Learning the MMSE Channel Estimator

TL;DR

This paper introduces a machine learning-based approach to estimate MMSE channels in communication systems, leveraging structured covariance matrices for efficiency and neural networks for generalization to unstructured models.

Contribution

It proposes a neural network architecture inspired by structured MMSE estimators to efficiently estimate channels with unstructured covariance matrices, improving computational complexity.

Findings

Efficient O(M log M) complexity for structured covariance matrices.

Neural network learns MMSE estimator within a class of structured estimators.

Good generalization to realistic channel models in simulations.

Abstract

We present a method for estimating conditionally Gaussian random vectors with random covariance matrices, which uses techniques from the field of machine learning. Such models are typical in communication systems, where the covariance matrix of the channel vector depends on random parameters, e.g., angles of propagation paths. If the covariance matrices exhibit certain Toeplitz and shift-invariance structures, the complexity of the MMSE channel estimator can be reduced to O(M log M) floating point operations, where M is the channel dimension. While in the absence of structure the complexity is much higher, we obtain a similarly efficient (but suboptimal) estimator by using the MMSE estimator of the structured model as a blueprint for the architecture of a neural network. This network learns the MMSE estimator for the unstructured model, but only within the given class of estimators that contains the MMSE estimator for the structured model. Numerical simulations with typical spatial channel models demonstrate the generalization properties of the chosen class of estimators to realistic channel models.