2-D DOA estimation of incoherently distributed sources considering gain-phase perturbations in massive MIMO systems

In massive multiple-input multiple-output (MIMO) systems, accurate direction-of-arrival (DOA) estimation is important for the base station (BS) to perform effective downlink beamforming. So far, there have been few reports on DOA estimation considering gain-phase perturbations in massive MIMO systems. However, gain-phase perturbations indeed exist in practical applications and cannot be ignored. In this paper, an efficient method for two-dimensional (2-D) DOA estimation of incoherently distributed (ID) sources considering array gain-phase perturbations is proposed for massive MIMO systems. Firstly, a shift invariance structure is established in the subspace framework, and a constrained optimization problem is formulated to estimate the nominal azimuth and elevation DOAs as well as gain-phase perturbations with closed-form expressions, under the assumption that some of the BS antennas are well calibrated; secondly, the corresponding angular spreads are obtained with the aid of the estimated gain-phase perturbations. Theoretical analysis and an approximate Cramér-Rao bound are also provided. An improved estimation performance is achieved by the proposed method as demonstrated by numerical simulations.