The paper introduces a novel array geometry called "nested arrays," which significantly increases the degrees of freedom (DOF) of linear arrays. By nesting two or more uniform linear arrays, the proposed structure can achieve $O(N^2)$ DOF using only $N$ physical sensors when second-order statistics of the received data are utilized. The concept of nesting is shown to be extendable to multiple stages, and the optimal nesting strategy is analytically derived. The paper also proposes a spatial smoothing-based approach for direction-of-arrival (DOA) estimation, which does not require traditional assumptions like fourth-order cumulants or quasi-stationary signals. Additionally, a new nonlinear preprocessing-based beamforming technique is introduced, which can effectively utilize the increased DOF. Extensive computer simulations verify the effectiveness of the proposed methods.The paper introduces a novel array geometry called "nested arrays," which significantly increases the degrees of freedom (DOF) of linear arrays. By nesting two or more uniform linear arrays, the proposed structure can achieve $O(N^2)$ DOF using only $N$ physical sensors when second-order statistics of the received data are utilized. The concept of nesting is shown to be extendable to multiple stages, and the optimal nesting strategy is analytically derived. The paper also proposes a spatial smoothing-based approach for direction-of-arrival (DOA) estimation, which does not require traditional assumptions like fourth-order cumulants or quasi-stationary signals. Additionally, a new nonlinear preprocessing-based beamforming technique is introduced, which can effectively utilize the increased DOF. Extensive computer simulations verify the effectiveness of the proposed methods.