Optimal Precoders for Tracking the AoD and AoA of a mmWave Path
Journal article, 2018

In millimeter-wave channels, most of the received energy is carried by a few paths. Traditional precoders sweep the angle-of-departure (AoD) and angle-of-arrival (AoA) space with directional precoders to identify directions with largest power. Such precoders are heuristic and lead to suboptimal AoD/AoA estimation. We derive optimal precoders, minimizing the Cramér–Rao bound (CRB) of the AoD/AoA under a given uncertainty range, assuming a fully digital architecture at the transmitter and spatial filtering of a single path. The precoders are found by solving a suitable convex optimization problem. We demonstrate that the accuracy can be improved by at least a factor of two over traditional precoders, and show that there is an optimal number of distinct precoders beyond which the CRB does not improve.

antenna arrays

array signal processing




Millimeter wave communication


Radar tracking


Signal to noise ratio

Channel estimation

Cramér–Rao bounds

antenna radiation patterns



Nil Garcia

Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks

Henk Wymeersch

Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks

Dirk Slock


IEEE Transactions on Signal Processing

1053-587X (ISSN) 1941-0476 (eISSN)

Vol. 66 21 5718-5729 8466652

COPPLAR CampusShuttle cooperative perception & planning platform

VINNOVA (2015-04849), 2016-01-01 -- 2018-12-31.

High precision positioning for cooperative ITS applications

European Commission (EC) (EC/H2020/636537), 2015-01-01 -- 2017-12-31.

Fifth Generation Communication Automotive Research and innovation (5GCAR)

European Commission (EC) (EC/H2020/761510), 2017-06-01 -- 2019-05-31.

Areas of Advance

Information and Communication Technology

Subject Categories

Signal Processing



More information

Latest update

4/5/2022 6