Robust techniques in array signal processing

Array signal processing, which collects and combines signals from an array, can obtain high spatial discrimination and an adaptive response that a single sensor can not achieve. Various array processing techniques were developed to enhance signal-to-noise ratio or to estimate the temporal or spatial characteristics of the observed signal in harsh environments. In practical array systems, however, some of the assumptions on the environment, sources, or array can be wrong or imprecise. Such environmental imperfections and array uncertainties will cause a mismatch between the nominal and actual data vector, which leads to a degraded performance. The impaired effects are especially fatal for adaptive beamformers. In this thesis, we analyzed the degraded performance of the data-independent and adaptive arrays using a perturbation model. Some analytical expressions of the performance measures, e.g., the expected beam pattern and the expected SINR (signal-to-noise-plus-interference-ratio) using the proposed perturbation model are derived and discussed. This is helpful in understanding how the perturbations affect the performance of arrays qualitatively and quantitatively. Several robust methods which combat the calibration errors in the two types of arrays are proposed in this thesis. For data-independent arrays, two methods based on the MSE (mean square error) criterion are presented. The first robust method minimizes the MSE between the perturbed and ideal responses, and it can be considered as the most insensitive array in the perturbed situation. The second robust method has a pre-defined set of quiescent weights and the robustness is obtained by minimizing the MSE between the perturbed and quiescent responses. The numerical results show that the robust II method can offer higher resolution and lower sidelobes performances when the perturbation is not very large, while the robust I method can offer a more stable performance in perturbed situations.DOCTOR OF PHILOSOPHY (EEE