Joint Angle Estimation and Signal Reconstruction for Coherently Distributed Sources in Massive MIMO Systems Based on 2-D Unitary ESPRIT

We consider the challenging problem of joint angle estimation and signal reconstruction for coherently distributed (CD) sources in massive multiple-input-multiple-output (MIMO) systems employing uniform rectangular arrays. A simplified method inspired by the two-dimensional (2-D) unitary estimating signal parameters via rotational invariance technique (ESPRIT) is proposed to estimate both the central angle and the angular spread without the need for a spectrum peak search and covariance matrix matching process. We first approximate the 2-D generalized steering vector expressed as a Schur-Hadamard product by a pair of one-dimensional generalized steering vectors. Then, we obtain two approximate rotational invariance relationships with respect to the central angles of the CD sources using a linear approximation of the individual generalized steering vectors of the azimuth and elevation subarrays. With the aid of this approximate decomposition, a new unitary ESPRIT-inspired algorithm is conceived to automatically pair the 2-D central angle estimations and a novel method capable of bypassing the high-complexity search process is proposed for angular spread estimation. Furthermore, the closed-form approximate Cramer-Rao lower bounds are derived for the estimators of both the central angles and the angular spreads. The complexity of the proposed estimator is also analyzed. Additionally, the orthogonality of the generalized steering vectors is proved, which enables us to propose a low-complexity method to reconstruct the CD signal matrix by replacing the inversion operator with the conjugate transpose operator. The simulation results demonstrate the efficiency of our proposed approach.