Christopher Kraus

Christopher Kraus

Master's Thesis

Compression of spatial information in wideband channel measurements using generative models

Thomas Altstidl (M.Sc.), Sebastian Kram (M.Sc.), Prof. Dr. Björn Eskofier

06 / 2022 – 12 / 2022


In radio-frequency (RF) positioning, distance measurements like time of arrival (TOA) emitted from beacons with known positions are used to track moving agents. Hereby, multipath (MP) propagation like reflection and scattering can occur in industrial environments with many obstacles. Normally, MP is considered a detrimental factor for performance, but it is possible to exploit the inherent spatial information [1].

Modern communication systems relying on high bandwidths and enhanced signaling allow for the recording of channel measurements (CMs) [2]. CMs are large, complex-valued time-series vectors that encode characteristic MP components. In this representation, the information is overlapped due to bandwidth and signalling limitations [3]. Therefore, significant statistical interdependence exists within the time series. To employ CMs for tracking, a lower-dimensional representation of the encoded information can be used [5].

Previous work [4] has already shown that the information can be effectively compressed into the latent space of autoencoder (AE) deep neural networks (DNNs) while retaining spatial information. However, this representation does not ensure statistical independence in the representation space, which is a necessary property for the use of the feature space representation in an observation likelihood model suited for observation-level information fusion with other approaches focused on the line-of-sight component and specular MP components [5, 1]. Furthermore, statistical independence in the representation space is desirable since it can help to learn disentangled representations, i.e. representations where each factor only explains single factors of variation in data [6]. It can be presumed that disentangling the representation space improves the meaningfulness of the encoded information and thus yields better positioning performance.

Therefore, in this thesis at least two alternative encoding models are to be investigated for this tasks. Previous work has shown that normalizing flows like RealNVP [7], a set of learnable functions that transform the desired data distribution into an isotropic Gaussian, can be used on the latent space of AEs and hence decorrelate it [8]. Furthermore, disentangled latent variable representations have been accomplished by manipulating the optimization term in variational AEs [9] [10]. The performance is to be evaluated based on reconstruction performance, positioning performance based on an existing tracking framework [5] and analysis of the latent space representation by means of its spatial distribution based on fingerprinting positional data and statistical properties like correlation using data simulated with an existing simulation environment and available pre-recorded data.

[1] Aditya, Sundar et al., “A survey on the impact of multipath on wideband time-of-arrival based localization”, in Proc. of the IEEE, 2018.
[2] Witrisal, K. et al., “High-Accuracy Localization for Assisted Living: 5G systems will turn multipath channels from foe to friend”, in IEEE Signal Process. Mag., 2016.
[3] Molisch, Andreas, “Ultra-Wide-Band Propagation Channels”, in Proc. of the IEEE, 2009.
[4] Altstidl, Thomas et. al., “Accuracy-aware compression of channel impulse responses using deep learning.”, in Int. Conf. Indoor Positioning and Indoor Navigation, 2021.
[5] Kram, Sebastian et al., “Position Tracking using Likelihood Modeling of Channel Features with Gaussian Processes”, arXiv preprint arXiv:2203.13110, 2022.
[6] Yang, Xiaojiang et. al., “Towards Better Understanding of Disentangled Representations via Mutual Information”, arXiv preprint arXiv:1911.10922, 2019.
[7] Dinh, Laurent et al., “Density estimaion using Real NVP”, arXiv preprint arXiv:1605.08803, 2016.
[8] Cramer, Eike et al., “Nonlinear Isometric Manifold Learning for Injective Normalizing Flows”, arXiv preprint arXiv:2203.03934, 2022.
[9] Chen, Ricky T. Q., “Isolating Sources of Disentanglement in Variational Autoencoders”, in Advances in neural information processing systems 31, Montreal, Canada, 2018.
[10] Kumar, Abhishek, et al., “Variational Inference of Disentangled Latent Concepts from Unlabeled Observations”, arXiv preprint arXiv:1711.00848, 2017.