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

Adaptive data reduction for signals observed in spatially colored noise

We address the problem of human detection with mobile platforms such as robots. Instead of using an optical system, we propose to employ an acoustic 2D array to reliably obtain an image of a human in a 3D spatial power spectrum which is independent of lighting conditions and uses cheap acoustic sensors. We show that humans have a distinct acoustic signature and propose to model the echoes from reflecting parts of objects in the scene by a Gaussian-Mixture-Model. When it is fitted to the acoustic image, we can extract geometric relations between the present echoes and represent the acoustic signatures in a low-dimensional parameter space. We present results based on real data measurements that demonstrate that different objects can be reconstructed from the data and discriminated. The obtained parameter space forms the basis for subsequent detection and classification of humans.

Parametrization of acoustic images for the detection of human presence by mobile platforms

Recursive methods for subspace tracking with applications to 'on-line' direction of arrival estimation, have lately drawn considerable interest. Instrumental variable (IV) generalizations of the projection approximation subspace tracking (PAST) algorithm are proposed. The IV-approach is motivated by the fact that PAST delivers biased estimates when the noise vectors are not spatially white. The resulting basic IV-algorithm has a computational complexity of 3mn+O(n/sup 2/) complex multiplications, where m is the dimension of the measurement vector and n is the subspace dimension. The performance of the proposed algorithms in tracking sinusoids in colored noise is illustrated by computer simulations.

Instrumental variable subspace tracking with applications to sensor array processing and frequency estimation

For arrays with position and channel errors the calibration becomes very crucial. In the traditional calibration methods one can choose between an optimal SNR and a beam pattern with low side lobes. In this paper we formulate a beam pattern synthesis method which optimize the trade-off between the two criteria. A classical problem with position errors in an array, is that it is difficult to get low side lobes over the whole side lobe region, since the position errors give rise to direction dependent errors. In this paper this problem is solved by using local (direction dependent) correction matrices in the beam pattern optimization. The new way of using local correction matrices leads to the lowest possible uniform side lobe level, for the chosen SNR, beamwidth and beam pointing direction.

Optimized Beamforming Calibration in the Presence of Array Imperfections

The problem of estimating signal parameters from sensor array data is addressed. If the array is composed of two identical subarrays, (i.e. one invariance) the ESPRIT algorithm is known to yield parameter estimates in a very cost efficient manner. Recently, the total least squares (TLS) version of ESPRIT has been formulated in a subspace fitting framework. In this formulation, the ESPRIT concept is easily generalized to arrays exhibiting more than one invariance. The asymptotic properties for this class of algorithms are derived. The estimates are shown to be statistically efficient under certain assumptions. The case of a uniform linear array is studied in more detail, and a generalization of the ESPRIT algorithm is proposed by introducing row weighting of the subspace estimate. >

Mats Viberg

Papers

Adaptive data reduction for signals observed in spatially colored noise

Parametrization of acoustic images for the detection of human presence by mobile platforms

Instrumental variable subspace tracking with applications to sensor array processing and frequency estimation

Optimized Beamforming Calibration in the Presence of Array Imperfections

Analysis of algorithms for sensor arrays with invariance structure