5,495 research outputs found
Kronecker Product Correlation Model and Limited Feedback Codebook Design in a 3D Channel Model
A 2D antenna array introduces a new level of control and additional degrees
of freedom in multiple-input-multiple-output (MIMO) systems particularly for
the so-called "massive MIMO" systems. To accurately assess the performance
gains of these large arrays, existing azimuth-only channel models have been
extended to handle 3D channels by modeling both the elevation and azimuth
dimensions. In this paper, we study the channel correlation matrix of a generic
ray-based 3D channel model, and our analysis and simulation results demonstrate
that the 3D correlation matrix can be well approximated by a Kronecker
production of azimuth and elevation correlations. This finding lays the
theoretical support for the usage of a product codebook for reduced complexity
feedback from the receiver to the transmitter. We also present the design of a
product codebook based on Grassmannian line packing.Comment: 6 pages, 5 figures, to appear at IEEE ICC 201
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
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
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
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