Direction-of-Arrival Estimation in Subarrays-Based Linear Sparse Arrays with Gain/Phase Uncertainties

Sparse arrays are of great interest in practical applications owing to their enlarged array apertures, which enable us to achieve better performance in direction finding. A kind of linear sparse arrays (LSpAs) composed of multiple uniform linear subarrays (ULSAs) with gain/phase uncertainties is considered. The problem of direction-of-arrival (DOA) estimation using such kinds of arrays is addressed. In particular two different cases are studied. In the first case all ULSAs are well calibrated, whereas there are unknown gains/phases among them. Using a new ESPRIT-like method, we show that the DOAs can be estimated in closed form. Interestingly, it is found that the unknown gains/phases can also be estimated in closed form by taking advantage of the subspace principle. In the second case we consider a more general situation where some of the ULSAs themselves are suffering from unknown sensor gain/phase responses. Again, we exploit the ESPRIT algorithm and propose a new approach to DOA and gain/phase estimation using this class of arrays. In our proposed methods the unknown parameters (i.e., DOAs and gains/phases) are estimated in closed form without performing spectral search. Representative numerical results are demonstrated to assess the effectiveness of the methods.