Channel estimation is a critical task in multiple-input multiple-output (MIMO) digital communications that substantially affects end-to-end system performance. In this work, we introduce a novel approach for channel estimation using deep score-based generative models. A model is trained to estimate the gradient of the logarithm of a distribution and is used to iteratively refine estimates given measurements of a signal. We introduce a framework for training score-based generative models for wireless MIMO channels and performing channel estimation based on posterior sampling at test time. We derive theoretical robustness guarantees for channel estimation with posterior sampling in single-input single-output scenarios, and experimentally verify performance in the MIMO setting. Our results in simulated channels show competitive in-distribution performance, and robust out-of-distribution performance, with gains of up to 5 dB in end-to-end coded communication performance compared to supervised deep learning methods. Simulations on the number of pilots show that high fidelity channel estimation with 25% pilot density is possible for MIMO channel sizes of up to$64 \times 256$. Complexity analysis reveals that model size can efficiently trade performance for estimation latency, and that the proposed approach is competitive with compressed sensing in terms of floating-point operation (FLOP) count.

Channel estimation is a critical task in digital communications that greatly impacts end-to-end system performance. In this work, we introduce a novel approach for multiple-input multiple-output (MIMO) channel estimation using score-based generative models. Our method uses a deep neural network that is trained to estimate the gradient of the log-prior of wireless channels at any point in high-dimensional space, and leverages this model to solve channel estimation via posterior sampling. We train a score-based model on channel realizations from the CDL-D model for two antenna spacings and show that the approach leads to competitive in- and out-of-distribution performance when compared to generative adversarial network (GAN) and compressed sensing (CS) methods. When tested on CDL-D channels, the approach leads to a gain of at least 5 dB in channel estimation error compared to GAN methods in-distribution at λ/2 antenna spacing. When tested on CDL-C channels which are never seen during training or fine-tuned on, the approach leads to end-to-end coded performance gains of up to 3 dB compared to CS methods and losses of only 0.5 dB compared to ideal channel knowledge.

Deep learning has been recently applied to physical layer processing in digital communication systems in order to improve end-to-end performance. In this work, we introduce a novel deep learning solution for soft bit quantization across wideband channels. Our method is trained end-to-end with quantization-and entropy-aware augmentations to the loss function and is used at inference in conjunction with source coding to achieve near-optimal compression gains over wideband channels. We prove and verify that a proper weight initialization scheme leads to a reduced feature variance, which allows us to use a fixed latent feature quantization scheme. When tested on channel distributions never seen during training, the proposed method achieves a compression gain of up to 10% in the high SNR regime versus previous state-of-the-art methods.

The CSGM framework (Bora-Jalal-Price-Dimakis'17) has shown that deepgenerative priors can be powerful tools for solving inverse problems.However, to date this framework has been empirically successful only oncertain datasets (for example, human faces and MNIST digits), and itis known to perform poorly on out-of-distribution samples. In thispaper, we present the first successful application of the CSGMframework on clinical MRI data. We train a generative prior on brainscans from the fastMRI dataset, and show that posterior sampling viaLangevin dynamics achieves high quality reconstructions. Furthermore,our experiments and theory show that posterior sampling is robust tochanges in the ground-truth distribution and measurement process.Our code and models are available at: \url{https://github.com/utcsilab/csgm-mri-langevin}.

We propose a relax-and-round approach combined with a greedy search strategy for performing complex lattice basis reduction. Taking an optimization perspective, we introduce a relaxed version of the problem that, while still nonconvex, has an easily identifiable family of solutions. We construct a subset of such solutions by performing a greedy search and applying a projection operator (element-wise rounding) to enforce the original constraint. We show that, for lattice basis reduction, such a family of solutions to the relaxed problem is the set of unitary matrices multiplied by a real, positive constant and propose a search strategy based on modifying the complex eigenvalues. We apply our algorithm to lattice-reduction aided multipleinput multiple-output (MIMO) detection and show a considerable performance gain compared to state of the art algorithms. We perform a complexity analysis to show that the proposed algorithm has polynomial complexity.