# A Block Sparsity Based Estimator for mmWave Massive MIMO Channels with Beam Squint

## TL;DR

This paper introduces a novel block sparsity-based channel estimator for mmWave massive MIMO systems that accounts for beam squint effects, improving channel estimation accuracy by exploiting angle-delay sparsity and reciprocity.

## Contribution

It proposes a new compressive sensing algorithm that models beam squint effects with block sparsity, enabling more accurate off-grid angle and delay estimation in mmWave MIMO channels.

## Key findings

- Enhanced channel estimation accuracy over traditional methods.
- Effective joint off-grid angle and delay estimation.
- Applicability to both uplink and downlink in FDD systems.

## Abstract

Multiple-input multiple-output (MIMO) millimeter wave (mmWave) communication is a key technology for next generation wireless networks. One of the consequences of utilizing a large number of antennas with an increased bandwidth is that array steering vectors vary among different subcarriers. Due to this effect, known as beam squint, the conventional channel model is no longer applicable for mmWave massive MIMO systems. In this paper, we study channel estimation under the resulting non-standard model. To that aim, we first analyze the beam squint effect from an array signal processing perspective, resulting in a model which sheds light on the angle-delay sparsity of mmWave transmission. We next design a compressive sensing based channel estimation algorithm which utilizes the shift-invariant block-sparsity of this channel model. The proposed algorithm jointly computes the off-grid angles, the off-grid delays, and the complex gains of the multi-path channel. We show that the newly proposed scheme reflects the mmWave channel more accurately and results in improved performance compared to traditional approaches. We then demonstrate how this approach can be applied to recover both the uplink as well as the downlink channel in frequency division duplex (FDD) systems, by exploiting the angle-delay reciprocity of mmWave channels.