# Spatial Channel Covariance Estimation for Hybrid Architectures Based on Tensor Decompositions

## TL;DR

This paper introduces a tensor decomposition-based method for estimating spatial channel covariance in hybrid architectures, improving accuracy especially at low SNR levels by leveraging low-rank tensor representations.

## Contribution

It proposes a novel tensor decomposition approach for covariance estimation in hybrid MIMO systems, outperforming existing compressive sensing and angle-of-arrival methods.

## Key findings

- Achieves higher estimation accuracy than prior methods.
- Performs better at low SNR conditions.
- Provides theoretical bounds on estimation accuracy.

## Abstract

Spatial channel covariance information can replace full instantaneous channel state information for the analog precoder design in hybrid analog/digital architectures. Obtaining spatial channel covariance estimation, however, is challenging in the hybrid structure due to the use of fewer radio frequency (RF) chains than the number of antennas. In this paper, we propose a spatial channel covariance estimation method based on higher-order tensor decomposition for spatially sparse time-varying frequency-selective channels. The proposed method leverages the fact that the channel can be represented as a low-rank higher-order tensor. We also derive the Cram\'er-Rao lower bound on the estimation accuracy of the proposed method. Numerical results and theoretical analysis show that the proposed tensor-based approach achieves higher estimation accuracy in comparison with prior compressive-sensing-based approaches or conventional angle-of-arrival estimation approaches. Simulation results reveal that the proposed approach becomes more beneficial at low signal-to-noise (SNR) region.