Title page for ETD etd-12062005-083802

Type of Document

Dissertation

Author

Kamath, Ajith Mulki,

Author's Email Address

amkamath@gmail.com

URN

etd-12062005-083802

Title

Asymptotic Analysis of Large Antenna Arrays for Communications and Radar Applications

Degree

PhD

Graduate Program

Electrical Engineering

Advisory Committee

Advisor Name	Title
Brian L.Hughes	Committee Chair
Hamid Krim	Committee Member
Alexandra Duel-Hallen	Committee Member
Jack W. Silverstein	Committee Member

Keywords

diversity multiplexing tradeoff
outage capacity
capacity
polarization
vector antenna
asymptotic
mutual information
Cramer Rao bound
antenna array
tripole array
radar
MIMO

Date of Defense

2005-12-05

Availability

unrestricted

Abstract

In recent years there has been a growing interest in using antenna
arrays at both ends of a wireless communication link. Such multiple
input multiple output (MIMO) systems are beneficial both in terms of
providing greatly improved data rates, as well as in terms of
robustness in combating errors compared to systems which use only
one antenna. These benefits are obtained without requiring extra
transmit power or spectral bandwidth, but come at the cost of
additional processing power. In radar, multiple antenna arrays have
been in use for several decades. Even so, the idea of measuring the
full received electro-magnetic (EM) wave for parameter estimation
has been a recent one. In this dissertation, we address two issues
through asymptotics: in MIMO systems, we develop insights into
finite MIMO array performance by deriving precise results for
asymptotically large MIMO arrays, and in radar we derive the gain
from measuring the complete field over a spherical surface versus
measuring only one polarization component using an equal number of
sensors.

First, we consider the distribution of the mutual information of a
MIMO system with an uncorrelated Rayleigh fading channel. We show
that, as the transmit and receive array sizes tend to infinity while
maintaining their ratio constant, the mutual information
distribution tends to Gaussian distribution at all signal to noise
ratios (SNRs), and give a closed-form expression for its mean and
variance. Through simulations, we observe that the mutual
information distribution of a finite MIMO system with as few as 4
array elements at either end has a variance which depends only on
the ratio of the two arrays and is also closely approximated by the
asymptotic distribution variance. We show that the mean of the
distribution can also be approximated much closer than previously
shown, and hence combined with the asymptotic variance, this yields
close approximations for outage capacities.

We next consider the problem of determining the best possible
tradeoff between diversity and multiplexing gains in an uncorrelated
Rayleigh fading channel. Zheng and Tse have characterized this
tradeoff in the large signal to noise ratio(SNR) limit. We apply our
asymptotic results on mutual information to compute the finite SNR
diversity-multiplexing tradeoffs at high outage probabilities in the
range of practical interest. We show that the asymptotic results
match the tradeoffs derived by Zheng and Tse only in the equal
antenna MIMO array case. We then propose a linear dispersion coding
scheme which modulates a block of data by picking a random unitary
matrix, which was previously shown to produce full-rank
full-diversity code-books with probability one. Through simulations
using rectangular code-books, we show that these may also achieve
the full Zheng-Tse diversity multiplexing tradeoff after using a
maximum likelihood (ML) decoder.

Having developed fundamental insights into MIMO arrays through the
use of asymptotic analysis, we consider the impact of using vector
antennas in large radar arrays. Specifically, we compare the
performance of range and direction-of-arrival (DOA) estimation of a
single source using an array of vector electro-magnetic (EM) sensors
packed densely on the surface of a sphere, with a similarly shaped
array with identically oriented dipole elements. We compute the
Cramer-Rao lower bound on maximum-likelihood range and DOA
estimation using either array. By taking the ratio of the confidence
volumes as the gain, we compare the vector array estimate with the
uni-polarized array as a function of target location.

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