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

The problem of estimating the parameters of superimposed signals using an array of sensors has received considerable research interest in the last two decades. Many theoretical studies have been carried out and deep insight has been gained. Traditional applications of array processing include source localization and interference suppression in radar and sonar. The proliferation of estimation algorithms has, however, recently spurred an increasing interest in new applications, such as spatial diversity in personal communications, medical applications and line detection in images. The goal of this manuscript is to provide a brief review of the recent research activities in sensor array signal processing. The focus is on estimation algorithms. These are classified into spectral-based and parametric methods respectively, depending on the way the estimates are computed. Some of the most well-known algorithms are presented, and their relative merits and shortcomings are described. References to more detailed analyses and special research topics are also given. Some applications of sensor array processing methods are also commented upon, and potential new ones are mentioned. The results of real data experiments are also presented, demonstrating the usefulness of recently proposed estimation techniques .

Sensor array signal processing : two decades later

AbstmclThe problem of estimating tlie dircetioes of arrival of n&ow band signals, impinging on an array of sensors is addressed. An estimation procedure. which nw plies to arbitrary nrray structures and signnl correlation i? ptopo*cecl.. The method ia bared on thc rrcvntly iutrodnccd Weighted Subspace Fitti+ (WSF) crit.crios. A Gauss-Newlon type algorithm is suggested for minimizing the WSF criterion. A new doteelion scheme ia "1.0 formtiInted, bmod on tho nsymptntic distribution of tho WSF cost function: Siniulntioiis are presented, demonstrating the improv&inent of tho proposed WSF bnsed approaches, over similar tcchniqii6s hnscd on deterministic Mnximoni Likelihood (ML) .

Direction-of-arrival estimation and detection using weighted subspace fitting

Antenna arrays can be used to increase system capacity in PCS networks by supporting multiple co-channel users per cell in receive and in transmit. We propose a novel approach for separating multiple digital signals received at an antenna array. Our approach exploits the temporal structure of digital signals to simultaneously determine the array response and the symbol sequence for each signal. Uniqueness of the estimates is established for signals with BPSK modulation format. This approach for separating digital signals is applicable to an unknown array geometry and propagation environment, which is particularly useful in PCS applications. Simulation results are presented to demonstrate the performance of this new technique. >

Reception of multiple co-channel digital signals using antenna arrays with applications to PCS

The maximum obtainable resolution of a strip-map synthetic aperture radar (SAR) system can be retained by simply avoiding weighting, or tapering, data samples in the along-track compression process. However, this will lead to hazardous artifacts caused by strong sidelobes of the corresponding adjacent scatterers whose interference might severely weaken the desired targets or even introduce false targets. On the other hand, some residual artifacts, even after tapering process, may still deteriorate the quality (contrast) of the SAR image. These issues can be remedied by applying the so-called CLEAN technique, which can mitigate these ill-effects in strip-map SAR imagery while maintaining the maximum resolution. This, indeed, is carried out as a post processing step, i.e., after the azimuth compression is accomplished, in the SAR system. The objective of this paper is to extend the CLEAN technique to strip-map SAR system to produce high-quality images with a very good along-track resolution. The algorithm is then applied to data from a ground-based circular SAR (CSAR) system to verify its implementation as well as this new application of the CLEAN technique.

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CLEAN technique in strip-map SAR for high-quality imaging

This paper investigates the consistency of the LASSO-based DOA estimation of the narrow-band signals in infinitely high SNR. Such a method provides a robust and accurate approximation of the Maximum Likelihood estimation. However, as we show, unlike the standard techniques such as subspace methods the LASSO-based estimation is generally not consistent in high SNRs. In return, considering the true DOA's, we show that the method is consistent for certain configuration of the sources. This approach leads us to relate such a conditional consistency to the resolution concept. We next give a condition to verify the consistency of a given set of directions and simplify it to a computationally fast equivalent algorithm. The results show that the resolution in infinitely high SNR case for m sensors decreases by speed 1 over m.

Mats Viberg

Papers

Sensor array signal processing : two decades later

Direction-of-arrival estimation and detection using weighted subspace fitting

Reception of multiple co-channel digital signals using antenna arrays with applications to PCS

CLEAN technique in strip-map SAR for high-quality imaging

On the resolution of The LASSO-based DOA estimation method