Direction-of-arrival estimation performance of sparse linear arrays

Direction-of-arrival (DOA) estimation involves estimating the angle of arrival of a plane wave or multiple plane waves observed by an array of sensors. This problem arises in many fields such as radar, sonar, wireless communications, seismology, electronic surveillance, spectroscopy, and radio astronomy. Large arrays with many sensors provide accurate DOA estimates but may be very costly due to receiver hardware and computational complexity. Sparse arrays have fewer elements for the same size aperture as compared to fully populated arrays. They provide similar performance in terms of angular accuracy, resolution, and detection of targets close to interference directions with reduced size, weight, power consumption, and cost. However, they are subject to significant ambiguities due to high sidelobes in the array beampattern, which give rise to large estimation errors.;Lower bounds on mean square estimation error (MSE) that are independent of any particular estimation technique are useful as benchmarks against which the performance of a particular estimation scheme may be compared, and for performing system tradeoff studies, such as choosing the best geometrical configuration of the sparse array elements. Bounds such as the Cramer-Rao bound (CRB) and Weiss-Weinstein bound (WWB) have been used previously to study the performance of sparse arrays, however the CRB does not characterize ambiguity error and the WWB requires complicated numerical computations. In this dissertation, the degradation in MSE performance due to the sidelobe ambiguities is quantified using the Ziv-Zakai bound (ZZB). Like the WWB, the ZZB is a Bayesian bound that usually requires a numerical implementation.;The first contribution of this dissertation is the derivation of an explicit closed-form expression for the ZZB for sparse linear arrays (SLAs) with high sidelobes. The expression consists of three terms which correspond to the three types of estimation errors: small mainlobe errors, errors due to sidelobe ambiguities, and random errors. The significance of this result is that the closed form expression is much easier to compute than the numerically evaluated ZZB and WWB, but more importantly, it provides great insight into the physical processes that are contributing to the estimation performance. The derived bound is a function of system parameters such as the number of snapshots, the signal-to-noise ratio (SNR), the array geometry, the location and heights of the beampattern sidelobes, and the a priori parameter distribution, and it determines which sidelobes are significant as a function of the number of snapshots and SNR.;The second contribution of this dissertation is a comprehensive simulation study of various SLA configurations using maximum likelihood (ML) estimation. Simulation results verify that the bound closely characterizes the performance that can be achieved for different array configurations. Furthermore, the simulations confirm the contribution of the different types of estimation error predicted by the bound and show that much of the performance degradation attributed to ambiguities are in fact random errors that cannot be controlled by array design. Additional degradation due to sidelobe ambiguities is exhibited by some arrays, but other SLAs have very little performance loss due to their sidelobe structure. Isolating the contributions of the three types of errors provides greater understanding of the behavior of sparse arrays, allowing for more effective system design and analysis.