Optimization of Massive Full-Dimensional MIMO for Positioning and Communication

Massive Full-Dimensional multiple-input multiple-output (FD-MIMO) base stations (BSs) have the potential to bring multiplexing and coverage gains by means of three-dimensional (3D) beamforming. Key technical challenges for their deployment include the presence of limited-resolution front ends and the acquisition of channel state information (CSI) at the BSs. This paper investigates the use of FD-MIMO BSs to provide simultaneously high-rate data communication and mobile 3D positioning in the downlink. The analysis concentrates on the problem of beamforming design by accounting for imperfect CSI acquisition via Time Division Duplex (TDD)-based training and for the finite resolution of analog-to-digital converter (ADC) and digital-to-analog converter (DAC) at the BSs. Both \textit{unstructured beamforming} and a low-complexity \textit{Kronecker beamforming} solution are considered, where for the latter the beamforming vectors are decomposed into separate azimuth and elevation components. The proposed algorithmic solutions are based on Bussgang theorem, rank-relaxation and successive convex approximation (SCA) methods. Comprehensive numerical results demonstrate that the proposed schemes can effectively cater to both data communication and positioning services, providing only minor performance degradations as compared to the more conventional cases in which either function is implemented. Moreover, the proposed low-complexity Kronecker beamforming solutions are seen to guarantee a limited performance loss in the presence of a large number of BS antennas.Comment: 30 pages, 6 figure

Kronecker Sum Decompositions of Space-Time Data

In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a smooth tradeoff between the reduction in the number of parameters (to reduce estimation variance) and the accuracy of the covariance approximation (affecting estimation bias), we introduce a diagonally loaded modification of the sum of kronecker products representation [1]. We derive a Cramer-Rao bound (CRB) on the minimum attainable mean squared predictor coefficient estimation error for unbiased estimators of Kronecker structured covariance matrices. We illustrate the accuracy of the diagonally loaded Kronecker sum decomposition by applying it to video data of human activity.Comment: 5 pages, 8 figures, accepted to CAMSAP 201

A three domain covariance framework for EEG/MEG data

In this paper we introduce a covariance framework for the analysis of EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. We perform a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. Apart from that, we illustrate our method on real EEG and MEG data sets. The proposed covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed for accurate dipole localization, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, such as in combined EEG/fMRI experiments in which the correlation between EEG and fMRI signals is investigated.Comment: 25 pages, 8 figures, 1 tabl

Modeling of wide-band MIMO radio channels based on NLoS indoor measurements

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Hybrid Beamforming via the Kronecker Decomposition for the Millimeter-Wave Massive MIMO Systems

Despite its promising performance gain, the realization of mmWave massive MIMO still faces several practical challenges. In particular, implementing massive MIMO in the digital domain requires hundreds of RF chains matching the number of antennas. Furthermore, designing these components to operate at the mmWave frequencies is challenging and costly. These motivated the recent development of hybrid-beamforming where MIMO processing is divided for separate implementation in the analog and digital domains, called the analog and digital beamforming, respectively. Analog beamforming using a phase array introduces uni-modulus constraints on the beamforming coefficients, rendering the conventional MIMO techniques unsuitable and call for new designs. In this paper, we present a systematic design framework for hybrid beamforming for multi-cell multiuser massive MIMO systems over mmWave channels characterized by sparse propagation paths. The framework relies on the decomposition of analog beamforming vectors and path observation vectors into Kronecker products of factors being uni-modulus vectors. Exploiting properties of Kronecker mixed products, different factors of the analog beamformer are designed for either nulling interference paths or coherently combining data paths. Furthermore, a channel estimation scheme is designed for enabling the proposed hybrid beamforming. The scheme estimates the AoA of data and interference paths by analog beam scanning and data-path gains by analog beam steering. The performance of the channel estimation scheme is analyzed. In particular, the AoA spectrum resulting from beam scanning, which displays the magnitude distribution of paths over the AoA range, is derived in closed-form. It is shown that the inter-cell interference level diminishes inversely with the array size, the square root of pilot sequence length and the spatial separation between paths.Comment: Submitted to IEEE JSAC Special Issue on Millimeter Wave Communications for Future Mobile Networks, minor revisio

Why Does a Kronecker Model Result in Misleading Capacity Estimates?

Many recent works that study the performance of multi-input multi-output (MIMO) systems in practice assume a Kronecker model where the variances of the channel entries, upon decomposition on to the transmit and the receive eigen-bases, admit a separable form. Measurement campaigns, however, show that the Kronecker model results in poor estimates for capacity. Motivated by these observations, a channel model that does not impose a separable structure has been recently proposed and shown to fit the capacity of measured channels better. In this work, we show that this recently proposed modeling framework can be viewed as a natural consequence of channel decomposition on to its canonical coordinates, the transmit and/or the receive eigen-bases. Using tools from random matrix theory, we then establish the theoretical basis behind the Kronecker mismatch at the low- and the high-SNR extremes: 1) Sparsity of the dominant statistical degrees of freedom (DoF) in the true channel at the low-SNR extreme, and 2) Non-regularity of the sparsity structure (disparities in the distribution of the DoF across the rows and the columns) at the high-SNR extreme.Comment: 39 pages, 5 figures, under review with IEEE Trans. Inform. Theor