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# The Adaptive Multi-Resolution Frequency-Domain ParFlow (MR-FDPF) Method for Indoor Radio Wave Propagation Simulation. Part I : Theory and Algorithms

1 ARES - Architectures of networks of services
Inria Grenoble - Rhône-Alpes, CITI - CITI Centre of Innovation in Telecommunications and Integration of services
Abstract : This report presents the theoretical background and new developments of the multi-resolution frequency domain ParFlow (MR-FDPF) approach for the calculus or radio propagation in Indoor environments for centimetric waves. This method has been developed to face the need of a best understanding of Indoor propagation and to help the WiFi network planning task. Indeed, the development of a wireless design tool is based firstly on a radio propagation engine to predict accurately the radio coverage of access points, with a limited computational load. Usual approaches in the literature are based on either empiric modeling, deducted from measurements, or geometrical optic formalism leading to ray-tracing. While the former suffers a lake of accuracy, the later needs a trade-off between accuracy and computational load, often difficult to assess. The approach proposed herein is based on a finite element approach. Once the problem developed in the frequency domain, the linear system thus obtained is solved in two steps: a pre-processing step which consists in an adaptive multi-resolution (multi-grid) pre-conditioning and a propagation step. The second step computes the coverage of a point source with an up-and-down propagation through the binary tree associated with the multi-resolution description. This approach solves exactly the linear system but with a strongly reduced computational complexity when compared to the time domain approach. For example, a full AP coverage at a macroscopic resolution and for an environment of 1000x600 pixels (i.e. $6000m2$ at a $10cm$ resolution) lasts less than $200ms$.
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Cited literature [61 references]

https://hal.inria.fr/inria-00070278
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Submitted on : Friday, May 19, 2006 - 7:51:33 PM
Last modification on : Friday, February 4, 2022 - 3:10:57 AM
Long-term archiving on: : Tuesday, February 22, 2011 - 11:40:55 AM

### Identifiers

• HAL Id : inria-00070278, version 1

### Citation

Jean-Marie Gorce, Katia Jaffrès-Runser, Guillaume de la Roche. The Adaptive Multi-Resolution Frequency-Domain ParFlow (MR-FDPF) Method for Indoor Radio Wave Propagation Simulation. Part I : Theory and Algorithms. RR-5740, INRIA. 2005, pp.57. ⟨inria-00070278⟩

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