Mats Viberg

Bio: Mats Viberg is an academic researcher from Chalmers University of Technology. The author has contributed to research in topics: Sensor array & Estimation theory. The author has an hindex of 41, co-authored 231 publications receiving 11749 citations. Previous affiliations of Mats Viberg include Linköping University & Blekinge Institute of Technology.

Performance Analysis of Sparsity-Based Parameter Estimation

Abstract: Since the advent of the $\ell _1$ regularized least squares method (LASSO), a new line of research has emerged, which has been geared toward the application of the LASSO to parameter estimation problems. Recent years witnessed a considerable progress in this area. The notorious difficulty with discretization has been settled in the recent literature, and an entirely continuous estimation method is now available. However, an adequate analysis of this approach lacks in the current literature. This paper provides a novel analysis of the LASSO as an estimator of continuous parameters. This analysis is different from the previous ones in that our parameters of interest are associated with the support of the LASSO solution. In other words, our analysis characterizes the error in the parameterization of the support. We provide a novel framework for our analysis by studying nearly ideal sparse solutions. In this framework, we quantify the error in the high signal-to-noise ratio regime. As the result depends on the choice of the regularization parameter, our analysis also provides a new insight into the problem of selecting the regularization parameter. Without loss of generality, the results are expressed in the context of direction of arrival estimation problem.

Asymptotic properties of nonlinear weighted least squares in radar array processing

Abstract: This paper treats nonlinear weighted least squares parameter estimation of sinusoidal signals impinging on a sensor array. We give a consistency proof for a more general model than what has been previously considered in the analysis of two-dimensional (2-D) sinusoidal fields. Specifically, the array can have an arbitrary shape, and spatially colored noise is allowed. Further, we do not impose the restriction of unique frequencies within each dimension, and the number of samples is assumed large in only the temporal dimension. In addition to consistency, we establish that the parameter estimates are multivariate Gaussian distributed under a large class of noise distributions. The finite sample performance is investigated via computer simulations, which illustrate that a recommended two-step procedure yields asymptotically efficient estimates when the noise is Gaussian. The first step is necessary for estimating the weighting matrix, which has a dramatic influence on the performance in the studied scenarios. The number of samples required to attain the Crame/spl acute/r-Rao lower bound is found to coincide with the point where the signal sources are separated by more than one discrete Fourier transform bin. This remains true even when the signals emanate from the same direction of arrival (DOA).

Asymptotic Analysis Of The Total Least Squares ESPRIT Algorithm

Abstract: This paper considers the problem of estimating the parameters of multiple narrowband signals arriving at an array of sensors. Modern approaches to this problem often involve costly procedures for calculating the estimates. The ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm was recently proposed as a means for obtaining accurate estimates without requiring a costly search of the parameter space. This method utilizes an array invariance to arrive at a computationally efficient multidimensional estimation procedure. Herein, the asymptotic distribution of the estimation error is derived for the Total Least Squares (TLS) version of ESPRIT. The Cramer-Rao Bound (CRB) for the ESPRIT problem formulation is also derived and found to coincide with the variance of the asymptotic distribution through numerical examples. The method is also compared to least squares ESPRIT and MUSIC as well as to the CRB for a calibrated array. Simulations indicate that the theoretic expressions can be used to accurately predict the performance of the algorithm.

Bayesian Channel Estimation Techniques for AF MIMO Relaying Systems

Abstract: In this paper, we consider the fundamental problem of channel estimation in multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying systems operating over random channels. Using the Bayesian framework, linear minimum mean square error (LMMSE) and expectation-maximization (EM) based maximum a posteriori (MAP) channel estimation algorithms are developed, that provide the destination with full knowledge of all channel parameters involved in the transmission. The performance of the proposed algorithms is evaluated in terms of the mean square error (MSE) as a function of the signal-tonoise ratio (SNR) during the training interval. Our simulation results show that the incorporation of prior knowledge into the channel estimation algorithm offers improved performance, especially in the low SNR regime.

Reconstruction of Clipped Signals in Quantized Uplink Massive MIMO Systems

Abstract: This paper considers the uplink of a single-cell multiuser massive multiple-input multiple-output system. Each receiver antenna of the base station (BS) is assumed to be equipped with a pair of analog-to-digital converters to quantize the real and imaginary part of the received signal. We propose a novel clipping-aware receiver (CA-MMSE), which performs minimum mean square error (MMSE) reconstruction only on the clipped received samples, while the granular samples are left unchanged after the quantization. On this basis, we present an iterative algorithm to implement the CA-MMSE receiver and derive a sufficient condition for its geometrical convergence to a fixed point. We show that as long as the number of BS antennas or the quantization resolution is sufficiently high, then, the performance of the CA-MMSE is as good as the optimal MMSE receiver which reconstructs all quantized received symbols. Additionally, we propose a novel Bussgang-based weighted zero-forcing (B-WZF) receiver which distinguishes the clipping and granular distortion and it is shown that as long as the received training symbols per antenna are correlated, the CA-MMSE brings significant improvements compared to conventional receivers in the literature while for users that do not experience deep large-scale fading the simpler B-WZF is near to the CA-MMSE for sufficiently high signal-to-noise ratio and quantization resolution.

On Limits of Wireless Communications in a Fading Environment when UsingMultiple Antennas

Abstract: This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver. We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon‘s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99% of the channels the capacity is about 7, 19 and 88 bits/cycle respectively, while if n = 1 there is only about 1.2 bit/cycle at the 99% level. For say a symbol rate equal to the channel bandwith, since it is the bits/symbol/dimension that is relevant for signal constellations, these higher capacities are not unreasonable. The 19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88 bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standard approaches such as selection and optimum combining are seen to be deficient when compared to what will ultimately be possible. New codecs need to be invented to realize a hefty portion of the great capacity promised.

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Two decades of array signal processing research: the parametric approach

Abstract: The quintessential goal of sensor array signal processing is the estimation of parameters by fusing temporal and spatial information, captured via sampling a wavefield with a set of judiciously placed antenna sensors. The wavefield is assumed to be generated by a finite number of emitters, and contains information about signal parameters characterizing the emitters. A review of the area of array processing is given. The focus is on parameter estimation methods, and many relevant problems are only briefly mentioned. We emphasize the relatively more recent subspace-based methods in relation to beamforming. The article consists of background material and of the basic problem formulation. Then we introduce spectral-based algorithmic solutions to the signal parameter estimation problem. We contrast these suboptimal solutions to parametric methods. Techniques derived from maximum likelihood principles as well as geometric arguments are covered. Later, a number of more specialized research topics are briefly reviewed. Then, we look at a number of real-world problems for which sensor array processing methods have been applied. We also include an example with real experimental data involving closely spaced emitters and highly correlated signals, as well as a manufacturing application example.

Survey of Wireless Indoor Positioning Techniques and Systems

Abstract: Wireless indoor positioning systems have become very popular in recent years. These systems have been successfully used in many applications such as asset tracking and inventory management. This paper provides an overview of the existing wireless indoor positioning solutions and attempts to classify different techniques and systems. Three typical location estimation schemes of triangulation, scene analysis, and proximity are analyzed. We also discuss location fingerprinting in detail since it is used in most current system or solutions. We then examine a set of properties by which location systems are evaluated, and apply this evaluation method to survey a number of existing systems. Comprehensive performance comparisons including accuracy, precision, complexity, scalability, robustness, and cost are presented.

Convergence of probability measures

Abstract: The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an