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

Multiple-Input Multiple-Output (MIMO) systems will play a crucial role in the future of wireless systems,
for example multiple antenna techniques can be a key to boost the performance of modern wireless
systems. In order to study the performance and complexity of MIMO systems, a suitable simulation tool is
essential. Simulation is important in system architecture exploration, algorithm optimization and
bottleneck detection. Simulation is also a powerful tool when designing various components in an antenna
system like electromagnetic solvers for radiation patterns and circuit simulation for amplifiers, but
simulating an entire antenna system is not usual. In this paper the capabilities of MathWorks Simulink as a
simulation platform for MIMO systems have been investigated and a typical MIMO-WCDMA link has
been developed. Some of the blocks were used from the WCDMA library and others were developed
accordingly. The Space-Time encoder and decoder for a general MIMO link were also developed.
Furthermore, in order to be able to test different antenna types in a system, the antenna block is separated
from the channel. Henceforth a double directional channel has been developed based on the SCM (spatial
channel model) proposed by 3GPP (3rd Generation Partnership Project), which is an environmental
channel independent from the antenna. The results of the simulation shows that Simulink is a capable
platform for simulation of an entire communication link.

Simulation of a wideband reconfigurable multi-antenna system with space-time coding

Remote estimation with an energy harvesting sensor with a limited data and energy buffer is considered. The sensor node observes an unknown temporally correlated field and communicates its observations to a remote fusion center using the energy it harvested. The fusion center employs linear minimum mean-square error estimation to reconstruct the unknown field. We provide performance guarantees for the estimation error under a block transmission scheme, where at each transmission block, data and energy buffers are completely emptied. Our bounds provide insights into how statistical properties of the energy harvesting process and buffer sizes may affect the estimation error. In particular, these bounds suggest insensitivity of the performance to buffer sizes for signals with low degree of freedom and suggest performance improvements with increasing buffer sizes for signals with relatively higher degree of freedom. Depending only on the mean, variance, and finite support of the energy arrival process, these results provide insights for the energy and data buffer sizes for deployment in future energy harvesting wireless sensing systems.

/pdf/remote-estimation-of-correlated-sources-under-energy-2uxl2drfit.pdf

Remote Estimation of Correlated Sources Under Energy Harvesting Constraints

In this paper, the Cramer-Rao Bound for the Direction-ofArrival parameter under the partial relaxation framework is derived. We introduce a non-redundant parameterization of the signal model corresponding to the partial relaxation framework, in which the array structure in part of the steering matrix is neglected while the rank of the relaxed steering matrix is maintained. We prove that the stochastic Cramer-Rao Bound for the Direction-of-Arrival parameter under the partial relaxation signal model is lower-bounded by that of the conventional stochastic Cramer-Rao Bound. Furthermore, we prove that the partial relaxation estimator for the Weighted Subspace Fitting criterion asymptotically achieves the conventional Cramer-Rao Bound in the case of uncorrelated source signals.

Mats Viberg

Papers

Simulation of a wideband reconfigurable multi-antenna system with space-time coding

Remote Estimation of Correlated Sources Under Energy Harvesting Constraints

CramÉr-rao Bound for DOA Estimators under the Partial Relaxation Framework

Likelihood Array Process

On the Direction Finding Accuracy of a Calibrated Array in the Presence of Mutual Coupling