# Deep CNN-Based Channel Estimation for mmWave Massive MIMO Systems

## TL;DR

This paper introduces deep CNN architectures that leverage spatial, frequency, and temporal correlations to enhance channel estimation in mmWave massive MIMO systems, reducing complexity and pilot overhead while maintaining high accuracy.

## Contribution

It proposes novel CNN-based methods, including SF-CNN, SFT-CNN, and SPR-CNN, for improved channel estimation exploiting multiple types of channel correlations.

## Key findings

- Outperform non-ideal MMSE estimator in accuracy
- Achieve near-ideal MMSE performance with reduced complexity
- Reduce pilot overhead by about one third using SPR-CNN

## Abstract

For millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, hybrid processing architecture is usually used to reduce the complexity and cost, which poses a very challenging issue in channel estimation. In this paper, deep convolutional neural network (CNN) is employed to address this problem. We first propose a spatial-frequency CNN (SF-CNN) based channel estimation exploiting both the spatial and frequency correlation, where the corrupted channel matrices at adjacent subcarriers are input into the CNN simultaneously. Then, exploiting the temporal correlation in time-varying channels, a spatial-frequency-temporal CNN (SFT-CNN) based approach is developed to further improve the accuracy. Moreover, we design a spatial pilot-reduced CNN (SPR-CNN) to save spatial pilot overhead for channel estimation, where channels in several successive coherence intervals are grouped and estimated by a channel estimation unit with memory. Numerical results show that the proposed SF-CNN and SFT-CNN based approaches outperform the non-ideal minimum mean-squared error (MMSE) estimator but with reduced complexity, and achieve the performance close to the ideal MMSE estimator that is very difficult to be implemented in practical situations. They are also robust to different propagation scenarios. The SPR-CNN based approach achieves comparable performance to SF-CNN and SFT-CNN based approaches while only requires about one third of spatial pilot overhead at the cost of complexity. Our work clearly shows that deep CNN can efficiently exploit channel correlation to improve the estimation performance for mmWave massive MIMO systems.