# Optimal Precoders for Tracking the AoD and AoA of a mm-Wave Path

## TL;DR

This paper derives optimal precoders for mm-Wave channels that minimize estimation error of AoD and AoA, outperforming traditional heuristic methods by at least a factor of two.

## Contribution

It introduces a convex optimization approach to design precoders that minimize the CRB for AoD/AoA estimation in mm-Wave channels, providing a systematic method for improved accuracy.

## Key findings

- Optimal precoders halve the CRB compared to traditional methods.
- There exists an optimal number of precoders beyond which no further improvement occurs.
- The approach assumes a fully digital architecture and single-path spatial filtering.

## Abstract

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 sub-optimal AoD/AoA estimation. We derive optimal precoders, minimizing the Cram\'{e}r-Rao bound (CRB) of the AoD/AoA, 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.