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

Long-range channel prediction is considered to be one of the most important enabling technologies to future wireless communication systems. The prediction of Rayleigh fading channels is studied in the frame of sinusoidal modeling in this paper. A stochastic sinusoidal model to represent a Rayleigh fading channel is proposed. Three different predictors based on the statistical sinusoidal model are proposed. These methods outperform the standard linear predictor (LP) in Monte Carlo simulations, but underperform with real measurement data, probably due to nonstationary model parameters. To mitigate these modeling errors, a joint moving average and sinusoidal (JMAS) prediction model and the associated joint least-squares (LS) predictor are proposed. It combines the sinusoidal model with an LP to handle unmodeled dynamics in the signal. The joint LS predictor outperforms all the other sinusoidal LMMSE predictors in suburban environments, but still performs slightly worse than the standard LP in urban environments.

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New approaches for channel prediction based on sinusoidal modeling

In this letter, we propose a novel framework to enhance the throughput in multiple-input single-output (MISO) mutually interfering channels via selecting the tilt angles at all base stations (BSs) in a coordinated fashion. In the proposed framework, multiple BSs adjust their tilt angles jointly to maximize the sum throughput of the scheduled users, denoted as coordinated user-specific tilting. Assuming the availability of location information of the scheduled users at all BSs, accurate analytical expression for user ergodic rate is provided, which enables a decentralized deployment of the proposed framework at each BS. Simulation results show that the proposed coordinated user-specific tilting scheme outperforms the conventional schemes employing a fixed tilt angle at each BS.

Throughput Optimization for MISO Interference Channels via Coordinated User-Specific Tilting

The problem of resolving closely spaced signal sources using an antenna array remains a difficult one, although several estimation methods are available in the literature. When the array correlation matrix is known, the resolution capability of subspace algorithms is infinitely high. However, in the presence of modeling errors the resolution deteriorates, even for a known correlation matrix. In this paper, we analyze the MUSIC method, by way of three different definitions of the resolution. Assuming Gaussian circular random modeling errors, we determine the corresponding expressions of the probability of source resolution versus the model mismatch. A first series of simulations validates the mathematical expression of the three resolution probabilities. A second series of simulations is used to select among them the tightest one to the empirical one. The results are useful, e.g., for determining the necessary antenna calibration accuracy to achieve a target performance.

On the Resolution Probability of MUSIC in Presence of Modeling Errors

High-resolution direction-or-arrival estimation has been an active area of research since late 1970's. The methods find a wide range of applications, including passive listening arrays, radar and sonar, and spatial (or space-time) characterization of wireless communication channels. Conventional beamforming-based techniques for direction estimation are limited by the aperture (or physical size) of the array. In contrast, parametric methods promise an unlimited resolution in theory. These methods take advantage of a precise mathematical model of the received array data, for example due to incoming plane waves. In practice, the resolution and estimation accuracy is limited by noise as well as errors in the assumed data model. The focus of this chapter is on modeling errors, and in particular calibration techniques to mitigate such errors. Perhaps the most natural and common approach is to measure the response of the array in an anechoic chamber. These calibration measurements are then used to update the data model, either in the form of explicit unknown parameters or in a non-parametric way. Under favorable conditions it is also possible to estimate the response model together with the unknown directions, so-called auto-calibration. The purpose of this chapter is to give an overview of existing techniques and discuss their respective pros and cons. We will also elaborate on how the methods can be extended to more general situations, for example including frequency and polarization dependence. It should be mentioned that practical calibration also involves hardware adjustments, to compensate for temperature drift etc. The methods considered here can be classified as software calibration, where errors are handled by adjusting the assumed data model rather than correcting for it.

Calibration in Array Processing

In this paper, we study the impact of in-phase and quadrature imbalance (IQI) on single-cell multiuser multiple-input multiple-output systems with large antenna arrays. Moreover, we consider a time-division duplex system, where we assume uplink/downlink channel reciprocity in the downlink precoding design. First, we investigate the effect of transceiver IQI on the uplink channel estimation by deriving the linear minimum-mean-square-error estimator for the IQ-impaired model and prove that only the receiver IQI at the base station (BS) limits the estimation accuracy. Then, we study the impact of uplink/downlink channel mismatch on the downlink rate caused by different IQI at the BS and user equipments (UEs). We prove that the achievable downlink rate of each UE is limited either by the receiver IQI at the UEs or jointly by the transmit and receive IQI at the BS, when there is mismatch between the uplink and downlink channels.

Mats Viberg

Papers

New approaches for channel prediction based on sinusoidal modeling

Throughput Optimization for MISO Interference Channels via Coordinated User-Specific Tilting

On the Resolution Probability of MUSIC in Presence of Modeling Errors

Calibration in Array Processing

Massive MIMO Systems With IQ Imbalance: Channel Estimation and Sum Rate Limits