Matrix Pencil-Based DoA Estimation for Hybrid Receivers in Snapshot-Limited Scenarios

The goal of this paper is to estimate the directions of arrival (DoAs) for hybrid analog/digital (HAD) receivers when the number of snapshots is too small for statistical averaging to be reliable. This goal is achieved in fully-digital receivers by employing the matrix pencil method (MPM). Unfortunately, the MPM cannot be directly applied in HAD receivers because of the entanglement induced by the underlying analog combiners on the output signals. Furthermore, these analog combiners project the received signal onto a low-dimensional space, jeopardizing the reception of signals arriving from particular DoA ranges. To circumvent these difficulties, we propose two approaches to enable the MPM to extract the DoAs in HAD receivers. The two approaches avoid severe attenuation induced by low-dimensional projection by cycling over an exhaustive set of analog combiners, collectively spanning the entire space. The first approach can be applied to both fully-connected (FC) and partially-connected (PC) HADs and relies on the availability of periodic, potentially unknown, signals to disentangle the output of the HAD receiver. The second approach applies to PC-HADs only, and eliminates contingency on periodic signals by exploiting the underlying block diagonal structure. The superiority of the proposed approaches is demonstrated via numerical simulations and comparisons with the Cram\'er-Rao lower bound.