1. The Urban Channel Model Capri Wireless School Sept. 13 -17, 2004 Electromagnetic Propagation in Urban Areas Giorgio Franceschetti University Federico II of Napoli (Italy) and University of California at Los Angeles (UCLA) Numerical and Graphical Solvers for Urban Propagation Daniele Riccio University Federico II of Napoli (Italy) Analytical Approaches to Propagation in Urban Areas Massimo Franceschetti University of California at San Diego (UCSD)

2. Electromagnetic Propagation in Urban Areas Capri Wireless School Sept. 13 -17, 2004 Giorgio Franceschetti University Federico II of Napoli, Italy and University of California at Los Angeles (UCLA) The city ensemble The deterministic approach The probabilistic approach Topics

3. The city ensemble Capri Wireless School Sept. 13 -17, 2004 The cities distribution may be considered as a stochastic process, each city being an element of this ensemble

4. The Deterministic Geometrical Model DGM Capri Wireless School Sept. 13 -17, 2004 Buildings schematisation Ray tracing procedures

5. DGM cnd Capri Wireless School Sept. 13 -17, 2004 Buildings schematisation

6. DGM cnd Capri Wireless School Sept. 13 -17, 2004 Ray tracing procedures

7. DGM cnd Capri Wireless School Sept. 13 -17, 2004 Canyon effect well described Illumination in geometrically obscured areas is provided Modulated signal can be accounted for Attractive features

8. DGM cnd Capri Wireless School Sept. 13 -17, 2004 Model validity Adopted algorithm precision Computational efficiency Limitations

9. DGM cnd Capri Wireless School Sept. 13 -17, 2004 Computational efficiency exploited Equation: For stopping at iteration I, total number of equivalent sources For total number of equivalent sources

10. The Stochastic Environment Model SEM Capri Wireless School Sept. 13 -17, 2004 Stochastic Environment Small–scatterers Model SESM Stochastic Environment Large–scatterers Model SELM Description of general features of urban propagation, relying in a minimum number of physically meaningful parameters

11. SEM cnd Capri Wireless School Sept. 13 -17, 2004 SESM: scattering mechanism dominated by myriads of small scatterers present in the city body SELM: probabilistic description of building distribution as a percolative lattice

12. Capri Wireless School Sept. 13 -17, 2004 Examples of percolative lattices SEM cnd

13. Stochastic Environment Small–scatterers Model SESM Capri Wireless School Sept. 13 -17, 2004 Power summation issue Doppler shift issue

14. Capri Wireless School Sept. 13 -17, 2004 SESM cnd

15. Capri Wireless School Sept. 13 -17, 2004 Pdf of injected photon to undergo its first hit at P(r) Photons absorbed with pdf, and scattered around with pdf Pdf of total power absorbed at P(r) is the sum of those lost by photons that reach P(r) after one hit, two hits, three hits, ………

16. SESM cnd Capri Wireless School Sept. 13 -17, 2004 Radio – link equation

17. Capri Wireless School Sept. 13 -17, 2004 Stochastic Environment Large–scatterers Model SELM

18. Capri Wireless School Sept. 13 -17, 2004