83 research outputs found
Eigenvalue Dynamics of a Central Wishart Matrix with Application to MIMO Systems
We investigate the dynamic behavior of the stationary random process defined
by a central complex Wishart (CW) matrix as it varies along a
certain dimension . We characterize the second-order joint cdf of the
largest eigenvalue, and the second-order joint cdf of the smallest eigenvalue
of this matrix. We show that both cdfs can be expressed in exact closed-form in
terms of a finite number of well-known special functions in the context of
communication theory. As a direct application, we investigate the dynamic
behavior of the parallel channels associated with multiple-input
multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the
complex random matrix that defines the MIMO channel, we characterize the
second-order joint cdf of the signal-to-noise ratio (SNR) for the best and
worst channels. We use these results to study the rate of change of MIMO
parallel channels, using different performance metrics. For a given value of
the MIMO channel correlation coefficient, we observe how the SNR associated
with the best parallel channel changes slower than the SNR of the worst
channel. This different dynamic behavior is much more appreciable when the
number of transmit () and receive () antennas is similar. However, as
is increased while keeping fixed, we see how the best and worst
channels tend to have a similar rate of change.Comment: 15 pages, 9 figures and 1 table. This work has been accepted for
publication at IEEE Trans. Inf. Theory. Copyright (c) 2014 IEEE. Personal use
of this material is permitted. However, permission to use this material for
any other purposes must be obtained from the IEEE by sending a request to
[email protected]
Limited Feedback Design for Interference Alignment on MIMO Interference Networks with Heterogeneous Path Loss and Spatial Correlations
Interference alignment is degree of freedom optimal in K -user MIMO
interference channels and many previous works have studied the transceiver
designs. However, these works predominantly focus on networks with perfect
channel state information at the transmitters and symmetrical interference
topology. In this paper, we consider a limited feedback system with
heterogeneous path loss and spatial correlations, and investigate how the
dynamics of the interference topology can be exploited to improve the feedback
efficiency. We propose a novel spatial codebook design, and perform dynamic
quantization via bit allocations to adapt to the asymmetry of the interference
topology. We bound the system throughput under the proposed dynamic scheme in
terms of the transmit SNR, feedback bits and the interference topology
parameters. It is shown that when the number of feedback bits scales with SNR
as C_{s}\cdot\log\textrm{SNR}, the sum degrees of freedom of the network are
preserved. Moreover, the value of scaling coefficient C_{s} can be
significantly reduced in networks with asymmetric interference topology.Comment: 30 pages, 6 figures, accepted by IEEE transactions on signal
processing in Feb. 201
Finite Random Matrix Theory Analysis of Multiple Antenna Communication Systems
Multiple-antenna systems are capable of providing substantial improvement to wireless communication networks, in terms of
data rate and reliability. Without utilizing extra spectrum or power resources, multiple-antenna technology has already been supported
in several wireless communication standards, such as LTE, WiFi and WiMax. The surging popularity and enormous prospect of
multiple-antenna technology require a better understanding to its fundamental performance over practical environments.
Motivated by this, this thesis provides analytical characterizations of several seminal performance measures in advanced multiple-antenna
systems. The analytical derivations are mainly based on finite dimension random matrix theory and a collection of novel random matrix theory
results are derived.
The closed-form probability density function of the output of multiple-input multiple-output (MIMO) block-fading channels is studied.
In contrast to the existing results, the proposed expressions are very general, applying for arbitrary number of antennas, arbitrary signal-to-noise
ratio and multiple classical fading models. Results are presented assuming two input structures in the system: the independent identical distributed
(i.i.d.) Gaussian input and a product form input. When the channel is fed by the i.i.d. Gaussian input, analysis is focused on the channel matrices
whose Gramian is unitarily invariant. When the channel is fed by a product form input, analysis is conducted with respect to two capacity-achieving
input structures that are dependent upon the relationship between the coherence length and the number of antennas. The mutual information
of the systems can be computed numerically from the pdf expression of the output. The computation is relatively easy to handle, avoiding the
need of the straight Monte-Carlo computation which is not feasible in large-dimensional networks.
The analytical characterization of the output pdf of a single-user MIMO block-fading channels with imperfect channel state information at the receiver
is provided. The analysis is carried out under the assumption of a product structure for the input. The model can be thought of as a perturbation
of the case where the statistics of the channel are perfectly known. Specifically, the average singular values of the channel are given, while the
channel singular vectors are assumed to be isotropically distributed on the unitary groups of dimensions given by the number of transmit and
receive antennas. The channel estimate is affected by a Gaussian distributed error, which is modeled as a matrix with i.i.d. Gaussian entries of
known covariance.
The ergodic capacity of an amplify-and-forward (AF) MIMO relay network over asymmetric channels is investigated. In particular, the source-relay
and relay-destination channels undergo Rayleigh and Rician fading, respectively. Considering arbitrary-rank means for the relay-destination channel,
the marginal distribution of an unordered eigenvalue of the cascaded AF channel is presented, thus the analytical expression of the ergodic capacity
of the system is obtained. The results indicate the impact of the signal-to-noise ratio and of the Line-of-Sight component on such asymmetric
relay network
Estimating the rank of the spectral density matrix
The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. This note shows how to estimate the rank of the spectral density matrix at any given frequency. The method presented is valid for any hermitian positive de?nite matrix estimate that has a normal asymptotic distribution with a covariance matrix whose rank is known. JEL Classification: C12, C32, C52Spectral Density Matrix, Tests of Rank
Signal Processing in Large Systems: a New Paradigm
For a long time, detection and parameter estimation methods for signal
processing have relied on asymptotic statistics as the number of
observations of a population grows large comparatively to the population size
, i.e. . Modern technological and societal advances now
demand the study of sometimes extremely large populations and simultaneously
require fast signal processing due to accelerated system dynamics. This results
in not-so-large practical ratios , sometimes even smaller than one. A
disruptive change in classical signal processing methods has therefore been
initiated in the past ten years, mostly spurred by the field of large
dimensional random matrix theory. The early works in random matrix theory for
signal processing applications are however scarce and highly technical. This
tutorial provides an accessible methodological introduction to the modern tools
of random matrix theory and to the signal processing methods derived from them,
with an emphasis on simple illustrative examples
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