# A Frame-Theoretic Scheme for Robust Millimeter Wave Channel Estimation

## TL;DR

This paper introduces a novel frame-theoretic approach for robust mmWave channel estimation, optimizing sensing dictionaries to enhance sparse reconstruction accuracy and providing new insights into MIMO channel estimation trade-offs.

## Contribution

It presents a new sparse formulation combined with frame theory for improved mmWave channel estimation, including an optimized sensing dictionary and a Kronecker decomposition method.

## Key findings

- Significant improvement in estimation accuracy over existing methods
- Enhanced understanding of the trade-off between correlation and variation in MIMO channels
- Effective decomposition of sensing frames into precoding and beamforming vectors

## Abstract

We propose a new scheme for the robust estimation of the millimeter wave (mmWave) channel. Our approach is based on a sparse formulation of the channel estimation problem coupled with a frame theoretic representation of the sensing dictionary. To clarify, under this approach, the combined effect of transmit precoders and receive beamformers is modeled by a single frame, whose design is optimized to improve the accuracy of the sparse reconstruction problem to which the channel estimation problem is ultimately reduced. The optimized sensing dictionary frame is then decomposed via a Kronecker decomposition back into the precoding and beamforming vectors used by the transmitter and receiver. Simulation results illustrate the significant gain in estimation accuracy obtained over state of the art alternatives. As a bonus, the work offers new insights onto the sparse mmWave-multiple-input multiple-output (MIMO) channel estimation problem by casting the trade-off between correlation and variation range in terms of frame coherence and tightness