Optimal robust precoders for tracking the AoD and AoA of a mm-wave path

Due to high penetration losses at millimeter wave frequencies, channels are usually sparse in the sense that only a few paths carry non-negligible energy. Such channel structure is exploited by most channel estimation procedures which, in general, sound the channel in multiple directions and identify those yielding the largest power. The prior knowledge on the multipath parameters is then carried on to subsequent iterations in order to track the channel. Whether in initial access or tracking mode, the beams for sweeping the angles-of-departure and angles-of-arrival at the transmitter and receiver, respectively, of the multipath usually have a "sector shape", meaning that their gain is large for a small range of angles and low for all other angles. Such beams are heuristic in nature and may not lead the best channel estimation/tracking performance. In this paper, we focus on the tracking phase, and investigate what are the optimal precoders for estimating the parameters of a single path according to the well known Cramer-Rao lower bound. ´ A procedure based on orthogonal matching pursuit (OMP) is proposed for generating such optimal precoders in a hybrid analog-digital architecture. Contrary to previous approaches which relied on approximations of OMP, we show that OMP can be computed exactly, leading to a substantial decrease in the number of required RF chains. To validate the theoretical results, the maximum likelihood estimator (MLE) and quasioptimal estimators of the channel parameters are derived and their accuracy evaluated.