Blind phase-offset estimation in sparse partly calibrated arrays

Spatial frequency estimation from a superposition of impinging waveforms in the presence of noise is important in many applications. While subspace-based methods offer high-resolution parameter estimation at a low computational cost, they heavily rely on precise array calibration with a synchronized clock, posing challenges for large distributed antenna arrays. In this study, we focus on direction-of-arrival (DoA) estimation within sparse partly calibrated rectangular arrays. These arrays consist of multiple perfectly calibrated sub arrays with unknown phase-offsets among them. We present a gridless sparse formulation for DoA estimation leveraging the multiple shift-invariance properties in the partly calibrated array. Additionally, an efficient blind calibration technique is proposed based on semidefinite relaxation to estimate the intersubarray phase-offsets accurately.