# Super-Resolution Channel Estimation for Arbitrary Arrays in Hybrid Millimeter-Wave Massive MIMO Systems

## TL;DR

This paper introduces a super-resolution channel estimation method for hybrid millimeter-wave massive MIMO systems with arbitrary array geometries, using a generalized array manifold separation and efficient algorithms to improve accuracy and speed.

## Contribution

It proposes a novel angle-based super-resolution channel estimation technique that handles arbitrary array geometries and hybrid hardware constraints in mmWave MIMO systems.

## Key findings

- Effective super-resolution angle estimation in arbitrary array geometries.
- Significant reduction in sensing time for channel acquisition.
- Improved accuracy demonstrated through simulations.

## Abstract

This paper develops efficient channel estimation techniques for millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems under practical hardware limitations, including an arbitrary array geometry and a hybrid hardware structure. Taking on an angle-based approach, this work adopts a generalized array manifold separation approach via Jacobi-Anger approximation, which transforms a non-ideal, non-uniform array manifold into a virtual array domain with a desired uniform geometric structure to facilitate super-resolution angle estimation and channel acquisition. Accordingly, structure-based optimization techniques are developed to effectively estimate both the channel covariance and the instantaneous channel state information (CSI) within a short sensing time. In particular, the difference in time-variation of channel path angles and path gains is capitalized to design a two-step CSI estimation scheme that can quickly sense fading channels. Theoretical results are provided on the fundamental limits of the proposed technique in terms of sample efficiency. For computational efficiency, a fast iterative algorithm is developed via the alternating direction method of multipliers. Other related issues such as spurious-peak cancellation in nonuniform linear arrays and extensions to higher-dimensional cases are also discussed. Simulations testify the effectiveness of the proposed approaches in hybrid mmWave massive MIMO systems with arbitrary arrays.