This thesis explores advanced array signal processing techniques for both fully and partially calibrated arrays. We introduce novel sparse array geometries based on sparse linear subarrays and develop new direction-of-arrival (DOA) estimation algorithms for narrowband electromagnetic signals, framed within statistical signal processing principles. The proposed algorithms, named Generalized Coarray MUSIC (GCA-MUSIC) and Generalized Coarray Root MUSIC (GCA-rMUSIC), extend the classical Multiple Signal Classification (MUSIC) framework to sparse subarrays configurations. Sparse linear subarray design techniques were proposed, as well as an analysis of the degrees of freedom of subarrays (sDoF) as a function of degrees of freedom of the whole array (DoF). Additionally, we develop Variable Window Size (VWS) versions of these algorithms, which incorporate flexible spatial smoothing apertures. These methods provide high-accuracy DoA estimates and offer the key advantage of resolving more sources than the number of physical sensors in each subarray by exploiting coarray structures. Performance analysis demonstrates that GCA-MUSIC and GCA-rMUSIC, along with its VWS variants, improve accuracy in the context of partially-calibrated arrays, where calibration uncertainties may exist. Furthermore, VWS variants of the Coarray MUSIC (CA-MUSIC) algorithm are presented for fully calibrated (coherent) arrays, enabling adaptable smoothing strategies for enhanced performance. In addition to algorithmic development, we compute the Fisher Information Matrices (FIMs) for the complete set of parameters in this generalized data model, including both self and cross-coupled parameter relationships. These matrices account for source directions, source powers, noise power, and the real and imaginary components of all calibration parameters, representing both correlated and uncorrelated source scenarios. This work significantly advances the theoretical understanding of DoA estimation performance limits by providing a more rigorous quantification of the Cramér-Rao bounds. These bounds are particularly relevant in scenarios with partially calibrated arrays and uncorrelated sources, as demonstrated using the Khatri-Rao product-based data model.