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.

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

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.

Pattern Recognition and Machine Learning

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.

Two decades of array signal processing research: the parametric approach

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.

Survey of Wireless Indoor Positioning Techniques and Systems

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

Convergence of probability measures

An LMMSE channel prediction algorithm based on sinusoidal modeling is proposed for SIMO systems, assuming random amplitudes and equal mean powers. The potentially ill-conditioned LS estimates of the complex amplitudes is mitigated by regularization. This is interpreted as an LMMSE prediction, where the complex amplitudes are modeled as random (Rayleigh fading). Evaluated by simulations in SISO scenarios without loss of generality the LMMSE predictor presents a similar performance to the non-regularized LS prediction. The CRB of the frequency estimate of the sinusoidal modeling is derived. The performance of the LMMSE prediction with frequencies estimated by Unitary-ESPRIT is very close to those using the "best possible" frequency estimates according to the CRB. It also outperforms by far the AR modeling based linear prediction in the investigated scenarios.

LMMSE channel prediction based on sinusoidal modeling

https://publications.lib.chalmers.se/records/fulltext/201625/local_201625.pdf

Global monitoring of fluidized-bed processes by means of microwave cavity resonances

Dynamic programming has previously been used when measuring Lumen Diameter (LD) and Intima-Media Thickness (IMT) in single frame ultrasound carotid artery images [1]. An extension to multiframe detection of that procedure is proposed in this paper. Our new method transforms a three dimensional problem into multiple two dimensional problems that can again be solved by dynamic programming. First, several “candidate boundaries” are detected in each image. Then, one boundary from each image in the sequence is selected in such a way that the sequence of boundaries is optimal among the considered possibilities. A model of the movements of the boundaries is used in the second step. Our proposed method shows promising performance on both synthetic and real ultrasound data.

A new method based on dynamic programming for boundary detection in ultrasound image sequences

Array response interpolation and DOA estimation with array response decomposition

Atomic norm denoising has been recently introduced as a generalization of the Least Absolute Shrinkage and Selection Operator (LASSO) to overcome the problem of off-grid parameters. The method has been found to possess many interesting theoretical properties. However, its implementation has been only discussed in a special case of spectral line estimation by uniform sampling. In this paper, we propose a general numerical method to solve the atomic norm denoising problem. The complexity of the proposed algorithm is proportional to the complexity of a single-parameter search in the parameter space and thus in many interesting cases, including frequency estimation it enjoys fast realization.

Mats Viberg

Papers

LMMSE channel prediction based on sinusoidal modeling

Global monitoring of fluidized-bed processes by means of microwave cavity resonances

A new method based on dynamic programming for boundary detection in ultrasound image sequences

Array response interpolation and DOA estimation with array response decomposition

A numerical implementation of gridless compressed sensing