1. NETW 707 Modeling and Simulation Amr El Mougy Maggie Mashaly

2. Lecture (8) Network Modeling

3. Modeling the PHY Layer  Modeling and simulation at the PHY layer are generally concerned with bit or packet error performance  Used mainly for transceiver design or wireless channel modeling  Wireless propagation is affected by three phenomena: Reflection Diffraction Scattering

4. Main Causes of Bit Errors  Attenuation: decrease in signal strength at the receiver (decreases signal to noise ratio)  Inter-symbol interference (ISI): caused by delay spread (current symbol is delayed and interferes with the next symbol)  Doppler shift: frequency shift in the received signal due to relative velocities of transmitter and receiver (may cause inter-carrier interference in OFDM systems)  Multipath fading: leads to fluctuations in amplitude, phase and angle of the received signal

5. Large/Small Scale Fading

6. Wireless Channel Models: Free Space and Two-Ray

7. Wireless Channel Models: Log-distance Path Model Path loss at reference distance d 0 Path loss exponent Normal RV with zero mean and std σ

8. Wireless Channel Models: Rayleigh and Rician

9. Wireless Channel Models: Nakagami-m

10. Modeling the Coverage Range of a Node Traditional ‘disk model’ Some systems consider i.i.d. random fading d

11. Modeling the Coverage Range of a Node d  Transmitted signals are affected by path loss, shadowing, and multi-path fading Path loss alone Path loss and shadowing Path loss, shadowing and multi-path fading Path Loss (dB) Log (d)

12. Correlated Shadowing  Links in close proximity experience similar shadowing effects  Degree of correlation depends on several factors such as position of nodes in the coverage area, and the relative position of the nodes from each other  Without considering correlation, connectivity can be over-estimated by large factors (as high as 380%) ρ = 0.21 ρ = 0.01 ρ = 0.24 ρ = 0.05

13. Correlated Shadowing α = 2 γ = 6 α = 4 γ = 9 α = 2 γ = 3

14. Topology Modeling

15. Common Topology Models  Random graphs: for a fixed number of nodes and probability p, then each two nodes will be connected by an edge with probability p  For large n, the degree distribution follows a Poisson distribution

16. Common Topology Models

18. Random Graph Random Geometric GraphBarabasi-Albert Graph

19. Dijkstra’s Routing Algorithm

20. Shortest Path Tree  Shortest path tree from u  Forwarding table for node u: DestinationNext hopCost vv2 xx1 yx2 wx3 zx4