short-time-Fourier-transform (cSTFT). We propose a series of desirable properties for the linear transform used in a multichannel source separation scenario: stationary invertibility, relative delay, relative attenuation, and finally delay invariant relative windowed-disjoint orthogonality (DIRWDO). Multisensor source separation techniques which operate in the time-frequency domain, have an inherent error unless consideration is given to the multichannel properties proposed in this paper. The sSTFT preserves these relationships for multichannel data. The crucial innovation of the sSTFT is to locally synchronize the analysis to the observations as opposed to a global clock. Improvement in separation performance can be achieved because assumed properties of the time-frequency transform are satisfied when it is appropriately synchronized. Numerical experiments show the sSTFT improves instantaneous subsample relative parameter estimation in low noise conditions and achieves good synthesis.

  • 58.
    del Aguila Pla, Pol
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.
    Jaldén, Joakim
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.
    Cell detection by functional inverse diffusion and non-negative group sparsity – Part I: Modeling and Inverse Problems2018In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 20, p. 5407-5421Article in journal (Refereed)
    Abstract [en]

    In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this first part, we start by presenting a physical partial differential equations (PDE) model up to image acquisition for these biochemical assays. Then, we use the PDEs' Green function to derive a novel parametrization of the acquired images. This parametrization allows us to propose a functional optimization problem to address inverse diffusion. In particular, we propose a non-negative group-sparsity regularized optimization problem with the goal of localizing and characterizing the biological cells involved in the said assays. We continue by proposing a suitable discretization scheme that enables both the generation of synthetic data and implementable algorithms to address inverse diffusion. We end Part I by providing a preliminary comparison between the results of our methodology and an expert human labeler on real data. Part II is devoted to providing an accelerated proximal gradient algorithm to solve the proposed problem and to the empirical validation of our methodology.

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  • 59.
    del Aguila Pla, Pol
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.
    Jaldén, Joakim
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.
    Cell detection by functional inverse diffusion and non-negative group sparsity – Part II: Proximal optimization and Performance evaluation2018In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 20, p. 5422-5437Article in journal (Refereed)
    Abstract [en]

    In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this second part, we focus on our algorithmic contributions. We provide an algorithm for functional inverse diffusion that solves the variational problem we posed in Part I. As part of the derivation of this algorithm, we present the proximal operator for the non-negative group-sparsity regularizer, which is a novel result that is of interest in itself, also in comparison to previous results on the proximal operator of a sum of functions. We then present a discretized approximated implementation of our algorithm and evaluate it both in terms of operational cell-detection metrics and in terms of distributional optimal-transport metrics.

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  • 60.
    Do, Tan Tai
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Oechtering, Tobias J.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Optimal Transmission for the MIMO Bidirectional Broadcast Channel in the Wideband Regime2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 20, p. 5103-5116Article in journal (Refereed)
    Abstract [en]

    This paper considers a transmit strategy for an AWGN MIMO bidirectional broadcast channel in the wideband regime. In order to characterize the boundaries of the wideband capacity and energy per bit regions, the transmit strategy at the relay is designed to maximize the weighted wideband rate sum. A closed form of the optimal transmit covariance matrix is derived, which shows that a single beam transmit strategy is optimal. The transmit strategies for some special cases are also analyzed. The fairness versus energy efficiency tradeoff is then discussed. In addition, an extension to multipair MIMO bidirectional broadcast channel is studied in which we show that serving a certain pair with full power is optimal in the sense of maximizing the achievable weighted wideband rate sum. Finally, a discussion on the conjecture of the minimum energy per bit for multi-pair systems is provided.

  • 61.
    Dong, Jianfei
    et al.
    Delft University of Technology, The Netherlands .
    Verhaegen, Michel
    Delft University of Technology, The Netherlands .
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robust Fault Detection With Statistical Uncertainty in Identified Parameters2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 10, p. 5064-5076Article in journal (Refereed)
    Abstract [en]

    Detection of faults that appear as additive unknown input signals to an unknown LTI discrete-time MIMO system is considered. State of the art methods consist of the following steps. First, either the state space model or certain projection matrices are identified from data. Then, a residual generator is formed based on these identified matrices, and this residual generator is used for online fault detection. Existing techniques do not allow for compensating for the identification uncertainty in the fault detection. This contribution explores a recent data-driven approach to fault detection. We show first that the identified parametric matrices in this method depend linearly on the noise contained in the identification data, and then that the on-line computed residual also depends linearly on the noise. This allows an analytic design of a robust fault detection scheme, that takes both the noise in the online measurements as well as the identification uncertainty into account. We illustrate the benefits of the new method on a model of aircraft dynamics extensively studied in literature.

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  • 62.
    Dong, Jianfei
    et al.
    Delft University of Technology, The Netherlands .
    Verhaegen, Michel
    Delft University of Technology, The Netherlands .
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Robust Fault Isolation With Statistical Uncertainty in Identified Parameters2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 10, p. 5556-5561Article in journal (Refereed)
    Abstract [en]

    This correspondence is a companion paper to [J. Dong, M. Verhaegen, and F. Gustafsson, "Robust Fault Detection With Statistical Uncertainty in Identified Parameters," IEEE Trans. Signal Process., vol. 60, no. 10, Oct. 2012], extending it to fault isolation. Also, here, use is made of a linear in the parameters model representation of the input-output behavior of the nominal system (i.e. fault-free). The projection of the residual onto directions only sensitive to individual faults is robustified against the stochastic errors of the estimated model parameters. The correspondence considers additive error sequences to the input and output quantities that represent failures like drift, biased, stuck, or saturated sensors/actuators.

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  • 63.
    Eftekhari, Armin
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Over-parametrized matrix factorization in the presence of spurious stationary points2022In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 70, p. 482-496Article in journal (Refereed)
    Abstract [en]

    Motivated by the emerging role of interpolating machines in signal processing and machine learning, this work considers the computational aspects of over-parametrized matrix factorization. In this context, the optimization landscape may contain spurious stationary points (SSPs), which are proved to be full-rank matrices. The presence of these SSPs means that it is impossible to hope for any global guarantees in over-parametrized matrix factorization. For example, when initialized at an SSP, the gradient flow will be trapped there forever. Nevertheless, despite these SSPs, we establish in this work that the gradient flow of the corresponding merit function converges to a global minimizer, provided that its initialization is rank-deficient and sufficiently close to the feasible set of the optimization problem. We numerically observe that a heuristic discretization of the proposed gradient flow, inspired by primal-dual algorithms, is successful when initialized randomly. Our result is in sharp contrast with the local refinement methods which require an initialization close to the optimal set of the optimization problem. More specifically, we successfully avoid the traps set by the SSPs because the gradient flow remains rank-deficient at all times, and not because there are no SSPs nearby. The latter is the case for the local refinement methods. Moreover, the widely-used restricted isometry property plays no role in our main result.

  • 64.
    Eghbali, Amir
    et al.
    Linköping University, Department of Electrical Engineering, Electronics System. Linköping University, The Institute of Technology.
    Johansson, Håkan
    Linköping University, Department of Electrical Engineering, Electronics System. Linköping University, The Institute of Technology.
    On Efficient Design of High-Order Filters With Applications to Filter Banks and Transmultiplexers With Large Number of Channels2014In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 5, p. 1198-1209Article in journal (Refereed)
    Abstract [en]

    This paper proposes a method for designing high-order linear-phase finite-length impulse response (FIR) filters which are required as, e.g., the prototype filters in filter banks (FBs) and transmultiplexers (TMUXs) with a large number of channels. The proposed method uses the Farrow structure to express the polyphase components of the desired filter. Thereby, the only unknown parameters, in the filter design, are the coefficients of the Farrow subfilters. The number of these unknown parameters is considerably smaller than that of the direct filter design methods. Besides these unknown parameters, the proposed method needs some predefined multipliers. Although the number of these multipliers is larger than the number of unknown parameters, they are known a priori. The proposed method is generally applicable to any linear-phase FIR filter irrespective of its order being high, low, even, or odd as well as the impulse response being symmetric or antisymmetric. However, it is more efficient for filters with high orders as the conventional design of such filters is more challenging. For example, to design a linear-phase FIR lowpass filter of order 131071 with a stopband attenuation of about 55 dB, which is used as the prototype filter of a cosine modulated filter bank (CMFB) with 8192 channels, our proposed method requires only 16 unknown parameters. The paper gives design examples for individual lowpass filters as well as the prototype filters for fixed and flexible modulated FBs.

  • 65.
    Eghbali, Amir
    et al.
    Linköping University, Department of Electrical Engineering. Linköping University, The Institute of Technology.
    Saramaki, T.
    Tampere University of Technology.
    Johansson, Håkan
    Linköping University, Department of Electrical Engineering, Electronics System. Linköping University, The Institute of Technology.
    On two-stage Nyquist pulse shaping filters2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 1, p. 483-488Article in journal (Refereed)
    Abstract [en]

    This correspondence outlines a method for designing two-stage Nyquist filters. The Nyquist filter is split into two equal and linear-phase finite-length impulse response spectral factors. The per-time-unit multiplicative complexity, of the overall structure, is included as the objective function. Examples are then provided where Nyquist filters are designed so as to minimize the multiplicative complexity subject to the constraints on the overall Nyquist filter. In comparison to the single-stage case, the two-stage realization reduces the multiplicative complexity by an average of 48%. For two-stage sampling rate conversion (SRC), the correspondence shows that it is better to have a larger SRC ratio in the first stage. © 2006 IEEE.

  • 66.
    Elbornsson, Jonas
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering.
    Gustafsson, Fredrik
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Eklund, JE
    Blind equalization of time errors in a time-interleaved ADC system2005In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 53, no 4, p. 1413-1424Article in journal (Refereed)
    Abstract [en]

    To significantly increase the sampling rate of an analog-to-digital converter (ADC), a time-interleaved ADC system is a good option. The drawback of a time-interleaved ADC system is that the ADCs are not exactly identical due to errors in the manufacturing process. This means that time, gain, and offset mismatch errors are introduced in the ADC system. These errors cause distortion in the sampled signal. In this paper, we present a method for estimation and compensation of the time mismatch errors. The estimation method requires no knowledge about the input signal, except that it should be band limited to the foldover frequency pi/T-s for the complete ADC system. This means that the errors can be estimated while the ADC is running. The method is also adaptive to slow changes in the time errors. The Cramer-Rao bound (CRB) for the time error estimates is also calculated and compared. to Monte Carlo simulations. The estimation method has also been validated on measurements from a real time-interleaved ADC system with 16 ADCs.

  • 67.
    Elvander, Filip
    et al.
    Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden..
    Jakobsson, Andreas
    Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden..
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport2018In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 20, p. 5285-5298Article in journal (Refereed)
    Abstract [en]

    In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal mass transport problem in the spectral domain. This may then be interpreted in the covariance domain, suggesting a natural way of interpolating and extrapolating Toeplitz matrices, such that the positive semidefiniteness and the Toeplitz structure of these matrices are preserved. The proposed distance measure is also shown to be contractive with respect to both additive and multiplicative noise and thereby allows for a quantification of the decreased distance between signals when these are corrupted by noise. Finally, we illustrate how this approach can be used for several applications in signal processing. In particular, we consider interpolation and extrapolation of Toeplitz matrices, as well as clustering problems and tracking of slowly varying stochastic processes.

  • 68.
    Elvander, Filip
    et al.
    Aalto University, Department of Information and Communications Engineering, Espoo, Finland, 02150.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Variance Analysis of Covariance and Spectral Estimates for Mixed-Spectrum Continuous-Time Signals2023In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 71, p. 1395-1407Article in journal (Refereed)
    Abstract [en]

    The estimation of the covariance function of a stochastic process, or signal, is of integral importance for a multitude of signal processing applications. In this work, we derive closed-form expressions for the covariance of covariance estimates for mixed-spectrum continuous-time signals, i.e., spectra containing both absolutely continuous and singular parts. The results cover both finite-sample and asymptotic regimes, allowing for assessing the exact speed of convergence of estimates to their expectations, as well as their limiting behavior. As is shown, such covariance estimates may converge even for non-ergodic processes. Furthermore, we consider approximating signals with arbitrary spectral densities by sequences of singular spectrum, i.e., sinusoidal, processes, and derive the limiting behavior of covariance estimates as both the sample size and the number of sinusoidal components tend to infinity. We show that the asymptotic-regime variance can be described by a time-frequency resolution product, with dramatically different behavior depending on how the sinusoidal approximation is constructed. In numerical examples, we illustrate the theory and its implications for signal and array processing applications.

  • 69.
    Eng, Frida
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gunnarsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Frequency Domain Analysis of Signals with Stochastic Sampling Times2008In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 56, no 7, p. 3089-3099Article in journal (Refereed)
    Abstract [en]

    In nonuniform sampling (NUS), signal amplitudes and time stamps are delivered in pairs. Several methods to compute an approximate Fourier transform (AFT) have appeared in literature, and their posterior properties in terms of alias suppression and leakage have been addressed. In this paper, the sampling times are assumed to be generated by a stochastic process. The main result gives the prior distribution of several AFTs expressed in terms of the true Fourier transform and variants of the characteristic function of the sampling time distribution. The result extends leakage and alias suppression with bias and variance terms due to NUS. Specific sampling processes as described in literature are analyzed in detail. The results are illustrated on simulated signals, with particular focus to the implications for spectral estimation.

  • 70. Ericsson, Stefan
    et al.
    Grip, Niklas
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Efficient wavelet prefilters with optimal time-shifts2005In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 53, no 7, p. 2451-2461Article in journal (Refereed)
    Abstract [en]

    A wavelet prefilter maps sample values of an analyzed signal to the scaling function coefficient input of standard discrete wavelet transform (DWT) algorithms. The prefilter is the inverse of a certain postfilter convolution matrix consisting of integer sample values of a noninteger-shifted wavelet scaling function. For the prefilter and the DWT algorithms to have similar computational complexity, it is often necessary to use a "short enough" approximation of the prefilter. In addition to well-known quadrature formula and identity matrix prefilter approximations, we propose a Neumann series approximation, which is a band matrix truncation of the optimal prefilter, and derive simple formulas for the operator norm approximation error. This error shows a dramatic dependence on how the postfilter noninteger shift is chosen. We explain the meaning of this shift in practical applications, describe how to choose it, and plot optimally shifted prefilter approximation errors for 95 different Daubechies, Symlet, and B-spline wavelets. Whereas the truncated inverse is overall superior, the Neumann filters are by far the easiest ones to compute, and for some short support wavelets, they also give the smallest approximation error. For example, for Daubechies 1-5 wavelets, the simplest Neumann prefilter provide an approximation error reduction corresponding to 100-10 000 times oversampling in a nonprefiltered system.

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  • 71.
    Eriksson, Markus
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Olofsson, Tomas
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Signals and Systems Group.
    Computationally Efficient Off-Line Joint Change Point Detection in Multiple Time Series2019In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 67, no 1, p. 149-163Article in journal (Refereed)
    Abstract [en]

    In this paper, a computationally efficient algorithm for Bayesian joint change point (CP) detection (CPD) in multiple time series is presented. The data generation model includes a number of change configurations (CC), each affecting a unique subset of the time series, which introduces correlation between the positions of CPs in the monitored time series. The inference objective is to identify joint changes and the associated CC. The algorithm consists of two stages: First a univariate CPD algorithm is applied separately to each of the involved time series. The outcomes of this step are maximum a posteriori (MAP) detected CPs and posterior distributions of CPs conditioned on the MAP CPs. These outcomes are used in combination to approximate the posterior for the CCs. In the second algorithm stage, dynamic programming is used to find the maxima of this approximate CC posterior. The algorithm is applied to synthetic data and it is shown to be both significantly faster and more accurate compared to a previously proposed algorithm designed to solve similar problems. Also, the initial algorithm is extended with steps from the Maximization-Maximization algorithm which allows the hyperparameters of the data generation model to be estimated jointly with the CCs, and we show that these estimates coincide with estimates obtained from a Markov Chain Monte Carlo algorithm.

  • 72. Fan, H.
    et al.
    Söderström, T.
    Mossberg, Magnus
    Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.
    Carlsson, B.
    Zou, Y.
    Estimation of continuous-time AR process parameters from discrete-time data1999In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 47, no 5, p. 1232-1244Article in journal (Refereed)
    Abstract [en]

    The problem of estimating continuous-time autoregressive process parameters from discrete-time data is considered. The basic approach used here is based on replacing the derivatives in the model by discrete-time differences, forming a linear regression, and using the least squares method. Such a procedure is simple to apply, computationally flexible and efficient, and may have good numerical properties. It is known, however, that all standard approximations of the highest order derivative, such as repeated use of the delta operator, gives a biased least squares estimate, even as the sampling interval tends to zero. Some of our previous approaches to overcome this problem are reviewed. Then. two new methods, which avoid the shift in our previous results, are presented. One of them, which is termed bias compensation, is computationally very efficient. Finally, the relationship of the above least squares approaches with an instrumental variable method is investigated. Comparative simulation results are also presented

  • 73. Fan, Wenzhe
    et al.
    Xia, Yili
    Li, Chunguo
    Huang, Yongming
    Ottersten, Björn
    Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg, Luxembourg, L-1359, Luxembourg.
    Joint Parameter Estimation From Binary Observations Over Decentralized Channels2022In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 70, p. 509-522Article in journal (Refereed)
    Abstract [en]

    In wireless sensor networks, due to the bandwidth constraint, the distributed nodes (DNs) might only provide binary representatives of the source signal, and then transmit them to the central node (CN). In this paper, we consider the joint estimation of signal amplitude and background noise variance from binary observations over decentralized channels. We first analyze the Cramér-Rao lower bounds (CRLBs) of the parameters of interest and develop a quasilinear estimator (QLE), in which the desirable estimates can be obtained from several intermediate parameters linearly. Next, we consider a more realistic situation where the decentralized channel is noisy during the data transmission. Based on the error propagation model, the asymptotic analysis shows that the performance of the proposed QLE is mainly dominated by the thresholds of the quantizers, which encourages us to adopt a correlated quantization (CQ) scheme by exploiting the spatial correlation among background noises/channel noises. To ease the implementation of QLE in practice, an adaptive quantization (AQ) scheme is also proposed so as to obtain reasonable selections of the required thresholds. Finally, numerical simulations are provided to validate our theoretical findings.

  • 74.
    Felsberg, Michael
    et al.
    Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
    Sommer, Gerald
    n/a.
    The monogenic signal2001In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 49, no 12, p. 3136-3144Article in journal (Refereed)
    Abstract [en]

    This paper introduces a two-dimensional generalization of the analytic signal. This novel approach is based on the Riesz transform, which is used instead of the Hilbert transform. The combination of a 2D signal with the Riesz transformed one yields a sophisticated 2D analytic signal, the monogenic signal. The approach is derived analytically from irrotational and solenoidal vector fields. Based on local amplitude and local phase, an appropriate local signal representation is presented which preserves the split of identity, i.e., the invariance – equivariance property of signal decomposition. This is one of the central properties of the 1D analytic signal that decomposes a signal into structural and energetic information. We show that further properties of the analytic signal concerning symmetry, energy, allpass transfer function, and orthogonality are also preserved, and we compare this to the behavior of other approaches for a 2D analytic signal. As a central topic of this paper, a geometric phase interpretation is introduced which is based on the relation between the 1D analytic signal and the 2D monogenic signal established by the Radon transform. Possible applications of this relationship are sketched and references to other applications of the monogenic signal are given. This report is a revised version of the technical report 2009 [7], and therefore supercedes it.

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  • 75. Fertl, Peter
    et al.
    Jaldén, Joakim
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Matz, Gerald
    Performance Assessment of MIMO-BICM Demodulators Based on Mutual Information2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 3, p. 1366-1382Article in journal (Refereed)
    Abstract [en]

    We provide a comprehensive performance comparison of soft-output and hard-output demodulators in the context of non-iterative multiple-input multiple-output bit-interleaved coded modulation (MIMO-BICM). Coded bit error rate (BER), widely used in literature for demodulator comparison, has the draw-back of depending strongly on the error correcting code being used. This motivates us to propose the mutual information of the equivalent modulation channel (comprising modulator, wireless channel, and demodulator) as a code-independent performance measure. We present extensive numerical results for spatially independent identically distributed (i.i.d.) ergodic and quasi-static fading channels under perfect and imperfect channel state information. These results reveal that the performance ranking of MIMO demodulators is rate-dependent and provide new insights regarding MIMO-BICM system design, i.e., the choice of antenna configuration, symbol constellation, and demodulator for a given target rate.

  • 76. Flam, J. T.
    et al.
    Zachariah, Dave
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Vehkaperä, mikko
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    The linear model under mixed gaussian inputs: Designing the transfer matrix2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 21, p. 5247-5259Article in journal (Refereed)
    Abstract [en]

    Suppose a linear model Y = Hx+n, where inputs x, n are independent Gaussian mixtures. The problem is to design the transfer matrix so as to minimize the mean square error (MSE) when estimating x from . This problem has important applications, but faces at least three hurdles. Firstly, even for a fixed H, the minimum MSE (MMSE) has no analytical form. Secondly, theMMSE is generally not convex in . Thirdly, derivatives of the MMSEw.r.t. are hard to obtain. This paper casts theproblemas a stochastic program and invokes gradient methods. The study is motivated by two applications in signal processing. One concerns the choice of error-reducing precoders; the other deals with selection of pilot matrices for channel estimation. In either setting, our numerical results indicate improved estimation accuracy-markedly better than those obtained by optimal design based on standard linear estimators. Some implications of the non-convexities of the MMSE are noteworthy, yet, to our knowledge, not well known. For example, there are cases in which more pilot power is detrimental for channel estimation. This paper explains why.

  • 77.
    Forsling, Robin
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Sjanic, Zoran
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Löfberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Conservative Linear Unbiased Estimation Under Partially Known Covariances2022In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 70, p. 3123-3135Article in journal (Refereed)
    Abstract [en]

    Mean square error optimal estimation requires the full correlation structure to be available. Unfortunately, it is not always possible to maintain full knowledge about the correlations. One example is decentralized data fusion where the cross-correlations between estimates are unknown, partly due to information sharing. To avoid underestimating the covariance of an estimate in such situations, conservative estimation is one option. In this paper the conservative linear unbiased estimator is formalized including optimality criteria. Fundamental bounds of the optimal conservative linear unbiased estimator are derived. A main contribution is a general approach for computing the proposed estimator based on robust optimization. Furthermore, it is shown that several existing estimation algorithms are special cases of the optimal conservative linear unbiased estimator. An evaluation verifies the theoretical considerations and shows that the optimization based approach performs better than existing conservative estimation methods in certain cases.

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  • 78.
    Fritsche, Carsten
    et al.
    IFEN GmbH, Germany .
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bounds on the Optimal Performance for Jump Markov Linear Gaussian Systems2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 1, p. 92-98Article in journal (Refereed)
    Abstract [en]

    The performance of an optimal filter is lower bounded by the Bayesian Cramer-Rao Bound (BCRB). In some cases, this bound is tight (achieved by the optimal filter) asymptotically in information, i.e., high signal-to-noise ratio (SNR). However, for jump Markov linear Gaussian systems (JMLGS) the BCRB is not necessarily achieved for any SNR. In this paper, we derive a new bound which is tight for all SNRs. The bound evaluates the expected covariance of the optimal filter which is represented by one deterministic term and one stochastic term that is computed with Monte Carlo methods. The bound relates to and improves on a recently presented BCRB and an enumeration BCRB for JMLGS. We analyze their relations theoretically and illustrate them on a couple of examples.

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  • 79.
    Garcia, Nil
    et al.
    Chalmers, Sweden.
    Wymeersch, Henk
    Chalmers, Sweden.
    Larsson, Erik G
    Linköping University, Department of Electrical Engineering, Communication Systems. Linköping University, Faculty of Science & Engineering.
    Haimovich, Alexander M.
    New Jersey Institute Technology, NJ 07102 USA.
    Coulon, Martial
    University of Toulouse, France.
    Direct Localization for Massive MIMO2017In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 65, no 10, p. 2475-2487Article in journal (Refereed)
    Abstract [en]

    Large-scale MIMO systems are well known for their advantages in communications, but they also have the potential for providing very accurate localization, thanks to their high angular resolution. A difficult problem arising indoors and outdoors is localizing users over multipath channels. Localization based on angle of arrival (AOA) generally involves a two-step procedure, where signals are first processed to obtain a users AOA at different base stations, followed by triangulation to determine the users position. In the presence of multipath, the performance of these methods is greatly degraded due to the inability to correctly detect and/or estimate the AOA of the line-of-sight (LOS) paths. To counter the limitations of this two-step procedure which is inherently suboptimal, we propose a direct localization approach in which the position of a user is localized by jointly processing the observations obtained at distributed massive MIMO base stations. Our approach is based on a novel compressed sensing framework that exploits channel properties to distinguish LOS from non-LOS signal paths, and leads to improved performance results compared to previous existing methods.

  • 80.
    Georgiou, Tryphon T.
    et al.
    Department of Electrical Engineering, University of Minnesota.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Takyar, Mir Shahrouz
    Department of Electrical Engineering, University of Minnesota.
    Metrics for Power Spectra: An Axiomatic Approach2009In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 57, no 3, p. 859-867Article in journal (Refereed)
    Abstract [en]

    We present an axiomatic framework for seeking distances between power spectral density functions. The axioms require that the sought metric respects the effects of additive and multiplicative noise in reducing our ability to discriminate spectra, as well as they require continuity of statistical quantities with respect to perturbations measured in the metric. We then present a particular metric which abides by these requirements. The metric is based on the Monge-Kantorovich transportation problem and is contrasted with an earlier Riemannian metric based on the minimum-variance prediction geometry of the underlying time-series. It is also being compared with the more traditional Itakura-Saito distance measure, as well as the aforementioned prediction metric, on two representative examples.

  • 81. Gezici, Sinan
    et al.
    Bayram, Suat
    Kurt, Mehmet Necip
    Gholami, Mohammad Reza
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Optimal Jammer Placement in Wireless Localization Systems2016In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 64, no 17, p. 4534-4549Article in journal (Refereed)
    Abstract [en]

    In this study, the optimal jammer placement problem is proposed and analyzed for wireless localization systems. In particular, the optimal location of a jammer node is obtained by maximizing the minimum of the Cramer-Rao lower bounds (CRLBs) for a number of target nodes under location related constraints for the jammer node. For scenarios with more than two target nodes, theoretical results are derived to specify conditions underwhich the jammer node is located as close to a certain target node as possible, or the optimal location of the jammer node is determined by two of the target nodes. Also, explicit expressions are provided for the optimal location of the jammer node in the presence of two target nodes. In addition, in the absence of distance constraints for the jammer node, it is proved, for scenarios with more than two target nodes, that the optimal jammer location lies on the convex hull formed by the locations of the target nodes and is determined by two or three of the target nodes, which have equalized CRLBs. Numerical examples are presented to provide illustrations of the theoretical results in different scenarios.

  • 82.
    Ghadimi, Euhanna
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Shames, Iman
    Johansson, Mikael
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Multi-Step Gradient Methods for Networked Optimization2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 21, p. 5417-5429Article in journal (Refereed)
    Abstract [en]

    We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function, we determine the algorithm parameters that guarantee the fastest convergence and characterize situations when significant speed-ups over the standard gradient method are obtained. Furthermore, we quantify how uncertainty in problem data at design-time affects the run-time performance of the gradient method and its multi-step counterpart, and conclude that in most cases the multi-step method outperforms gradient descent. Finally, we apply the proposed technique to three engineering problems: resource allocation under network-wide budget constraint, distributed averaging, and Internet congestion control. In all cases, our proposed algorithms converge significantly faster than the state-of-the art.

  • 83.
    Ghauch, Hadi
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Communication Theory.
    Kim, Taejoon
    City University of Hong Kong.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Distributed Low-Overhead Schemes for Multi-stream MIMO Interference Channels2015In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 7, p. 1737-1749Article in journal (Refereed)
    Abstract [en]

    Our aim in this work is to propose fully distributed schemes for transmit and receive filter optimization. The novelty of the proposed schemes is that they only require a few forward-backward iterations, thus causing minimal communication overhead. For that purpose, we relax the well-known leakage minimization problem, and then propose two different filter update structures to solve the resulting non-convex problem: though one leads to conventional full-rank filters, the other results in rank-deficient filters, that we exploit to gradually reduce the transmit and receive filter rank, and greatly speed up the convergence. Furthermore, inspired from the decoding of turbo codes, we propose a turbo-like structure to the algorithms, where a separate inner optimization loop is run at each receiver (in addition to the main forward-backward iteration). In that sense, the introduction of this turbo-like structure converts the communication overhead required by conventional methods to computational overhead at each receiver (a cheap resource), allowing us to achieve the desired performance, under a minimal overhead constraint. Finally, we show through comprehensive simulations that both proposed schemes hugely outperform the relevant benchmarks, especially for large system dimensions.

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  • 84. Ghayem, Fateme
    et al.
    Sadeghi, Mostafa
    Babaie-Zadeh, Massoud
    Chatterjee, Saikat
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.
    Skoglund, Mikael
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Information Science and Engineering.
    Jutten, Christian
    Sparse Signal Recovery Using Iterative Proximal Projection2018In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 4, p. 879-894Article in journal (Refereed)
    Abstract [en]

    This paper is concerned with designing efficient algorithms for recovering sparse signals from noisy underdetermined measurements. More precisely, we consider minimization of a nonsmooth and nonconvex sparsity promoting function subject to an error constraint. To solve this problem, we use an alternating minimization penalty method, which ends up with an iterative proximal-projection approach. Furthermore, inspired by accelerated gradient schemes for solving convex problems, we equip the obtained algorithm with a so-called extrapolation step to boost its performance. Additionally, we prove its convergence to a critical point. Our extensive simulations on synthetic as well as real data verify that the proposed algorithm considerably outperforms some well-known and recently proposed algorithms.

  • 85.
    Granström, Karl
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Orguner, Umut
    Department of Electrical and Electronics Engineering, Middle East Technical University.
    A PHD Filter for Tracking Multiple Extended Targets using Random Matrices2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 11, p. 5657-5671Article in journal (Refereed)
    Abstract [en]

    This paper presents a random set based approach to tracking of an unknown number of extended targets, in the presence of clutter measurements and missed detections, where the targets extensions are modeled as random matrices. For this purpose, the random matrix framework developed recently by Koch et al. is adapted into the extended target PHD framework, resulting in the Gaussian inverse Wishart PHD (GIW-PHD) filter. A suitable multiple target likelihood is derived, and the main filter recursion is presented along with the necessary assumptions and approximations. The particularly challenging case of close extended targets is addressed with practical measurement clustering algorithms. The capabilities and limitations of the resulting extended target tracking framework are illustrated both in simulations and in experiments based on laser scans.

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  • 86.
    Granström, Karl
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Orguner, Umut
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    On Spawning and Combination of Extended/Group Targets Modeled with Random Matrices2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 3, p. 678-692Article in journal (Refereed)
    Abstract [en]

    In extended/group target tracking, where the extensions of the targets are estimated, target spawning and combination events might have significant implications on the extensions. This paper investigates target spawning and combination events for the case that the target extensions are modeled in a random matrix framework. The paper proposes functions that should be provided by the tracking filter in such a scenario. The results, which are obtained by a gamma Gaussian inverse Wishart implementation of an extended target probability hypothesis density filter, confirms that the proposed functions improve the performance of the tracking filter for spawning and combination events.

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  • 87.
    Gunnarsson, Svante
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    On the Quality of Recursively Identified FIR Models1992In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 40, no 3, p. 679-682Article in journal (Refereed)
    Abstract [en]

    The author considers recursive identification of time-varying systems having finite impulse response, focusing on the tradeoff between tracking capability and disturbance rejection. Approximate, but simple and explicit, frequency-domain expressions for the model quality are derived for three different identification algorithms. The results, derived under the assumption of slow adaptation, slow system variation, and high model order, are extensions of the results presented by Gunnarsson and Ljung (see ibid., vol.37, p.1072, 1989) to the case where the system output is affected by correlated disturbances.

  • 88.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Determining the Initial States in Forward-Backward Filtering1996In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 46, no 4, p. 988-992Article in journal (Refereed)
    Abstract [en]

    Forward-backward filtering is a common tool in off-line filtering for implementing noncausal filters. Filtering first forward and then backward or the other way around does not generally give the same result. Here, we propose a method to choose the initial state to obtain uniqueness and to remove transients at both ends.

  • 89.
    Gustafsson, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gunnarsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Bergman, Niclas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Forsell, Urban
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Jansson, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Karlsson, Rickard
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Nordlund, Per-Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Particle Filters for Positioning, Navigation and Tracking2002In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 50, no 2, p. 425-437Article in journal (Refereed)
    Abstract [en]

    A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general non-linear measurement equation in position. A general algorithm is presented, which is parsimonious with the particle dimension. It is based on marginalization, enabling a Kalman filter to estimate all position derivatives, and the particle filter becomes low-dimensional. This is of utmost importance for high-performance real-time applications. Automotive and airborne applications illustrate numerically the advantage over classical Kalman filter based algorithms. Here the use of non-linear models and non-Gaussian noise is the main explanation for the improvement in accuracy. More specifically, we describe how the technique of map matching is used to match an aircraft's elevation profile to a digital elevation map, and a car's horizontal driven path to a street map. In both cases, real-time implementations are available, and tests have shown that the accuracy in both cases is comparable to satellite navigation (as GPS), but with higher integrity. Based on simulations, we also argue how the particle filter can be used for positioning based on cellular phone measurements, for integrated navigation in aircraft, and for target tracking in aircraft and cars. Finally, the particle filter enables a promising solution to the combined task of navigation and tracking, with possible application to airborne hunting and collision avoidance systems in cars.

  • 90.
    Gustafsson, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gunnarsson, Svante
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Shaping Frequency-Dependent Time Resolution when Estimating Spectral Properties with Parametric Methods1997In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 45, no 4, p. 1025-1035Article in journal (Refereed)
    Abstract [en]

    The problem of tracking time-varying properties of a signal is studied. The somewhat contradictory notion of “time-varying spectrum” and how to estimate the “current” spectrum in an on-line fashion is discussed. The traditional concepts and relations between time and frequency resolution are crucial for this problem. We introduce two definitions for the time resolution of filters, essentially measuring the effective number of past data that are used to form the estimate. In, for example, wavelet transform techniques, frequency-dependent time resolutions are used so that fewer data are used at higher frequencies, thus enabling faster tracking of high-frequency components (at the price of worse frequency resolution). The main contribution of the paper is to show how this same feature can be introduced when estimating spectra via a time-varying, autoregressive model of the signal. This is achieved by a special choice of nominal covariance matrix for the underlying parameter changes.

  • 91.
    Gustafsson, Fredrik
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hendeby, Gustaf
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Some Relations Between Extended and Unscented Kalman Filters2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 2, p. 545-555Article in journal (Refereed)
    Abstract [en]

    The unscented Kalman filter (UKF) has become a popular alternative to the extended Kalman filter (EKF) during the last decade. UKF propagates the so called sigma points by function evaluations using the unscented transformation (UT), and this is at first glance very different from the standard EKF algorithm which is based on a linearized model. The claimed advantages with UKF are that it propagates the first two moments of the posterior distribution and that it does not require gradients of the system model. We point out several less known links between EKF and UKF in terms of two conceptually different implementations of the Kalman filter: the standard one based on the discrete Riccati equation, and one based on a formula on conditional expectations that does not involve an explicit Riccati equation. First, it is shown that the sigma point function evaluations can be used in the classical EKF rather than an explicitly linearized model. Second, a less cited version of the EKF based on a second-order Taylor expansion is shown to be quite closely related to UKF. The different algorithms and results are illustrated with examples inspired by core observation models in target tracking and sensor network applications.

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  • 92.
    Göransson, Bo
    et al.
    KTH, Superseded Departments (pre-2005), Signals, Sensors and Systems.
    Ottersten, Björn
    KTH, Superseded Departments (pre-2005), Signals, Sensors and Systems.
    Direction estimation in partially unknown noise fields1999In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 47, no 9, p. 2375-2385Article in journal (Refereed)
    Abstract [en]

    The problem of direction of arrival estimation in the presence of colored noise with unknown covariance is considered, The unknown noise covariance is assumed to obey a linear parametric model. Using this model, the maximum likelihood directions parameter estimate is derived, and a large sample approximation is formed. It is shown that a priori information on the source signal correlation structure is easily incorporated into this approximate ML (AML) estimator. Furthermore, a closed-form expression of the Cramer-Rao bound on the direction parameter is provided. A perturbation analysis with respect to a small error in the assumed noise model is carried out, and an expression of the asymptotic bias due to the model mismatch is given. Computer simulations and an application of the proposed technique to a full-scale passive sonar experiment is provided to illustrate the results.

  • 93.
    Hammarwall, David
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Acquiring partial CSI for spatially selective transmission by instantaneous channel norm feedback2008In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 56, no 3, p. 1188-1204Article in journal (Refereed)
    Abstract [en]

    In the design of next-generation multiuser communication systems, multiple-antenna transmission is an essential part providing additional spatial degrees of freedom and allowing efficient use of resources. A major limiting factor in the resource allocation is the amount of channel state information (CSI) available at the transmitter, particularly in multiuser systems where the feedback from each user terminal must be limited. Herein, we show that the Euclidean norm of the instantaneous channel, when combined with long-term channel statistics provides sufficient information for the transmitter to efficiently utilize multiuser diversity in time, frequency, and space. We consider the downlink of a communication system where the base station has multiple transmit antennas whereas each user terminal has a single receive antenna. The CSI provided by channel statistics and feedback of the norm of the instantaneous channel vector is studied in depth for correlated Rayleigh and Ricean fading channels, within a minimum mean-square error (MMSE) estimation framework. An asymptotic analysis (high instantaneous SNR) is presented which shows that channel realizations with large channel norm provide additional spatial CSI at the transmitter. This makes the proposed scheme ideal for multiuser diversity transmission schemes, where resources are only allocated to users experiencing favorable channel conditions.

  • 94.
    Hammarwall, David
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On downlink beamforming with indefinite shaping constraints2006In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 54, no 9, p. 3566-3580Article in journal (Refereed)
    Abstract [en]

    Beamforming schemes have been proposed to exploit the spatial characteristics of multiple-input single-output (MISO) wireless radio channels. Several algorithms are available for optimal joint beamforming and power control for the downlink. Such optimal beamforming minimizes the total transmission power, while ensuring an individual target quality of service (QoS) for each user; alternatively the weakest QoS is maximized, subject to a power constraint. Herein, we consider both formulations and some of the available algorithms are generalized to enable indefinite quadratic shaping constraints on the beamformers. By imposing such additional constraints, the QoS measure can be extended to take other factors than the customary signal-to-interference-and-noise ratio (SINR) into account. Alternatively, other limitations such as interference requirements or physical constraints may be handled within the optimization. We also consider a more general SINR expression than previously analyzed, which allows for more accurate modeling, e.g., of nonzero self-interference in code-division multiple-access (CDMA) systems. Several applications for indefinite equality or inequality constraints are suggested and evaluated. For example, it is shown how such constraints may be used to ensure a minimum level of path diversity in a CDMA system. Other applications include limiting intercell interference in decentralized systems

  • 95.
    Hammarwall, David
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Utilizing the spatial information provided by channel norm feedback in SDMA systems2008In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 56, no 7, p. 3278-3293Article in journal (Refereed)
    Abstract [en]

    To achieve high performance, in terms of reliability and throughput, in future multiple-antenna communication systems, it is essential to fully exploit the spatial dimensions of the wireless propagation channel. In multiuser communication systems, the throughput can be significantly increased by simultaneously transmitting to several users in the same time-frequency slot by means of spatial-division multi-access (SDMA). A major limiting factor for downlink SDMA transmission is the amount of channel-state information (CSI) that is available at the transmitter. In most cases, CSI can be measured/estimated only at the user terminals and must be fed back to the base station. This procedure typically constrains the amount of CSI that can be conveyed to the base station. Herein, we develop several low-complexity, as well as optimized, SDMA downlink resource-allocation schemes that are particularly suitable for systems utilizing statistical channel information and partial CSI feedback. A framework is proposed for combining statistical channel information with a class of instantaneous channel norms. It is shown that, in wide-area scenarios, the feedback of such a scalar norm provides sufficient information for the proposed resource-allocation algorithms to perform efficient SDMA beamforming (BF) and scheduling.

  • 96. Hammes, C.
    et al.
    Bhavani Shankar, M. R.
    Ottersten, Björn
    Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg, Luxemburg, Luxembourg.
    Generalized Multiplexed Waveform Design Framework for Cost-Optimized MIMO Radar2021In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 69, p. 88-102, article id 9272873Article in journal (Refereed)
  • 97. Han, Duo
    et al.
    Mo, Yilin
    Wu, Junfeng
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Shi, Ling
    An Opportunistic Sensor Scheduling Solution to Remote State Estimation Over Multiple Channels2016In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 64, no 18, p. 4905-4917Article in journal (Refereed)
    Abstract [en]

    We consider a sensor scheduling problem where the sensors have multiple choices of communication channel to send their local measurements to a remote state estimator for state estimation. Specifically, the sensors can transmit high-precision data packets over an expensive channel or low-precision data packets, which are quantized in several bits, over some cheap channels. The expensive channel, though being able to deliver more accurate data which leads to good estimation quality at the remote estimator, can only be used scarcely due to its high cost (e.g., high energy consumption). On the other hand, the cheap channel, though having a small cost, delivers less accurate data which inevitably deteriorates the remote estimation quality. In this work we propose a new framework in which the sensors switch between the two channels to achieve a better tradeoff among the communication cost, the estimation performance and the computational complexity, where the two-channel case can be easily extended to a multiple-channel case. We propose an opportunistic sensor schedule which reduces the communication cost by randomly switching among the expensive and cheap channels, and in the meantime maintains low computational complexity while introducing data quantization into the estimation problem. We present a minimum mean square error (MMSE) estimator in a closed-form under the proposed opportunistic sensor schedule. We also formulate an optimization problem to search the best opportunistic schedule with a linear quantizer. Furthermore, we show that the MMSE estimator in the limiting case becomes the standard Kalman filter.

  • 98. Han, Duo
    et al.
    You, Keyou
    Xie, Lihua
    Wu, Junfeng
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Shi, Ling
    Optimal Parameter Estimation Under Controlled Communication Over Sensor Networks2015In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 24, p. 6473-6485Article in journal (Refereed)
    Abstract [en]

    This paper considers parameter estimation of linear systems under sensor-to-estimator communication constraint. Due to the limited battery power and the traffic congestion over a large sensor network, each sensor is required to reduce the rate of communication between the estimator and itself. We propose an observation-driven sensor scheduling policy such that the sensor transmits only the important measurements to the estimator. Unlike the existing deterministic scheduler, our stochastic scheduling is smartly designed to well compensate for the loss of the Gaussianity of the system. This results in a nice feature that the maximum-likelihood estimator (MLE) is still able to be recursively computed in a closed form, and the resulting estimation performance can be explicitly evaluated. Moreover, an optimization problem is formulated and solved to obtain the best parameters of the scheduling policy under which the estimation performance becomes comparable to the standard MLE with full measurements under a moderate transmission rate. Finally, simulations are included to validate the theoretical results.

  • 99. Haqiqatnejad, A.
    et al.
    Kayhan, F.
    Ottersten, Björn
    Interdisciplinary Centre for Security, University of Luxembourg, Luxembourg City, Luxembourg.
    Robust SINR-Constrained Symbol-Level Multiuser Precoding with Imperfect Channel Knowledge2020In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 68, p. 1837-1852, article id 9025051Article in journal (Refereed)
    Abstract [en]

    In this paper, we address robust design of symbol-level precoding (SLP) for the downlink of multiuser multiple-input single-output wireless channels, when imperfect channel state information (CSI) is available at the transmitter. In particular, we consider a well known model for the CSI imperfection, namely, stochastic Gaussian-distributed uncertainty. Our design objective is to minimize the total (per-symbol) transmission power subject to constructive interference (CI) constraints as well as the users' quality-of-service requirements in terms of signal-to-interference-plus-noise ratio. Assuming stochastic channel uncertainties, we first define probabilistic CI constraints in order to achieve robustness to statistically known CSI errors. Since these probabilistic constraints are difficult to handle, we resort to their convex approximations in the form of tractable (deterministic) robust constraints. Three convex approximations are obtained based on different conservatism levels, among which one is introduced as a benchmark for comparison. We show that each of our proposed approximations is tighter than the other under specific robustness settings, while both of them always outperform the benchmark. Using the proposed CI constraints, we formulate the robust SLP optimization problem as a second-order cone program. Extensive simulation results are provided to validate our analytic discussions and to make comparisons with conventional block-level robust precoding schemes. We show that the robust design of symbol-level precoder leads to an improved performance in terms of energy efficiency at the cost of increasing the computational complexity by an order of the number of users in the large system limit, compared to its non-robust counterpart.

  • 100. Haqiqatnejad, A.
    et al.
    Kayhan, F.
    Ottersten, Björn
    Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg.
    Symbol-Level Precoding Design Based on Distance Preserving Constructive Interference Regions2018In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 22, p. 5817-5832Article in journal (Refereed)
    Abstract [en]

    In this paper, we investigate the symbol-level precoding (SLP) design problem in the downlink of a multiuser multiple-input single-output channel. We consider generic two-dimensional constellations with any shape and size, and confine ourselves to one of the main categories of constructive interference regions (CIR), namely distance preserving CIR (DPCIR). We provide a comprehensive study of DPCIRs and derive several properties for these regions. Using these properties, we first show that any signal in a given DPCIR has a norm greater than or equal to the norm of the corresponding constellation point if and only if the convex hull of the constellation contains the origin. It is followed by proving that the power of the noise-free received signal in a DPCIR is a monotonic strictly increasing function of two parameters relating to the infinite Voronoi edges. Using the convex description of DPCIRs and their characteristics, we formulate two design problems, namely the SLP power minimization with signal-to-interference-plus-noise ratio (SINR) constraints, and the SLP SINR balancing problem under max-min fairness criterion. The SLP power minimization based on DPCIRs can straightforwardly be written as a quadratic programming. We derive a simplified reformulation of this problem, which is less computationally complex. The SLP max-min SINR, however, is non-convex in its original form, and hence difficult to tackle. We propose alternative optimization approaches, including semidefinite programming formulation and block coordinate descent optimization. We discuss and evaluate the loss due to the proposed alternative methods through extensive simulation results.

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