Gridless Parameter Estimation in Partly Calibrated Rectangular Arrays

Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. The widely used subspace-based methods provide super-resolution parameter estimation at a low computational cost. However, they require an accurate array calibration, which is difficult for large antenna arrays. Sparsity-based methods have been shown to be more robust than subspace-based methods in difficult scenarios, e.g., in the case with a small number of snapshots and/or correlated sources. In this paper, we consider the direction-of-arrival (DOA) estimation in partly calibrated rectangular arrays comprising several calibrated and identical subarrays. We derive a gridless sparse formulation for DOA estimation based on the shift-invariance properties of the array and develop an efficient algorithm in the alternating direction method of multipliers (ADMM) framework. Numerical simulations show the superior error performance of our proposed method compared to subspace-based methods.