# Massive MIMO Channel Estimation with an Untrained Deep Neural Network

## TL;DR

This paper introduces a novel untrained deep neural network-based channel estimator for massive MIMO systems that approaches MMSE performance without training, complex inversions, or covariance knowledge, and effectively mitigates pilot contamination.

## Contribution

It presents an untrained deep neural network approach for massive MIMO channel estimation that achieves near-MMSE performance and robustness to pilot contamination without requiring training.

## Key findings

- Approaches MMSE performance with 64 antennas and subcarriers.
- Does not require training or channel covariance knowledge.
- Effectively eliminates pilot contamination under certain conditions.

## Abstract

This paper proposes a deep learning-based channel estimation method for multi-cell interference-limited massive MIMO systems, in which base stations equipped with a large number of antennas serve multiple single-antenna users. The proposed estimator employs a specially designed deep neural network (DNN) to first denoise the received signal, followed by a conventional least-squares (LS) estimation. We analytically prove that our LS-type deep channel estimator can approach minimum mean square error (MMSE) estimator performance for high-dimensional signals, while avoiding MMSE's requirement for complex channel inversions and knowledge of the channel covariance matrix. This analytical result, while asymptotic, is observed in simulations to be operational for just 64 antennas and 64 subcarriers per OFDM symbol. The proposed method also does not require any training and utilizes several orders of magnitude fewer parameters than conventional DNNs. The proposed deep channel estimator is also robust to pilot contamination and can even completely eliminate it under certain conditions.