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

https://publications.lib.chalmers.se/records/fulltext/249664/local_249664.pdf

Microwave measurement system for dispersive dielectric properties of densely packed pellets

High-performance array applications often require an accurate array response model. A common way to achieve this is by array calibration which involves measuring the response for a finite number of given source directions and employing interpolation. This paper considers the array calibration problem by combing interpolation techniques and parametric modeling. The idea is to model the array response as a product of a mutual coupling matrix, an ideal array response vector (derived from the geometry of antenna array) and an angle-dependent correction vector. Since the major effects are captured by the physical model and the mutual coupling matrix, the correction vector will be a smoother function of angle as compared to direct interpolation of the measured array response. In numerical experiments of a real antenna array, the method is found to improve the performance of the array calibration significantly.

Array calibration using array response interpolation and parametric modeling

This paper considers the problem of maximum likelihood (ML) estimation for reduced-rank linear regression equations with noise of arbitrary covariance. An explicit expression for the ML estimate of the regression matrix is derived. A generalized likelihood ratio (GLRT) test as also proposed, for estimating the rank of the regression matrix. Computer simulations and numerical examples indicate the superiority of the proposed estimator, as compared to a traditional least-squares approach that does not exploit the reduced rank property in an optimal way.

Reduced-rank linear regression

Hybrid beamforming (HBF) is a potential solution to reduce the baseband hardware cost in massive multiple-input multiple-output (MIMO) systems that has drawn considerable attention recently. In this paper, we consider the uplink of a multiuser massive MIMO system in the presence of blockers. Such blockers, which arise from, for example, users served by other non-cooperative base stations (BSs), can limit the system performance if not handled properly. We propose a HBF scheme that can remove the impact of blockers, while preserving signals from intended users. Specifically, in our two-step receive beamforming scheme, the analog beamformer (ABF) is designed based on channel covariance matrices to minimize the powers of blockers, while the digital beamformer (DBF) deals with inter-user interference. We propose an iterative algorithm that efficiently gives a good sub-optimal solution to the NP-hard problem in the ABF design. Moreover, we consider a more complete BS architecture by incorporating automatic gain control (AGC) and analog-to-digital converter (ADC). As we show in the simulations, for a system with full-precision ADCs, our scheme approaches the sum rate of an ideal fully-digital system. Interestingly, for a system with low-resolution ADCs, our HBF scheme can even outperform a fully-digital system.

Mats Viberg

Papers

Microwave measurement system for dispersive dielectric properties of densely packed pellets

Array calibration using array response interpolation and parametric modeling

Reduced-rank linear regression

Hybrid beamforming in uplink massive MIMO systems in the presence of blockers

Effects of Unknown Noise Covariance on Parametric Array Processing Algorithms