Benedikt Fesl

B. Fesl, N. Turan, M. Koller et al.

A low-complexity convolutional neural network estimator which learns the minimum mean squared error channel estimator for single-antenna users was recently proposed. We generalize the architecture to the estimation of MIMO channels with multiple-antenna users and incorporate complexity-reducing assumptions based on the channel model. Learning is used in this context to combat the mismatch between the assumptions and real scenarios where the assumptions may not hold. We derive a high-level description of the estimator for arbitrary choices of the pilot sequence. It turns out that the proposed estimator has the implicit structure of a two-layered convolutional neural network, where the derived quantities can be relaxed to learnable parameters. We show that by using discrete Fourier transform based pilots the number of learnable network parameters decreases significantly and the online run time of the estimator is reduced considerably, where we can achieve linearithmic order of complexity in the number of antennas. Numerical results demonstrate performance gains compared to state-of-the-art algorithms from the field of compressive sensing or covariance estimation of the same or even higher computational complexity. The simulation code is available online.

Benedikt Fesl, Michael Baur, Florian Strasser et al.

This work proposes a novel channel estimator based on diffusion models (DMs), one of the currently top-rated generative models. Contrary to related works utilizing generative priors, a lightweight convolutional neural network (CNN) with positional embedding of the signal-to-noise ratio (SNR) information is designed by learning the channel distribution in the sparse angular domain. Combined with an estimation strategy that avoids stochastic resampling and truncates reverse diffusion steps that account for lower SNR than the given pilot observation, the resulting DM estimator has both low complexity and memory overhead. Numerical results exhibit better performance than state-of-the-art channel estimators utilizing generative priors.

Benedikt Fesl, Benedikt Böck, Florian Strasser et al.

Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy inspired by the structure of the MSE-optimal conditional mean estimator (CME). The resulting DM-based denoiser can be conveniently employed using a pre-trained DM, being particularly fast by truncating reverse diffusion steps and not requiring stochastic re-sampling. We present a comprehensive (non-)asymptotic optimality analysis of the proposed diffusion-based denoiser, demonstrating polynomial-time convergence to the CME under mild conditions. Our analysis also derives a novel Lipschitz constant that depends solely on the DM's hyperparameters. Further, we offer a new perspective on DMs, showing that they inherently combine an asymptotically optimal denoiser with a powerful generator, modifiable by switching re-sampling in the reverse process on or off. The theoretical findings are thoroughly validated with experiments based on various benchmark datasets

Benedikt Fesl, Aziz Banna, Wolfgang Utschick

Channel estimation in quantized systems is challenging, particularly in low-resolution systems. In this work, we propose to leverage a Gaussian mixture model (GMM) as generative prior, capturing the channel distribution of the propagation environment, to enhance a classical estimation technique based on the expectation-maximization (EM) algorithm for one-bit quantization. Thereby, a maximum a posteriori (MAP) estimate of the most responsible mixture component is inferred for a quantized received signal, which is subsequently utilized in the EM algorithm as side information. Numerical results demonstrate the significant performance improvement of our proposed approach over both a simplistic Gaussian prior and current state-of-the-art channel estimators. Furthermore, the proposed estimation framework exhibits adaptability to higher resolution systems and alternative generative priors.