Gerhard Steinböck

Modeling of Reverberant Radio Channels Using Propagation Graphs

In measurements of in-room radio channel responses, an avalanche effect can be observed: earliest signal components, which appear well separated in delay, are followed by an avalanche of components arriving with increasing rate of occurrence, gradually merging into a diffuse tail with exponentially decaying power. We model the channel as a propagation graph in which vertices represent transmitters, receivers, and scatterers, while edges represent propagation conditions between vertices. The recursive structure of the graph accounts for the exponential power decay and the avalanche effect. We derive a closed-form expression for the graphs transfer matrix. This expression is valid for any number of interactions and is straightforward to use in numerical simulations. We discuss an example where time dispersion occurs only due to propagation in between vertices. Numerical experiments reveal that the graphs recursive structure yields both an exponential power decay and an avalanche effect.

Tracking of Time-Variant Radio Propagation Paths Using Particle Filtering

In this contribution a low-complexity particle filtering algorithm is proposed to track the parameters of time-variant propagation paths in multiple-input multiple-output (MIMO) radio channels. A state-space model is used to describe the path evolution in delay, azimuth of arrival, azimuth of departure, Doppler frequency and complex amplitude dimensions. The proposed particle filter (PF) has an additional resampling step specifically designed for wideband MIMO channel sounding, where the posterior probability density functions of the path states is usually highly concentrated in the multi-dimensional state space. Preliminary investigations using measurement data show that the proposed PF can track paths stably with a small number of particles, e.g. 5 per path, even in the case where the paths are undetected by the conventional SAGE algorithm.

Distance Dependent Model for the Delay Power Spectrum of In-room Radio Channels

A model based on experimental observations of the delay power spectrum in closed rooms is proposed. The model includes the distance between the transmitter and the receiver as a parameter which makes it suitable for range based radio localization. The experimental observations motivate the proposed model of the delay power spectrum with a primary (early) component and a reverberant component (tail). The primary component is modeled as a Dirac delta function weighted according to an inverse distance power law (d-n). The reverberant component is an exponentially decaying function with onset equal to the propagation time between transmitter and receiver. Its power decays exponentially with distance. The proposed model allows for the prediction of, e.g., the path loss, mean delay, root mean squared (rms) delay spread, and kurtosis versus the distance. The model predictions are validated by measurements: they show good agreement with respect to distance dependent trends.

Experimental Validation of the Reverberation Effect in Room Electromagnetics

The delay power spectrum is widely used in both communication and localization communities for characterizing the temporal dispersion of the radio channel. Experimental investigations of in-room radio environments indicate that the delay power spectrum exhibits an exponentially decaying tail. This tail can be characterized with Sabines or Eyrings reverberation models, which were initially developed in acoustics. So far, these models were only fitted to data collected from radio measurements, but no thorough validation of their prediction ability in electromagnetics has been performed yet. This paper provides a contribution to fill this gap. We follow Sabines original experimental approach, which consists in comparing model predictions to experimental observations in a room, while varying its mean absorption coefficient and total room surface. We find that Eyrings model provides a more accurate prediction of the parameters characterizing the decaying tail, such as the reverberation time, than Sabines model. We further use the reverberation models to predict the parameters of a recently proposed model of a distance-dependent delay power spectrum. This model enables us to predict the path loss, mean delay, and root mean square (rms) delay spread versus transmitter-receiver distance. We observe good agreement between predictions and experimental results.

Model for the Path Loss of In-Room Reverberant Channels

A general path loss model for in-room radio channels is proposed. The model is based on experimental observations of the behavior of the delay-power spectrum in closed rooms. In such a room, the early part of the spectrum observed at different positions typically consists of a dominant component (peak) that vanishes as the transmitter-receiver distance increases; the late part decays versus distance according to the same exponential law in delay regardless of the distance. These observations motivate the proposed model of the delay-power spectrum with an early dominant component and a reverberant component. The dominant component is modeled as a Dirac delta function weighted with a factor decaying according to an inverse distance power law (

Hybrid Model For Reverberant Indoor Radio Channels Using Rays and Graphs

d^{-n}

Low-complexity geometry based MIMO channel emulation

). The reverberant component is an exponentially decaying function versus delay with distance-dependent onset. Its power decays exponentially with distance. The proposed model allows for the prediction of path loss, mean delay, and rms delay spread versus distance. We use measurements to validate the model. We observe good agreement of the model prediction for mean delay and rms delay spread.

A 5G hybrid channel model considering rays and geometric stochastic propagation graph

Ray tracing tools allow for deterministic simulation of the channel impulse response. Studies show that these tools work well when the impulse response consists only of a few distinct components. However, measurements of the channel impulse response in indoor environments reveal a diffuse tail. This diffuse tail is difficult to include in ray tracing due to the computational complexity. We propose a hybrid model to include deterministic components and the diffuse tail by combining ray tracing with a propagation graph. The recursive structure of the propagation graph allows for a computationally efficient calculation of the channel transfer function considering infinitely many components. We use ray tracing and the theory of room electromagnetics to obtain the parameter settings for the propagation graph. Thus, the proposed hybrid model does not require new or additional parameters in comparison to ray tracing. Simulation results show good agreement with measurements with respect to the inclusion of the diffuse tail in both the delay power spectrum and the azimuth-delay power spectrum.

Wireless indoor positioning relying on observations of received power and mean delay

The design and optimization of modern radio communication systems requires realistic models of the radio propagation channel. Especially for the test of mobile radio hardware devices, real-time implementations of such channel models are needed. Geometry based channel models are computationally intensive, since for every propagation path, every time instance and every delay or frequency bin a complex exponential has to be evaluated. On a real-time hardware channel emulator, like the ARC SmartSim, the number of paths P, that can be simulated, is limited by the available processing power. In this paper, a new method is introduced, that allows both to increase the number of paths P and to reduce the overall computational complexity.

Channel measurements and characteristics for cooperative positioning applications

We consider a ray-tracing tool, in particular the METIS map based model for deterministic simulation of the channel impulse response. The ray-tracing tool is extended by adding a geometric stochastic propagation graph to model additional stochastic paths and the dense multipath components observed in measurements. The computational complexity of ray-tracing typically prohibits the inclusion of the dense multipath component or limits it to the early part of the impulse response. Due to computational reasons and for lack of detailed information is the description of the environment for ray-tracing often very simplistic, e.g. plain walls and thus neglecting the structures on the building facades, window frames, window sills, etc. Thus in measurements there are often additional components observed that are not captured by these simplistic ray-tracing implementations. In this contribution we introduce a flexible concept of a hybrid model that allows to simulate computationally efficient deterministic paths and the dense multipath components in a spatially consistent way.