In this paper, the problem of joint time-of-arrival and two-dimensional direction-of-arrival (TOA/2D-DOA) estimation is solved using space-frequency nested array (SFNA) motion. SFNA is developed by incorporating the linear nested array structure and the frequency offset set generated by nested sampling, aiming to save on physical costs and computational resources. Additionally, a SFNA-based vertical movement strategy is proposed, which transforms the TOA/2D-DOA joint estimation into TOA/1D angle joint estimation and the other 1D angle estimation, significantly alleviating the enormous computational burden brought by 3D parameters joint estimation. Meanwhile, this strategy further reduces the number of sensors required, as it only needs a linear array to achieve 2D-DOA estimation. Based on the cross-covariance matrix of the novel signal model, the sparse iterative covariance-based estimation (SPICE) algorithm is applied to the TOA/1D angle joint estimation. However, the SPICE algorithm necessitates grid search, and its estimation accuracy degrades when the parameter values are not on the grids. Therefore, an improved SPICE (ISPICE) algorithm is proposed for off-grid TOA/1D angle joint estimation. Simultaneously, Euclidean distance-based grid estimation algorithm (EDGE) is developed to achieve accurate estimation of the other 1D angle. Multiple simulations are conducted to verify the effectiveness of the proposed strategy and algorithms.

Sparse arrays are widely employed in array signal processing due to their obvious advantages in array element distribution and uniform degrees of freedom (uDOFs). In this paper, a generalized augmented multi-subarray nested array (GAMSNA-I) and its variant, GAMSNA-II are proposed, with the objective of increasing uDOFs and reducing mutual coupling. Based on two subarrays of the prototype nested array (NA), GAMSNA-I is constructed by reconfiguring the dense uniform linear array (ULA) and forward-shifting the sparse ULA. GAMSNA-II is obtained by sparsifying the dense part of GAMSNA-I, ensuring constant uDOFs while further reducing mutual coupling. Subsequently, the closed-form expression for the uDOFs of GAMSNA-I with an arbitrary number of sensors is derived, and the proof is provided that the uDOFs of GAMSNA-II remain unchanged relative to that of GAMSNA-I. Compared to some existing array configurations, both GAMSNA-I and GAMSNA-II exhibit improved uDOFs, with GAMSNA-II achieving lower mutual coupling. Simulation results show the superior performance of the proposed GAMSNA-I and GAMSNA-II.