Applications of Continuous Spatial Models in Multiple Antenna Signal Processing

Abstract

This thesis covers the investigation and application of continuous spatial models for multiple antenna signal processing. The use of antenna arrays for advanced sensing and communications systems has been facilitated by the rapid increase in the capabilities of digital signal processing systems. The wireless communications channel will vary across space as different signal paths from the same source combine and interfere. This creates a level of spatial diversity that can be exploited to improve the robustness and overall capacity of the wireless channel. Conventional approaches to using spatial diversity have centered on smart, adaptive antennas and spatial beam forming. Recently, the more general theory of multiple input, multiple output (MIMO) systems has been developed to utilise the independent spatial communication modes offered in a scattering environment. Underlying any multiple antenna system is the basic physics of electromagnetic wave propagation. Whilst a MIMO system may present a set of discrete inputs and outputs, each antenna element must interact with the underlying continuous spatial field. Since an electromagnetic disturbance will propagate through space, the field at different positions in the space will be interrelated. In this way, each position in the field cannot assume an arbitrary independent value and the nature of wave propagation places a constraint on the allowable complexity of a wave-field over space. To take advantage of this underlying physical constraint, it is necessary to have a model that incorporates the continuous nature of the spatial wave-field. This thesis investigates continuous spatial models for the wave-field. The wave equation constraint is introduced by considering a natural basis expansion for the space of physically valid wave-fields. This approach demonstrates that a wave-field over a finite spatial region has an effective finite dimensionality. The optimal basis for representing such a field is dependent on the shape of the region of interest and the angular power distribution of the incident field. By applying the continuous spatial model to the problem of direction of arrival estimation, it is shown that the spatial region occupied by the receiver places a fundamental limit on the number and accuracy with which sources can be resolved. Continuous spatial models also provide a parsimonious representation for modelling the spatial communications channel independent of specific antenna array configurations. The continuous spatial model is also applied to consider limits to the problem of wireless source direction and range localisation.