arXiv subjects

Michael Baur

Publications and source records attributed to Michael Baur.

18 recordsLinked to original sources

arXiv2025

Precoder Design in Multi-User FDD Systems with VQ-VAE and GNN

Robust precoding is efficiently feasible in frequency division duplex (FDD) systems by incorporating the learnt statistics of the propagation environment through a generative model. We build on previous work that successfully designed site-specific precoders based on a combination of Gaussian mixture models (GMMs) and graph neural networks (GNNs). In this paper, by utilizing a vector quantized-variational autoencoder (VQ-VAE), we circumvent one of the key drawbacks of GMMs, i.e., the number of GMM components scales exponentially to the feedback bits. In addition, the deep learning architecture of the VQ-VAE allows us to jointly train the GNN together with VQ-VAE along with pilot optimization forming an end-to-end (E2E) model, resulting in considerable performance gains in sum rate for multi-user wireless systems. Simulations demonstrate the superiority of the proposed frameworks over the conventional methods involving the sub-discrete Fourier transform (DFT) pilot matrix and iterative precoder algorithms enabling the deployment of systems characterized by fewer pilots or feedback bits.

cs.IT↗

arXiv2025

Sparse Bayesian Generative Modeling for Joint Parameter and Channel Estimation

Leveraging the inherent connection between sensing systems and wireless communications can improve their overall performance and is the core objective of joint communications and sensing. For effective communications, one has to frequently estimate the channel. Sensing, on the other hand, infers properties of the environment mostly based on estimated physical channel parameters, such as directions of arrival or delays. This work presents a low-complexity generative modeling approach that simultaneously estimates the wireless channel and its physical parameters without additional computational overhead. To this end, we leverage a recently proposed physics-informed generative model for wireless channels based on sparse Bayesian generative modeling and exploit the feature of conditionally Gaussian generative models to approximate the conditional mean estimator.

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arXiv2024

Addressing Pilot Contamination in Channel Estimation with Variational Autoencoders

Pilot contamination (PC) is a well-known problem that affects massive multiple-input multiple-output (MIMO) systems. When frequency and pilots are reused between different cells, PC constitutes one of the main bottlenecks of the system's performance. In this paper, we propose a method based on the variational autoencoder (VAE), capable of reducing the impact of PC-related interference during channel estimation (CE). We obtain the first and second-order statistics of the conditionally Gaussian (CG) channels for both the user equipments (UEs) in a cell of interest and those in interfering cells, and we then use these moments to compute conditional linear minimum mean square error estimates. We show that the proposed estimator is capable of exploiting the interferers' additional statistical knowledge, outperforming other classical approaches. Moreover, we highlight how the achievable performance is tied to the chosen setup, making the setup selection crucial in the study of multi-cell CE.

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arXiv2024

Feedback Design with VQ-VAE for Robust Precoding in Multi-User FDD Systems

In this letter, we propose a vector quantized-variational autoencoder (VQ-VAE)-based feedback scheme for robust precoder design in multi-user frequency division duplex (FDD) systems. We demonstrate how the VQ-VAE can be tailored to specific propagation environments, focusing on systems with low pilot overhead, which is crucial in massive multiple-input multiple-output (MIMO). Extensive simulations with real-world measurement data show that our proposed feedback scheme outperforms state-of-the-art autoencoder (AE)-based compression schemes and conventional Discrete Fourier transform (DFT) codebook-based schemes. These improvements enable the deployment of systems with fewer feedback bits or pilots.

cs.IT↗

arXiv2024

Evaluation Metrics and Methods for Generative Models in the Wireless PHY Layer

Generative models are typically evaluated by direct inspection of their generated samples, e.g., by visual inspection in the case of images. Further evaluation metrics like the Fr\'echet inception distance or maximum mean discrepancy are intricate to interpret and lack physical motivation. These observations make evaluating generative models in the wireless PHY layer non-trivial. This work establishes a framework consisting of evaluation metrics and methods for generative models applied to the wireless PHY layer. The proposed metrics and methods are motivated by wireless applications, facilitating interpretation and understandability for the wireless community. In particular, we propose a spectral efficiency analysis for validating the generated channel norms and a codebook fingerprinting method to validate the generated channel directions. Moreover, we propose an application cross-check to evaluate the generative model's samples for training machine learning-based models in relevant downstream tasks. Our analysis is based on real-world measurement data and includes the Gaussian mixture model, variational autoencoder, diffusion model, and generative adversarial network as generative models. Our results under a fair comparison in terms of model architecture indicate that solely relying on metrics like the maximum mean discrepancy produces insufficient evaluation outcomes. In contrast, the proposed metrics and methods exhibit consistent and explainable behavior.

cs.IT↗

arXiv2024

A Statistical Characterization of Wireless Channels Conditioned on Side Information

Statistical prior channel knowledge, such as the wide-sense-stationary-uncorrelated-scattering (WSSUS) property, and additional side information both can be used to enhance physical layer applications in wireless communication. Generally, the wireless channel's strongly fluctuating path phases and WSSUS property characterize the channel by a zero mean and Toeplitz-structured covariance matrices in different domains. In this work, we derive a framework to comprehensively categorize side information based on whether it preserves or abandons these statistical features conditioned on the given side information. To accomplish this, we combine insights from a generic channel model with the representation of wireless channels as probabilistic graphs. Additionally, we exemplify several applications, ranging from channel modeling to estimation and clustering, which demonstrate how the proposed framework can practically enhance physical layer methods utilizing machine learning (ML).

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arXiv2024

Diffusion-based Generative Prior for Low-Complexity MIMO Channel Estimation

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.

eess.SP↗

arXiv2024

On the Asymptotic Mean Square Error Optimality of Diffusion Models

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

cs.LG↗

arXiv2023

Variational Autoencoder for Channel Estimation: Real-World Measurement Insights

This work utilizes a variational autoencoder for channel estimation and evaluates it on real-world measurements. The estimator is trained solely on noisy channel observations and parameterizes an approximation to the mean squared error-optimal estimator by learning observation-dependent conditional first and second moments. The proposed estimator significantly outperforms related state-of-the-art estimators on real-world measurements. We investigate the effect of pre-training with synthetic data and find that the proposed estimator exhibits comparable results to the related estimators if trained on synthetic data and evaluated on the measurement data. Furthermore, pre-training on synthetic data also helps to reduce the required measurement training dataset size.

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arXiv2023

Gohberg-Semencul Estimation of Toeplitz Structured Covariance Matrices and Their Inverses

When only few data samples are accessible, utilizing structural prior knowledge is essential for estimating covariance matrices and their inverses. One prominent example is knowing the covariance matrix to be Toeplitz structured, which occurs when dealing with wide sense stationary (WSS) processes. This work introduces a novel class of positive definiteness ensuring likelihood-based estimators for Toeplitz structured covariance matrices (CMs) and their inverses. In order to accomplish this, we derive positive definiteness enforcing constraint sets for the Gohberg-Semencul (GS) parameterization of inverse symmetric Toeplitz matrices. Motivated by the relationship between the GS parameterization and autoregressive (AR) processes, we propose hyperparameter tuning techniques, which enable our estimators to combine advantages from state-of-the-art likelihood and non-parametric estimators. Moreover, we present a computationally cheap closed-form estimator, which is derived by maximizing an approximate likelihood. Due to the ensured positive definiteness, our estimators perform well for both the estimation of the CM and the inverse covariance matrix (ICM). Extensive simulation results validate the proposed estimators' efficacy for several standard Toeplitz structured CMs commonly employed in a wide range of applications.

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arXiv2023

Channel Estimation in Underdetermined Systems Utilizing Variational Autoencoders

In this work, we propose to utilize a variational autoencoder (VAE) for channel estimation (CE) in underdetermined (UD) systems. The basis of the method forms a recently proposed concept in which a VAE is trained on channel state information (CSI) data and used to parameterize an approximation to the mean squared error (MSE)-optimal estimator. The contributions in this work extend the existing framework from fully-determined (FD) to UD systems, which are of high practical relevance. Particularly noteworthy is the extension of the estimator variant, which does not require perfect CSI during its offline training phase. This is a significant advantage compared to most other deep learning (DL)-based CE methods, where perfect CSI during the training phase is a crucial prerequisite. Numerical simulations for hybrid and wideband systems demonstrate the excellent performance of the proposed methods compared to related estimators.

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arXiv2023

Semirings of Evidence

In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models evidence by a semiring. Hence justification terms can be interpreted as polynomial functions on that semiring. This provides an adequate semantics for evidence terms and clarifies the role of variables in justification logic. Moreover, the algebraic structure makes it possible to compute with evidence. Depending on the chosen semiring this can be used to model trust, probabilities, cost, etc. Last but not least the semiring approach seems promising for obtaining a realization procedure for modal fixed point logics.

math.LO↗

arXiv2023

Leveraging Variational Autoencoders for Parameterized MMSE Estimation

In this manuscript, we propose to use a variational autoencoder-based framework for parameterizing a conditional linear minimum mean squared error estimator. The variational autoencoder models the underlying unknown data distribution as conditionally Gaussian, yielding the conditional first and second moments of the estimand, given a noisy observation. The derived estimator is shown to approximate the minimum mean squared error estimator by utilizing the variational autoencoder as a generative prior for the estimation problem. We propose three estimator variants that differ in their access to ground-truth data during the training and estimation phases. The proposed estimator variant trained solely on noisy observations is particularly noteworthy as it does not require access to ground-truth data during training or estimation. We conduct a rigorous analysis by bounding the difference between the proposed and the minimum mean squared error estimator, connecting the training objective and the resulting estimation performance. Furthermore, the resulting bound reveals that the proposed estimator entails a bias-variance tradeoff, which is well-known in the estimation literature. As an example application, we portray channel estimation, allowing for a structured covariance matrix parameterization and low-complexity implementation. Nevertheless, the proposed framework is not limited to channel estimation but can be applied to a broad class of estimation problems. Extensive numerical simulations first validate the theoretical analysis of the proposed variational autoencoder-based estimators and then demonstrate excellent estimation performance compared to related classical and machine learning-based state-of-the-art estimators.

eess.SP↗

arXiv2022

Unsupervised Parameter Estimation using Model-based Decoder

In this work, we consider the use of a model-based decoder in combination with an unsupervised learning strategy for direction-of-arrival (DoA) estimation. Relying only on unlabeled training data we show in our analysis that we can outperform existing unsupervised machine learning methods and classical methods. The proposed approach consists of introducing a model-based decoder in an autoencoder architecture which leads to a meaningful representation of the statistical model in the latent space of the autoencoder. Our numerical simulations show that the performance of the presented approach is not affected by correlated signals and performs well for both, uncorrelated and correlated, scenarios. This is a result of the fact, that, in the proposed framework, the signal covariance matrix and the DOAs are estimated simultaneously.

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arXiv2022

Variational Inference Aided Estimation of Time Varying Channels

One way to improve the estimation of time varying channels is to incorporate knowledge of previous observations. In this context, Dynamical VAEs (DVAEs) build a promising deep learning (DL) framework which is well suited to learn the distribution of time series data. We introduce a new DVAE architecture, called k-MemoryMarkovVAE (k-MMVAE), whose sparsity can be controlled by an additional memory parameter. Following the approach in [1] we derive a k-MMVAE aided channel estimator which takes temporal correlations of successive observations into account. The results are evaluated on simulated channels by QuaDRiGa and show that the k-MMVAE aided channel estimator clearly outperforms other machine learning (ML) aided estimators which are either memoryless or naively extended to time varying channels without major adaptions.

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arXiv2022

Model Order Selection with Variational Autoencoding

Classical methods for model order selection often fail in scenarios with low SNR or few snapshots. Deep learning-based methods are promising alternatives for such challenging situations as they compensate lack of information in the available observations with training on large datasets. This manuscript proposes an approach that uses a variational autoencoder (VAE) for model order selection. The idea is to learn a parameterized conditional covariance matrix at the VAE decoder that approximates the true signal covariance matrix. The method is unsupervised and only requires a small representative dataset for calibration after training the VAE. Numerical simulations show that the proposed method outperforms classical methods and even reaches or beats a supervised approach depending on the considered snapshots.

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arXiv2022

Variational Autoencoder Leveraged MMSE Channel Estimation

We propose to utilize a variational autoencoder (VAE) for data-driven channel estimation. The underlying true and unknown channel distribution is modeled by the VAE as a conditional Gaussian distribution in a novel way, parameterized by the respective first and second order conditional moments. As a result, it can be observed that the linear minimum mean square error (LMMSE) estimator in its variant conditioned on the latent sample of the VAE approximates an optimal MSE estimator. Furthermore, we argue how a VAE-based channel estimator can approximate the MMSE channel estimator. We propose three variants of VAE estimators that differ in the data used during training and estimation. First, we show that given perfectly known channel state information at the input of the VAE during estimation, which is impractical, we obtain an estimator that can serve as a benchmark result for an estimation scenario. We then propose practically feasible approaches, where perfectly known channel state information is only necessary in the training phase or is not needed at all. Simulation results on 3GPP and QuaDRiGa channel data attest a small performance loss of the practical approaches and the superiority of our VAE approaches in comparison to other related channel estimation methods.

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arXiv2021

CSI Clustering with Variational Autoencoding

The model order of a wireless channel plays an important role for a variety of applications in communications engineering, e.g., it represents the number of resolvable incident wavefronts with non-negligible power incident from a transmitter to a receiver. Areas such as direction of arrival estimation leverage the model order to analyze the multipath components of channel state information. In this work, we propose to use a variational autoencoder to group unlabeled channel state information with respect to the model order in the variational autoencoder latent space in an unsupervised manner. We validate our approach with simulated 3GPP channel data. Our results suggest that, in order to learn an appropriate clustering, it is crucial to use a more flexible likelihood model for the variational autoencoder decoder than it is usually the case in standard applications.

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