# Fundamental limits and joint design of wireless systems with vector antennas

Abstract (Summary)

KRISHNAMURTHY, SANDEEP H. Fundamental Limits and Joint Design of Wireless
Systems with Vector Antennas. (Under the direction of Prof. Brian L. Hughes.)
Multiple-antenna systems have generated tremendous research interest in the recent
past mainly because of their promise of significant gains in capacity and performance
as compared to single-antenna systems. Most work on multiple antennas
has focused on the design of coding and modulation schemes, channel estimation
algorithms and decoding architectures. Information is sent by the transmitter as
electromagnetic (EM) waves which subsequently undergo multipath fading before
they reach the receiver. The EM properties of the antennas and the nature of the
scattering environment jointly impact the performance of communication algorithms.
However, there are relatively few works in the literature that consider this interrelation
in the design of transmitter-receiver architectures. In this dissertation we study
three such problems: the dependence of capacity on the EM properties of antennas
and the scattering environment, the limits on performance of parameter estimation
algorithms at the receiver and finally, the fundamental limits on the capacity that
volume-limited multiple-antenna systems can achieve.
We first consider the joint design of multi-element antennas and capacity-optimal
signalling for a multiple-input multiple-output (MIMO) wireless channel. We use EM
theory and ray-tracing methods to derive a channel propagation model for antennas
that can detect or excite more than one component of the electric field vector (known
as vector antennas) in a discrete-multipath channel environment. This model provides
insights into the inter-relation between the spatial multiplexing gain and the nature
of the multipath environment for vector antennas. We then generalize this model to
the case of antennas with more general electric-field patterns in a fading environment
with clusters of scatterers. Capacity-optimal signalling and the impact of antenna
electric field patterns on capacity are studied. We focus on joint antenna-signal design
and derive optimality criterion for multi-element antenna systems for maximizing
the ergodic capacity. We show that antennas that have orthogonal and equal norm
electric-field patterns maximize the ergodic capacity. Vector antennas satisfy this
criteria, but a uniform linear array does not.
We next consider the problem of positioning and direction-of-arrival (DOA) estimation
with ultrawideband (UWB) vector antennas. Due to the wideband nature of
the antenna response and directional sensitivity of vector antennas, precise ranging
and DOA estimation of a transmitting source can be jointly performed. We first
derive a frequency-domain CramÃ©r-Rao Bound formula in the asymptotic case of a
large number of observation samples in stationary noise. We apply this formula to
two UWB vector antennas and obtain closed-form lower-bound expressions for the
ranging and DOA error covariances. A criterion based on the linearized confidence
region is used to design signal pulses that give uniform resolving capability to the
antennas for any DOA.
Finally, we consider the fundamental capacity limits that a multi-element antenna
system that is restricted to occupy a finite volume can achieve. For simplicity, we
consider the problem of a spherical volume current source radiating into space with a
receiver in the far-field capable of detecting the electric field on a concentric spherical
surface. The system is first described as a linear operator, and the exact singular
values of the system are derived in closed form. The singular values and hence the
capacity is shown to depend on the transmitter volume only through its radius. We
calculate the capacity of such a system, and provide capacity formulas that are accurate
at high signal-to-noise ratio.
Fundamental Limits and Joint Design of Wireless Systems with Vector
Antennas
by
Sandeep H. Krishnamurthy
A dissertation submitted to the Graduate Faculty of
North Carolina State University
in partial fulfillment of the
requirements for the Degree of
Doctor of Philosophy
Electrical Engineering
Raleigh, NC
2005
Bibliographical Information:

Advisor:

School:North Carolina State University

School Location:USA - North Carolina

Source Type:Master's Thesis

Keywords:north carolina state university

ISBN:

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