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

In this paper, we propose a sequential, fast DOA tracking technique using the measurements of a uniform linear sensor array in the far field of a set of narrow band sources. Our approach is based on sparse approximation technique LASSO (Least Absolute Shrincage and Selection Operator), which has recently gained considerable interest for DOA and other estimation problems. Considering the LASSO optimization as a Bayesian estimation, we first define a class of prior distributions suitable for the sparse representation of the model and discuss its relation to the priors over DOAs and waveforms. Inspired by the Kalman filtering method, we introduce a nonlinear sequential filter on this family of distributions. We derive the filter for a simple random walk motion model of the DOAs. The method consists of consecutive implementation of weighted LASSO optimizations using each new measurement and updating the LASSO weights for the next step.

https://publications.lib.chalmers.se/records/fulltext/local_156889.pdf

Fast LASSO based DOA tracking

Base station coordination is an efficient technique to transcend the limits on spectral efficiency imposed by intercell interference In this paper, we compare the performance of different coordination strategies with different amount of channel state information (CSI) and data sharing among the coordinating base stations We focus on the effect of limited backhaul capacity in a two-cell network Contrary to the common belief, we show that coordination strategies with no data and only limited CSI sharing is preferred to those with full data and CSI sharing when the backhaul capacity is relatively low and the edge SNR is high

http://publications.lib.chalmers.se/records/fulltext/local_130596.pdf

Coordinated single-cell vs multi-cell transmission with limited-capacity backhaul

Multi-component harmonic retrieval finds applications in many fields, including radar, sonar and wireless communications. In previous years, several high-resolution subspace-based techniques have been proposed to overcome the spectral leakage problems inherent in the conventional periodogram. However, these methods require high SNR and/or white noise, and are highly computationally intensive in scenarios with a large number of spectral components. We propose a frequency domain subspace algorithm which overcomes these limitations. The method is computationally efficient in providing estimates of the frequencies within a user-selected sub-band. The estimates are exact in the noise-free case, and exhibit low sensitivity to out-of-band signals and colored noise.

A robust frequency domain subspace algorithm for multi-component harmonic retrieval

The l 1 norm regularized least square technique has been proposed as an efficient method to calculate sparse solutions. However, the choice of the regularization parameter is still an unsolved problem, especially when the number of nonzero elements is unknown. In this paper we first design different ML estimators by interpreting the l 1 norm regularization as a MAP estimator with a Laplacian model for data. We also utilize the MDL criterion to decide on the regularization parameter. The performance of these new methods are evaluated in the context of estimating the Directions Of Arrival (DOA) for the simulated data and compared. The simulations show that the performance of the different forms of the MAP estimator are approximately equal in the one snapshot case, where MDL may not work. But for the multiple snapshot case both methods can be used.

http://publications.lib.chalmers.se/records/fulltext/local_150882.pdf

Maximum a posteriori based regularization parameter selection

Methods for estimating the parameters of narrowband signals arriving at an array of sensors are analyzed. Asymptotic results for several estimators have recently appeared in the literature. With few exceptions, the previous analysis requires the incident signal waveforms to be Gaussian random variables. These results are shown to be valid under much more general conditions, i.e. the actual distribution of the signal waveforms does not affect the asymptotic properties of the parameter. >

Mats Viberg

Papers

Fast LASSO based DOA tracking

Coordinated single-cell vs multi-cell transmission with limited-capacity backhaul

A robust frequency domain subspace algorithm for multi-component harmonic retrieval

Maximum a posteriori based regularization parameter selection

Asymptotic robustness of sensor array processing methods