arXiv subjects

Benedikt Fesl

Publications and source records attributed to Benedikt Fesl.

27 records · Page 2Linked to original sources

arXiv2023

Low-Rank Structured MMSE Channel Estimation with Mixtures of Factor Analyzers

This work proposes a generative modeling-aided channel estimator based on mixtures of factor analyzers (MFA). In an offline step, the parameters of the generative model are inferred via an expectation-maximization (EM) algorithm in order to learn the underlying channel distribution of a whole communication scenario inside a base station (BS) cell. Thereby, the wireless channels are effectively modeled on a piecewise linear subspace which is achieved by the low-rank structure of the learned covariances of the MFA. This suits the low-rank structure of wireless channels at high frequencies and additionally saves parameters and prevents overfitting. Afterwards, the trained MFA model is used online to perform channel estimation with a closed-form solution of the estimator which asymptotically converges to the minimum mean square error (MMSE) estimator. Numerical results based on real-world measurements demonstrate the great potential of the proposed approach for channel estimation.

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arXiv2023

On the Mean Square Error Optimal Estimator in One-Bit Quantized Systems

This paper investigates the mean square error (MSE)-optimal conditional mean estimator (CME) in one-bit quantized systems in the context of channel estimation with jointly Gaussian inputs. We analyze the relationship of the generally nonlinear CME to the linear Bussgang estimator, a well-known method based on Bussgang's theorem. We highlight a novel observation that the Bussgang estimator is equal to the CME for different special cases, including the case of univariate Gaussian inputs and the case of multiple pilot signals in the absence of additive noise prior to the quantization. For the general cases we conduct numerical simulations to quantify the gap between the Bussgang estimator and the CME. This gap increases for higher dimensions and longer pilot sequences. We propose an optimal pilot sequence, motivated by insights from the CME, and derive a novel closed-form expression of the MSE for that case. Afterwards, we find a closed-form limit of the MSE in the asymptotically large number of pilots regime that also holds for the Bussgang estimator. Lastly, we present numerical experiments for various system parameters and for different performance metrics which illuminate the behavior of the optimal channel estimator in the quantized regime. In this context, the well-known stochastic resonance effect that appears in quantized systems can be quantified.

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arXiv2023

Learning a Gaussian Mixture Model from Imperfect Training Data for Robust Channel Estimation

In this letter, we propose a Gaussian mixture model (GMM)-based channel estimator which is learned on imperfect training data, i.e., the training data are solely comprised of noisy and sparsely allocated pilot observations. In a practical application, recent pilot observations at the base station (BS) can be utilized for training. This is in sharp contrast to state-of-theart machine learning (ML) techniques where a training dataset consisting of perfect channel state information (CSI) samples is a prerequisite, which is generally unaffordable. In particular, we propose an adapted training procedure for fitting the GMM which is a generative model that represents the distribution of all potential channels associated with a specific BS cell. To this end, the necessary modifications of the underlying expectation-maximization (EM) algorithm are derived. Numerical results show that the proposed estimator performs close to the case where perfect CSI is available for the training and exhibits a higher robustness against imperfections in the training data as compared to state-of-the-art ML techniques.

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arXiv2023

Channel Estimation with Reduced Phase Allocations in RIS-Aided Systems

We consider channel estimation in systems equipped with a reconfigurable intelligent surface (RIS). In order to illuminate the additional cascaded channel as compared to systems without a RIS, commonly an unaffordable amount of pilot sequences has to be transmitted over different phase allocations at the RIS. However, for a given base station (BS) cell, there exist immanent structural characteristics of the environment which can be leveraged to reduce the necessary number of phase allocations. We verify this observation by a study on discrete Fourier transform (DFT)-based phase allocations where we exhaustively search for the best combination of DFT columns. Since this brute-force search is unaffordable in practice, we propose to learn a neural network (NN) for joint phase optimization and channel estimation because of the dependency of the optimal phase allocations on the channel estimator, and vice versa. We verify the effectiveness of the approach by numerical simulations where common choices for the phase allocations and the channel estimator are outperformed. By an ablation study, the learned phase allocations are shown to be beneficial in combination with a different state-of-the-art channel estimator as well.

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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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arXiv2022

Evaluation of a Gaussian Mixture Model-based Channel Estimator using Measurement Data

In this work, we use real-world data in order to evaluate and validate a machine learning (ML)-based algorithm for physical layer functionalities. Specifically, we apply a recently introduced Gaussian mixture model (GMM)-based algorithm in order to estimate uplink channels stemming from a measurement campaign. For this estimator, there is an initial (offline) training phase, where a GMM is fitted onto given channel (training) data. Thereafter, the fitted GMM is used for (online) channel estimation. Our experiments suggest that the GMM estimator learns the intrinsic characteristics of a given base station's whole radio propagation environment. Essentially, this ambient information is captured due to universal approximation properties of the initially fitted GMM. For a large enough number of GMM components, the GMM estimator was shown to approximate the (unknown) mean squared error (MSE)-optimal channel estimator arbitrarily well. In our experiments, the GMM estimator shows significant performance gains compared to approaches that are not able to capture the ambient information. To validate the claim that ambient information is learnt, we generate synthetic channel data using a state-of-the-art channel simulator and train the GMM estimator once on these and once on the real data, and we apply the estimator once to the synthetic and once to the real data. We then observe how providing suitable ambient information in the training phase beneficially impacts the later channel estimation performance.

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arXiv2022

An Asymptotically MSE-Optimal Estimator based on Gaussian Mixture Models

This paper investigates a channel estimator based on Gaussian mixture models (GMMs) in the context of linear inverse problems with additive Gaussian noise. We fit a GMM to given channel samples to obtain an analytic probability density function (PDF) which approximates the true channel PDF. Then, a conditional mean estimator (CME) corresponding to this approximating PDF is computed in closed form and used as an approximation of the optimal CME based on the true channel PDF. This optimal CME cannot be calculated analytically because the true channel PDF is generally unknown. We present mild conditions which allow us to prove the convergence of the GMM-based CME to the optimal CME as the number of GMM components is increased. Additionally, we investigate the estimator's computational complexity and present simplifications based on common model-based insights. Further, we study the estimator's behavior in numerical experiments including multiple-input multiple-output (MIMO) and wideband systems.

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arXiv2022

GMM-based Codebook Construction and Feedback Encoding in FDD Systems

We propose a precoder codebook construction and feedback encoding scheme which is based on Gaussian mixture models (GMMs). In an offline phase, the base station (BS) first fits a GMM to uplink (UL) training samples. Thereafter, it designs a codebook in an unsupervised manner by exploiting the GMM's clustering capability. We design one codebook entry per GMM component. After offloading the GMM-but not the codebook-to the mobile terminal (MT) in the online phase, the MT utilizes the GMM to determine the best fitting codebook entry. To this end, no channel estimation is necessary at the MT. Instead, the MT's observed signal is used to evaluate how responsible each component of the GMM is for the signal. The feedback consists of the index of the GMM component with the highest responsibility and the BS then employs the corresponding codebook entry. Simulation results show that the proposed codebook design and feedback encoding scheme outperforms conventional Lloyd clustering based codebook design algorithms, especially in configurations with reduced pilot overhead.

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arXiv2021

An Asymptotically Optimal Approximation of the Conditional Mean Channel Estimator based on Gaussian Mixture Models

This paper investigates a channel estimator based on Gaussian mixture models (GMMs). We fit a GMM to given channel samples to obtain an analytic probability density function (PDF) which approximates the true channel PDF. Then, a conditional mean channel estimator corresponding to this approximating PDF is computed in closed form and used as an approximation of the optimal conditional mean estimator based on the true channel PDF. This optimal estimator cannot be calculated analytically because the true channel PDF is generally not available. To motivate the GMM-based estimator, we show that it converges to the optimal conditional mean estimator as the number of GMM components is increased. In numerical experiments, a reasonable number of GMM components already shows promising estimation results.

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