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We propose decoupling networks for the reconfigurable intelligent surface (RIS) array as a solution to benefit from the mutual coupling between the reflecting elements. In particular, we show that when incorporating these networks, the system model reduces to the same structure as if no mutual coupling is present. Hence, all algorithms and theoretical discussions neglecting mutual coupling can be directly applied when mutual coupling is present by utilizing our proposed decoupling networks. For example, by including decoupling networks, the channel gain maximization in RIS-aided single-input single-output (SISO) systems does not require an iterative algorithm but is given in closed form as opposed to using no decoupling network. In addition, this closed-form solution allows to analytically analyze scenarios under mutual coupling resulting in novel connections to the conventional transmit array gain. In particular, we show that super-quadratic (up to quartic) channel gains w.r.t. the number of RIS elements are possible and, therefore, the system with mutual coupling performs significantly better than the conventional uncoupled system in which only squared gains are possible. We consider diagonal as well as beyond diagonal (BD)-RISs and give various analytical and numerical results, including the inevitable losses at the RIS array. In addition, simulation results validate the superior performance of decoupling networks w.r.t. the channel gain compared to other state-of-the-art methods.

This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular, sparse Bayesian learning (SBL), to integrate a strong regularization towards sparse solutions. At the same time, by leveraging the notion of conditional Gaussianity, it also incorporates the adaptability from generative models to training data. However, unlike most state-of-the-art generative models, it is able to learn from a few compressed and noisy data samples and requires no optimization algorithm for solving the inverse problem. Additionally, similar to Dirichlet prior networks, our model parameterizes a conjugate prior enabling its application for uncertainty quantification. We support our approach theoretically through the concept of variational inference and validate it empirically using different types of compressible signals.

In this paper, we solve a classical counting problem for non-degenerate quadratic forms defined on a vector space in odd characteristic; given a subspace $\pi$, we determine the number of non-singular subspaces that are trivially intersecting with $\pi$ and span a non-singular subspace with $\pi$. Lower bounds for the quantity of such pairs where $\pi$ is non-singular were first studied in `Glasby, Niemeyer, Praeger (Finite Fields Appl., 2022)', which was later improved for even-dimensional subspaces in `Glasby, Ihringer, Mattheus (Des. Codes Cryptogr., 2023)' and generalised in `Glasby, Niemeyer, Praeger (Linear Algebra Appl., 2022)'. The explicit formulae, which allow us to give the exact proportion and improve the known lower bounds were derived in the symplectic and Hermitian case in `De Boeck and Van de Voorde (Linear Algebra Appl. 2024)'. This paper deals with the more complicated quadratic case.

In this work, we propose a Gaussian mixture model (GMM)-based pilot design scheme for downlink (DL) channel estimation in single- and multi-user multiple-input multiple-output (MIMO) frequency division duplex (FDD) systems. In an initial offline phase, the GMM captures prior information during training, which is then utilized for pilot design. In the single-user case, the GMM is utilized to construct a codebook of pilot matrices and, once shared with the mobile terminal (MT), can be employed to determine a feedback index at the MT. This index selects a pilot matrix from the constructed codebook, eliminating the need for online pilot optimization. We further establish a sum conditional mutual information (CMI)-based pilot optimization framework for multi-user MIMO (MU-MIMO) systems. Based on the established framework, we utilize the GMM for pilot matrix design in MU-MIMO systems. The analytic representation of the GMM enables the adaptation to any signal-to-noise ratio (SNR) level and pilot configuration without re-training. Additionally, an adaption to any number of MTs is facilitated. Extensive simulations demonstrate the superior performance of the proposed pilot design scheme compared to state-of-the-art approaches. The performance gains can be exploited, e.g., to deploy systems with fewer pilots., Comment: arXiv admin note: substantial text overlap with arXiv:2403.17577

In this paper we investigate the explainability of transformer models and their plausibility for hate speech and counter speech detection. We compare representatives of four different explainability approaches, i.e., gradient-based, perturbation-based, attention-based, and prototype-based approaches, and analyze them quantitatively with an ablation study and qualitatively in a user study. Results show that perturbation-based explainability performs best, followed by gradient-based and attention-based explainability. Prototypebased experiments did not yield useful results. Overall, we observe that explainability strongly supports the users in better understanding the model predictions., Comment: conference, CBMI2024, 6 pages

In this paper, we solve a classical counting problem for non-degenerate forms of symplectic and hermitian type defined on a vector space: given a subspace $\pi$, we find the number of non-singular subspaces that are trivially intersecting with $\pi$ and span a non-singular subspace with $\pi$. Lower bounds for the quantity of such pairs where $\pi$ is non-singular were first studied in ``Glasby, Niemeyer, Praeger (Finite Fields Appl., 2022)'', which was later improved in ``Glasby, Ihringer, Mattheus (Des. Codes Cryptogr., 2023)'' and generalised in ``Glasby, Niemeyer, Praeger (Linear Algebra Appl., 2022)''. In this paper, we derive explicit formulae, which allow us to give the exact proportion and improve the known lower bounds.

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).

Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and Meulenberg. In this paper, we introduce the notion of $q$-analogs of divisible design graphs and show that all $q$-analogs of divisible design graphs come from spreads, and are actually $q$-analogs of strongly regular graphs. Deza graphs were introduced by Erickson, Fernando, Haemers and Hardy in 1999. In this paper, we introduce $q$-analogs of Deza graphs. Further, we determine possible parameters, give examples of $q$-analogs of Deza graphs and characterize all non-strongly regular $q$-analogs of Deza graphs with the smallest parameters., Comment: 17 pages

We study the energy stability of pressure-driven laminar magnetohydrodynamic flow in a rectangular duct with transverse homogeneous magnetic field and electrically insulating walls. For sufficiently strong fields, the laminar velocity distribution has a uniform core and convex Hartmann and Shercliff boundary layers on the walls perpendicular and parallel to the magnetic field. The problem is discretized by a double expansion in Chebyshev polynomials in the cross-stream coordinates. The linear eigenvalue problem for the critical Reynolds number depends on the streamwise wavenumber, Hartmann number and the aspect ratio. We consider the limits of small and large aspect ratios in order to compare with stability models based on one-dimensional base flows. For large aspect ratios we find good numerical agreement with results based on the quasi-two-dimensional approximation. The lift-up mechanism dominates in the limit of zero streamwise wavenumber and provides a linear dependence between the critical Reynolds and Hartmann number in the duct. The duct results for small aspect ratio converge to Orr's original energy stability result for spanwise uniform perturbations imposed on the plane Poiseuille base flow. We also examine different possible symmetries of eigenmodes as well as the purely hydrodynamic case in the duct geometry., Comment: 29 pages, 21 figures

Systematic in vivo validations of computational models of the aortic valve remain scarce, despite successful validation against in vitro data. Utilizing a combination of computed tomography and 4D flow magnetic resonance imaging data, we developed patient-specific fluid-structure interaction models of the aortic valve immersed in the aorta for five patients in the pre-transcatheter aortic valve replacement configuration. Incorporating also an in vitro setup of the valve, our computational models are subjected to rigorous validation against 4D flow measurements. Our results demonstrate the models' capacity to accurately replicate flow dynamics within established ranges of uncertainties mainly arising from 4D flow noise. In addition, we illustrate how computational models can serve as valuable cross-checks to reduce noise and erratic behaviour of in vivo data. This study represents a significant step towards integrating in silico technologies into real clinical contexts, providing a robust framework for improving aortic stenosis diagnosis and the design of next-generation aortic valve bioprostheses.

In this work, we propose to utilize Gaussian mixture models (GMMs) to design pilots for downlink (DL) channel estimation in frequency division duplex (FDD) systems. The GMM captures prior information during training that is leveraged to design a codebook of pilot matrices in an initial offline phase. Once shared with the mobile terminal (MT), the GMM is utilized to determine a feedback index at the MT in the online phase. This index selects a pilot matrix from a codebook, eliminating the need for online pilot optimization. The GMM is further used for DL channel estimation at the MT via observation-dependent linear minimum mean square error (LMMSE) filters, parametrized by the GMM. The analytic representation of the GMM allows adaptation to any signal-to-noise ratio (SNR) level and pilot configuration without re-training. With extensive simulations, we demonstrate the superior performance of the proposed GMM-based pilot scheme compared to state-of-the-art approaches.

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.

The development of superconducting qubit technology has shown great potential for the construction of practical quantum computers. As the complexity of quantum processors continues to grow, the need for stringent fabrication tolerances becomes increasingly critical. Utilizing advanced industrial fabrication processes could facilitate the necessary level of fabrication control to support the continued scaling of quantum processors. However, these industrial processes are currently not optimized to produce high coherence devices, nor are they a priori compatible with the commonly used approaches to make superconducting qubits. In this work, we demonstrate for the first time superconducting transmon qubits manufactured in a 300 mm CMOS pilot line, using industrial fabrication methods, with resulting relaxation and coherence times already exceeding 100 microseconds. We show across-wafer, large-scale statistics studies of coherence, yield, variability, and aging that confirm the validity of our approach. The presented industry-scale fabrication process, using exclusively optical lithography and reactive ion etching, shows performance and yield similar to the conventional laboratory-style techniques utilizing metal lift-off, angled evaporation, and electron-beam writing. Moreover, it offers potential for further upscaling by including three-dimensional integration and additional process optimization using advanced metrology and judicious choice of processing parameters and splits. This result marks the advent of more reliable, large-scale, truly CMOS-compatible fabrication of superconducting quantum computing processors., Comment: main text: 7 pages, 4 figures. bibliography: 55 references. supplement: 8 sections, 8 figures, 2 tables

In this work, we utilize a Gaussian mixture model (GMM) to capture the underlying probability density function (PDF) of the channel trajectories of moving mobile terminals (MTs) within the coverage area of a base station (BS) in an offline phase. We propose to leverage the same GMM for channel prediction in the online phase. Our proposed approach does not require signal-to-noise ratio (SNR)-specific training and allows for parallelization. Numerical simulations for both synthetic and measured channel data demonstrate the effectiveness of our proposed GMM-based channel predictor compared to state-ofthe-art channel prediction methods.

In this paper, we study association schemes on the anisotropic points of classical polar spaces. Our main result concerns non-degenerate elliptic and hyperbolic quadrics in PG$(n,q)$ with $q$ odd. We define relations on the anisotropic points of such a quadric that depend on the type of line spanned by the points and whether or not they are of the same "quadratic type". This yields an imprimitive $5$-class association scheme. We calculate the matrices of eigenvalues and dual eigenvalues of this scheme. We also use this result, together with similar results from the literature concerning other classical polar spaces, to exactly calculate the spectrum of orthogonality graphs on the anisotropic points of non-degenerate quadrics in odd characteristic and of non-degenerate Hermitian varieties. As a byproduct, we obtain a $3$-class association scheme on the anisotropic points of non-degenerate Hermitian varieties, where the relation containing two points depends on the type of line spanned by these points, and whether or not they are orthogonal., Comment: 29 pages. Update: an extra reference was added

This study introduces a method for the characterization of the magnetoelectric coupling in nanoscale Pb(Zr,Ti)O3/CoFeB thin film composites based on propagating spin-wave spectroscopy. Finite element simulations of the strain distribution in the devices indicated that the magnetoelastic effective field in the CoFeB waveguides was maximized in the Damon - Eshbach configuration. All-electrical broadband propagating spin-wave transmission measurements were conducted on Pb(Zr,Ti)O3/CoFeB magnetoelectric waveguides with lateral dimensions down to 700 nm. The results demonstrated that the spin-wave resonance frequency can be modulated by applying a bias voltage to Pb(Zr,Ti)O3. The modulation is hysteretic due to the ferroelastic behavior of Pb(Zr,Ti)O3. An analytical model was then used to correlate the change in resonance frequency to the induced magnetoelastic field in the magnetostrictive CoFeB waveguide. We observe a hysteresis magnetoelastic field strength with values as large as 5.61 mT, and a non-linear magnetoelectric coupling coefficient with a maximum value of 1.69 mT/V., Comment: This project has received funding from the European Union's Horizon Europe research and innovation programme under grant agreement No 101070536 - project MandMEMS

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., Comment: 6 pages, 6 figures, accepted at WSA 2024

Cameron-Liebler sets of generators in polar spaces were introduced a few years ago as natural generalisations of the Cameron-Liebler sets of subspaces in projective spaces. In this article we present the first two constructions of non-trivial Cameron-Liebler sets of generators in polar spaces. Also regular m-ovoids of k-spaces are introduced as a generalization of m-ovoids of polar spaces. They are used in one of the aforementioned constructions of Cameron-Liebler sets.

This work introduces a novel class of channel estimators tailored for coarse quantization systems. The proposed estimators are founded on conditionally Gaussian latent generative models, specifically Gaussian mixture models (GMMs), mixture of factor analyzers (MFAs), and variational autoencoders (VAEs). These models effectively learn the unknown channel distribution inherent in radio propagation scenarios, providing valuable prior information. Conditioning on the latent variable of these generative models yields a locally Gaussian channel distribution, thus enabling the application of the well-known Bussgang decomposition. By exploiting the resulting conditional Bussgang decomposition, we derive parameterized linear minimum mean square error (MMSE) estimators for the considered generative latent variable models. In this context, we explore leveraging model-based structural features to reduce memory and complexity overhead associated with the proposed estimators. Furthermore, we devise necessary training adaptations, enabling direct learning of the generative models from quantized pilot observations without requiring ground-truth channel samples during the training phase. Through extensive simulations, we demonstrate the superiority of our introduced estimators over existing state-of-the-art methods for coarsely quantized systems, as evidenced by significant improvements in mean square error (MSE) and achievable rate metrics.

Since the burgeoning days of IoT, Mirai has been established as the canonical IoT botnet. Not long after the public release of its code, researchers found many Mirai variants compete with one another for many of the same vulnerable hosts. Over time, the myriad Mirai variants evolved to incorporate unique vulnerabilities, defenses, and regional concentrations. In this paper, we ask: have Mirai variants evolved to the point that they are fundamentally distinct? We answer this question by measuring two of the most popular Mirai descendants: Hajime and Mozi. To actively scan both botnets simultaneously, we developed a robust measurement infrastructure, BMS, and ran it for more than eight months. The resulting datasets show that these two popular botnets have diverged in their evolutions from their common ancestor in multiple ways: they have virtually no overlapping IP addresses, they exhibit different behavior to network events such as diurnal rate limiting in China, and more. Collectively, our results show that there is no longer one canonical IoT botnet. We discuss the implications of this finding for researchers and practitioners.

We employ a linear stability analysis and direct numerical simulations to study the characteristics of wall-modes in thermal convection in a rectangular box under strong and inclined magnetic fields. The walls of the convection cell are electrically insulated. The stability analysis assumes periodicity in the spanwise direction perpendicular to the plane of the homogeneous magnetic field. Our study shows that for a fixed vertical magnetic field, the imposition of horizontal magnetic fields results in an increase of the critical Rayleigh number along with a decrease in the wavelength of the wall modes. The wall modes become tilted along the direction of the resulting magnetic fields and therefore extend further into the bulk as the horizontal magnetic field is increased. Once the modes localized on the opposite walls interact, the critical Rayleigh number decreases again and eventually drops below the value for onset with a purely vertical field. We find that for sufficiently strong horizontal magnetic fields, the steady wall modes occupy the entire bulk and therefore convection is no longer restricted to the sidewalls. The above results are confirmed by direct numerical simulations of the nonlinear evolution of magnetoconvection., Comment: 25 pages, 18 figures

A Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this work, we prove several results on the existence of small strictly Neumaier graphs. In particular, we present a theoretical proof of the uniqueness of the smallest strictly Neumaier graph with parameters $(16,9,4;2,4)$, we establish the existence of a strictly Neumaier graph with parameters $(25,12,5;2,5)$, and we disprove the existence of strictly Neumaier graphs with parameters $(25,16,9;3,5)$, $(28,18,11;4,7)$, $(33,24,17;6,9)$, $(35,22,12;3,5)$ and $(55,34,18;3,5)$. Our proofs use combinatorial techniques and a novel application of integer programming methods.

We discuss the effects of nonhomogeneous magnetic fields in liquid metal flows in two different configurations. In the first configuration, we briefly report the impact of fringing magnetic fields in a turbulent Rayleigh-B{\'e}nard convection setup, where it was shown that the global heat transport decreases with an increase of fringe-width. The convective motion in regions of strong magnetic fields is confined near the sidewalls. In the second configuration, we numerically study the effects of an oscillating magnetic obstacle with different frequencies of oscillation on liquid metal flow in a duct. The Reynolds number is low such that the wake of the stationary magnetic obstacle is steady. The transverse oscillation of the magnet creates a sinusoidal time-dependent wake reminiscent of the vortex shedding behind solid obstacles. We examine the behavior of the streamwise and spanwise components of the Lorentz forces as well as the work done by the magnets on the fluid. The frequency of the oscillation of the streamwise component of Lorentz force is twice that of the spanwise component as in the case of lift and drag on solid cylindrical obstacles. The total drag force and the energy transferred from the magnets to the fluid show a non-monotonic dependence on the frequency of oscillation of the magnetic obstacle indicative of a resonant excitation of the sinusoidal vortex shedding., Comment: 6 pages, 5 figures

Current-induced spin-orbit torques (SOTs) enable fast and efficient manipulation of the magnetic state of magnetic tunnel junctions (MTJs), making it attractive for memory, in-memory computing, and logic applications. However, the requirement of the external magnetic field to achieve deterministic switching in perpendicular magnetized SOT-MTJs limits its implementation for practical applications. Here, we introduce a field-free switching (FFS) solution for the SOT-MTJ device by shaping the SOT channel to create a "bend" in the SOT current. The resulting bend in the charge current creates a spatially non-uniform spin current, which translates into inhomogeneous SOT on an adjacent magnetic free layer enabling deterministic switching. We demonstrate FFS experimentally on scaled SOT-MTJs at nanosecond time scales. This proposed scheme is scalable, material-agnostic, and readily compatible with wafer-scale manufacturing, thus creating a pathway for developing purely current-driven SOT systems.

The fabrication of superconducting circuits requires multiple deposition, etch and cleaning steps, each possibly introducing material property changes and microscopic defects. In this work, we specifically investigate the process of argon milling, a potentially coherence limiting step, using niobium and aluminum superconducting resonators as a proxy for surface-limited behavior of qubits. We find that niobium microwave resonators exhibit an order of magnitude decrease in quality-factors after surface argon milling, while aluminum resonators are resilient to the same process. Extensive analysis of the niobium surface shows no change in the suboxide composition due to argon milling, while two-tone spectroscopy measurements reveal an increase in two-level system electrical dipole moments, indicating a structurally altered niobium oxide hosting larger two-level system defects. However, a short dry etch can fully recover the argon milling induced losses on niobium, offering a potential route towards state-of-the-art overlap Josephson junction qubits with niobium circuitry., Comment: Main text: 6 pages, 3 figures, 1 table. 5 appendices, with 6 additional figures and 3 additional tables. 62 references

This work aims to predict channels in wireless communication systems based on noisy observations, utilizing sequence-to-sequence models with attention (Seq2Seq-attn) and transformer models. Both models are adapted from natural language processing to tackle the complex challenge of channel prediction. Additionally, a new technique called reverse positional encoding is introduced in the transformer model to improve the robustness of the model against varying sequence lengths. Similarly, the encoder outputs of the Seq2Seq-attn model are reversed before applying attention. Simulation results demonstrate that the proposed ordering techniques allow the models to better capture the relationships between the channel snapshots within the sequence, irrespective of the sequence length, as opposed to existing methods., Comment: Submitted to IEEE for publication

We consider the problem of remotely tracking the state of and unstable linear time-invariant plant by means of data transmitted through a noisy communication channel from an algorithmic point of view. Assuming the dynamics of the plant are known, does there exist an algorithm that accepts a description of the channel's characteristics as input, and returns 'Yes' if the transmission capabilities permit the remote tracking of the plant's state, 'No' otherwise? Does there exist an algorithm that, in case of a positive answer, computes a suitable encoder/decoder-pair for the channel? Questions of this kind are becoming increasingly important with regards to future communication technologies that aim to solve control engineering tasks in a distributed manner. In particular, they play an essential role in digital twinning, an emerging information processing approach originally considered in the context of Industry 4.0. Yet, the abovementioned questions have been answered in the negative with respect to algorithms that can be implemented on idealized digital hardware, i.e., Turing machines. In this article, we investigate the remote state estimation problem in view of the Blum-Shub-Smale computability framework. In the broadest sense, the latter can be interpreted as a model for idealized analog computation. Especially in the context of neuromorphic computing, analog hardware has experienced a revival in the past view years. Hence, the contribution of this work may serve as a motivation for a theory of neuromorphic twins as a counterpart to digital twins for analog hardware.

We study the influence of fringing magnetic fields on turbulent thermal convection in a horizontally extended rectangular domain. The magnetic field is created in the gap between two semi-infinite planar magnetic poles, with the convection layer located near the edge of the gap. We employ direct numerical simulations in this setup for fixed Rayleigh and small Prandtl numbers, but vary the fringe-width by controlling the gap between the magnetic poles and the convection cell. The magnetic field generated by the magnets is strong enough to cease the flow in high magnetic flux region of the convection cell. We observe that as the local vertical magnetic field strength increases, the large scale structures become thinner and align themselves perpendicular to the longitudinal sidewalls. We determine the local Nusselt and Reynolds numbers as functions of the local Hartmann number (based on the vertical component of the magnetic field) and estimate the global heat and momentum transport. We show that the global heat transport decreases with increasing fringe-width for strong magnetic fields but increases with increasing fringe-width for weak magnetic fields. In the regions of large vertical magnetic fields, the convective motion becomes confined to the vicinity of the sidewalls. The amplitudes of these wall modes show a non-monotonic dependence on the fringe-width., Comment: 29 pages, 18 figures

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.

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., Comment: Accepted for publication at IEEE SPAWC 2023