Learning the MMSE Channel Estimator

By David Neumann, Thomas Wiese, Wolfgang Utschick. IEEE Transactions on Signal Processing, 2017

310 citations recorded by the source corpus.

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 minimum mean squared error (MMSE) channel estimator can be reduced to <inline-formula><tex-math notation="LaTeX">${\mathcal O}(M\log M)$ </tex-math></inline-formula> floating point operations, where <inline-formula><tex-math notation="LaTeX">$M$</tex-math> </inline-formula> 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.

Subfields: Computational Mechanics, Computer Networks and Communications, Signal Processing

View Paper: https://www.semanticscholar.org/paper/d26872921755f175380bdff1e874bd8106e53960

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Citations in the corpus

Machine Learning in the Air (2019, background): “In [27], the authors model the channel as conditionally Gaussian distributed given a set of (hyper)parameters.”
5G-Advanced Toward 6G: Past, Present, and Future (2023, methodology): “• AI/ML for MIMO channel estimation: A convolutional neural network (CNN) is adopted in [28] to learn the parameters of the minimum mean square error (MMSE) channel estimator.”
Massive MIMO Systems for 5G and beyond Networks—Overview, Recent Trends, Challenges, and Future Research Direction (2020, methodology): “Several experiments have been conducted recently to explore machine learning and deep learning for massive MIMO channel estimation, user scheduling, beamforming, and signal detection [90,149–167].”
Massive MIMO is a Reality - What is Next? Five Promising Research Directions for Antenna Arrays (2019, methodology): “Some recent examples include MIMO detection [141], blind channel equalization [142], channel estimation [143] and feedback [144], Massive MIMO power control [145], [146], user positioning [90], as well as full learning of transceiver implementations [147].”
Wireless Networks Design in the Era of Deep Learning: Model-Based, AI-Based, or Both? (2019, methodology): “In [175] it is shown that a deep neural network can reliably learn the MMSE channel estimator, while in [176] convolutional neural networks are successfully used to implement a fingerprinting-based scheme for user localization.”
A Very Brief Introduction to Machine Learning With Applications to Communication Systems (2018, background): “A similar approach – also based on the idea of directly maximizing the criterion of interest so as to obtain an approximate solution at the output of a neural network – was considered in [74] for minimum mean squared error channel estimation with non-Gaussian channels, e.”