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

A class of computationally efficient DOA estimators under the Partial Relaxation (PR) framework has recently been proposed. Conceptually different from conventional DOA estimation methods in the literature, the estimators under the PR framework rely on the non-complete relaxation of the array manifold while performing a spectral-search in the field of view. This particular type of relaxation essentially implies a modified signal model with partial information loss due to the relaxation. The information loss and its impact on the DOA estimation performance have not yet been analytically quantified in the literature. In this paper, the information loss induced by the relaxation of the array manifold is investigated through the Cramer-Rao Bound (CRB). The closed-form expression of the CRB for DOA estimation under the PR model, on the one hand, provides insight on the information loss in the asymptotic region where the number of snapshots tends to infinity. On the other hand, the proposed CRB characterizes the lower bound for the DOA estimation performance of all PR estimators. We prove that, under the assumptions of Gaussian source signal and noise, the CRB of the PR signal model is lower-bounded by the conventional stochastic CRB. We also prove that the previously proposed Weighted Subspace Fitting estimator under the PR framework asymptotically achieves the CRB of the PR signal model. Furthermore, it is shown that the asymptotic mean-squared errors of all Weighted Subspace Fitting estimators under the PR framework for any positive definite weighting matrix are identical.

Cramér-Rao Bound for DOA Estimators Under the Partial Relaxation Framework: Derivation and Comparison

Array signal processing is the common name for a large number of signal processing techniques involving parameter estimation from multichannel data. The prototype problem is to find the directions of incoming wavefronts using an antenna array. The applications are numerous, including unexpected problems not involving spatially distributed sensors. A vast number of estimation methods have been proposed and extensively analyzed over the last 2-3 decades. The paper provides an introduction to the various algorithms.

Two decades of statistical array processing

Mean shift is robust for image segmentation through local mode seeking. However, like most segmentation schemes it suffers from over-segmentation due to the lack of semantic information. This paper proposes an enhanced spatial-range mean shift segmentation approach, where over-segmented regions are reduced by exploiting the positions and frequencies at which mean shift filters converge. Based on our observation that edges are related to spatial positions with low mean shift convergence frequencies, merging of over-segmented regions can be guided away from the perceptually important image edges. Simulations have been performed and results have shown that the proposed scheme is able to reduce the over-segmentation while maintaining sharp region boundaries for semantically important objects.

Enhanced spatial-range mean shift color image segmentation by using convergence frequency and position

We propose a novel, coordinated user scheduling (CUS) algorithm for inter-cell interference (ICI) mitigation in the downlink of a multi-cell multi-user MIMO system. In the proposed algorithm, ICI mitigation is performed through the exchange of necessary channel state information (CSI) among the base stations, and the revision of the scheduling decisions and beamformer designs at each base station. Furthermore, ICI mitigation is performed only for the cell-edge users so that the amount of inter-base station signaling overhead is minimized. Our simulation results demonstrate that the proposed coordination scheduling algorithm significantly improves the cell-edge users' throughput compared to conventional systems with only a negligible amount of CSI sharing among the base stations and a relatively small throughput loss for the cell-interior users.

https://publications.lib.chalmers.se/records/fulltext/local_136544.pdf

Coordinated user scheduling in the multi-cell MIMO downlink

This paper considers the uplink of a single-cell multiuser massive multiple-input multiple-output (MIMO) system. Each receiver antenna of the base station is assumed to be equipped with a pair of analog-to-digital converters (ADCs) to quantize the real and imaginary part of the received signal. We propose a novel Bussgang-based weighted zero-forcing (B-WZF) receiver, which distinguishes the clipping and granular distortion. Numerical results demonstrate that for sufficiently high SNR and users that do not experience deep large-scale fading, the B-WZF brings significant performance gain over existing linear receivers in the literature, when the training sequence length is higher than the number of users.

Mats Viberg

Papers

Cramér-Rao Bound for DOA Estimators Under the Partial Relaxation Framework: Derivation and Comparison

Two decades of statistical array processing

Enhanced spatial-range mean shift color image segmentation by using convergence frequency and position

Coordinated user scheduling in the multi-cell MIMO downlink

Quantized Uplink Massive MIMO Systems with Linear Receivers