Spatial Spectrum Estimation of Incoherently Distributed Sources Based on Low-Rank Matrix Recovery

Abstract

This article considers the problem of two-dimensional (2-D) angle estimation of incoherently distributed (ID) sources in massive MIMO systems. We first show that the matrix representing the 2-D spatial spectrum of ID sources is of low-rank rather than sparse. Then, by exploiting the low-rank property, we formulate a rank minimization problem to estimate the spatial spectrum, which is solved by an efficient iterative re-weighted procedure. Finally, the key parameters of the spatial spectrum are obtained via an off-grid estimator. The performance analysis of the proposed method, and the Cramer-Rao bound (CRB) of the key parameters with unknown angular distributions are also presented. Contrary to the existing methods which presume a specific type of angular distribution, the proposed method is suitable for general angular distribution as long as it is of low-rank. Moreover, the proposed method is computationally more efficient than the conventional methods that require a multi-dimensional search. Extensive simulations are provided to verify the performance of the proposed method.