NETW 707 Modeling and Simulation Amr El Mougy Maggie Mashaly

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 • Simplest, no shadowing or fading effects • Free Space: • Two-Ray:

7. Wireless Channel Models:Log-distance Path Model • Models shadowing effects Path loss at reference distance d0 Normal RV with zero mean and stdσ Path loss exponent

8. Wireless Channel Models:Rayleigh and Rician • Model multipath fading without/with Line of Sight (LOS) • Rayleigh: • Rician: K-factor = ratio between LOS path and other paths Ω = total power from all paths

9. Wireless Channel Models:Nakagami-m • Worse performance than Rayleigh • Best fit for urban radio multipath environments m < 1: Worse than Rayleigh fading m = 1: Rayleigh fading m > 1: Better than Rayleigh fading

10. Modeling the Coverage Range of a Node d

11. Modeling the Coverage Range of a Node • Transmitted signals are affected by path loss, shadowing, and multi-path fading Path Loss (dB) Path loss alone Path loss and shadowing Path loss, shadowing and multi-path fading d 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 = 0.24 ρ = 0.21 ρ = 0.05 ρ = 0.01

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

14. Topology Modeling • A network can be abstracted as a graph, where vertices represent nodes and edges connect any two nodes that can communicate directly • |E| is the number of edges and |V| is the number of vertices • The average node degree is given by • The probability that a randomly selected node has degree k, called degree distribution where n(k) is the number of nodes with degree k • Poisson, exponential, and power law are commonly used

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 • Random graphs do not account for distances between nodes • Random geometric graph: vertices are placed randomly over the grid and an the probability P that an edge connects two nodes u and v is given by L is the maximal distance between two nodes. βdetermines the edge density while α determines the ratio of long to short edges

17. Common Topology Models • Previous two models have limited clustering effects • Barabasi-Albert graph: evolves network topologies by adding vertices. New vertices prefer to connect with high degree vertices • The probability P that a new vertex attaches to I • Start with m0 connected verticesand a predefined node degree k. Every time period a new vertex is added. This vertex lhas probability P(kl) that itis connected to j randomly selected nodes

18. Common Topology Models Random Geometric Graph Barabasi-Albert Graph Random Graph

19. Dijkstra’s Routing Algorithm

20. Shortest Path Tree • Shortest path tree from u • Forwardingtable for node u: