Antenna arrays play a central role in a wide variety of important estimation problems. Most existing literatures on array signal processing focus on conventional arrays, where antennas are separated by a relatively large distance so that they are uncoupled. While such arrays usually have good estimation accuracy and are easy to design, they may be too large for platforms with size limitations, such as cellular handsets and wireless sensor nodes. Instead, deploying multiple antennas on such platforms requires placing antennas close together, which can cause interactions among the elements. Such interactions can profoundly impact received power and estimation error. Moreover, estimation performance depends not only on the properties of the array, but also on aspects of the receiver front-end, such as antenna impedance matching, amplifier properties, and the dominant sources of noise. Although many prior works have studied the performance of compact arrays from different perspectives, to the best of our knowledge, no one has yet considered the impact of impedance matching on the performance of estimators using physical models of observation noise. Besides studying the performance of any given arrays, perhaps a more interesting yet challenging question to ask is how the properties of the array itself changes the estimation accuracy, which very few papers have looked into.;In this dissertation, we investigate three aspects of multiple antennas receiver design. Firstly, we consider a general class of Bayesian and non-Bayesian estimation problems, in which the signal of interest is observed through a sensor front-end consisting of coupled antennas, an impedance matching network, amplifiers, and physical noise sources. We derive the Fisher information associated with each problem and prove that one kind of matching network is universally optimal for all estimation problems in the class. Secondly, we consider the general problem of estimating the parameters of an incident Gaussian electromagnetic field using a sensor array that observes the field through the currents in an arbitrary conductor. We characterize the maximum Fisher information that can be achieved with this array and derive conditions under which the upper bound can be attained. Lastly, we study properties of the antenna conductor itself and show how the size and shape of the conductor impact the estimation accuracy. We apply our results to square and spherical conductors to demonstrate how the Fisher information increases with the antenna size. We further study the performance of several widely-studied compact arrays and evaluate their efficiency in observing the information contained in the spaces they occupy.
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