Robust DOA and Subspace Estimation for Hybrid Channel Sensing

This paper studies the problem of channel subspace estimation for a hybrid millimeter wave communication system, where the observed signal is a low-dimensional projection of the signal received at the antenna array. Due to the Toeplitz structure of the channel covariance matrix, the channel subspace can be estimated either by estimating the entries of the Toeplitz matrix or by an Angle of Arrival estimation approach. Our goal is to compare the performance of two different subspace estimation techniques. We derive the Cramér Rao Bounds for estimating the Toeplitz covariance matrix and Angle of Arrivals considering two different antenna selection schemes, namely uniform subsampling and nested subsampling. Our analysis reveals that nested array based compression can perform robust subspace estimation due to its superior estimation of angles despite exhibiting higher error in covariance estimation. 1