Direction finding in partly calibrated uniform linear arrays with unknown gains and phases

Recently, we considered the problem of direction finding with partly calibrated uniform linear arrays (ULAs) with unknown gains and phases and proposed an ESPRIT-like method for direction-of-arrival (DOA) estimation. It was shown that the DOAs, together with unknown sensor gains and phases in the uncalibrated portion of the array, can be estimated in closed form. However, the identifiability of DOA estimation has not yet been addressed. Moreover, though the proposed method performs better than existing ones, it uses the overlapping subarrays only. Thus it is possible to further improve the performance if the whole array aperture is employed. To fill this gap, two main issues are addressed in this paper. First, the ESPRIT-like algorithm is reinvestigated and conditions ensuring the uniqueness of DOA estimates and identifiability are derived. Second, by exploiting the subspace principle, a refining scheme is proposed that is able to improve the performance of the ESPRIT-like algorithm. Numerical examples are carried out to demonstrate the identifiability issue and performance of the refinement.