# Fundamental Limits and Joint Design of Wireless Systems with Vector Antennas

Abstract (Summary)

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 Cramer-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.
Bibliographical Information:

Advisor:Gianluca Lazzi; Hamid Krim; Moody Chu; Brian L. Hughes

School:North Carolina State University

School Location:USA - North Carolina

Source Type:Master's Thesis

Keywords:electrical engineering

ISBN:

Date of Publication:08/31/2005