# Channel Estimation in mmWave Hybrid MIMO System via Off-Grid Dirichlet Kernels

## TL;DR

This paper introduces a novel off-grid channel estimation method for mmWave hybrid MIMO systems using Dirichlet kernels, improving accuracy without increasing discretization complexity.

## Contribution

It proposes greedy algorithms leveraging Dirichlet kernel structures in Fourier domain for off-grid parameter estimation in mmWave MIMO systems.

## Key findings

- Proposed algorithms outperform standard OMP in off-grid scenarios.
- Numerical results show reduced reconstruction errors with the new methods.
- The approach effectively handles continuous angular parameters without dense discretization.

## Abstract

In this paper, we tackle channel estimation in millimeter-wave hybrid multiple-input multiple-output systems by considering off-grid effects. In particular, we assume that spatial parameters can take any value in the angular domain, and need not fall on predefined discretized angles. Instead of increasing the number of discretized points to combat off-grid effects, we use implicit Dirichlet kernel structure in the Fourier domain, which conventional compressed sensing methods do not use. We propose greedy low-complexity algorithms based on orthogonal matching pursuit (OMP); our core idea is to traverse the Dirichlet kernel peak using estimates of the discrete Fourier transform. We demonstrate the efficacy of our proposed algorithms compared to standard OMP reconstruction. Numerical results show that our proposed algorithms obtain smaller reconstruction errors when off-grid effects are accounted for.