NETW 707

Modeling and

SimulationAmr El Mougy

Maggie Mashaly

Lecture (8)Network Modeling

Modeling the PHY Layer Modeling and simulation at the PHY layer are generally concerned with

bit or packet error performanceUsed mainly for transceiver design or wireless channel modeling Wireless propagation is affected by three phenomena:• Reflection• Diffraction• Scattering

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

Large/Small Scale Fading

Wireless Channel Models:Free Space and Two-Ray

Simplest, no shadowing or fading effects

Free Space:

Two-Ray:

Wireless Channel Models:Log-distance Path Model

Models shadowing effects

Path loss at reference distance d0

Path loss exponent

Normal RV with zero mean and std σ

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 pathsΩ = total power from all paths

Wireless Channel Models:Nakagami-m

Worse performance than RayleighBest fit for urban radio multipath environments

m < 1: Worse than Rayleigh fadingm = 1: Rayleigh fadingm > 1: Better than Rayleigh fading

Modeling the Coverage Range of a Node

Traditional ‘disk model’

Some systems consider i.i.d. random fading

d

Modeling the Coverage Range of a Node

d

Transmitted signals are affected by path loss, shadowing, and multi-path fading

Path loss alonePath loss and shadowingPath loss, shadowing and multi-path fading

Path Loss (dB)

Log (d)

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

Correlated Shadowing

50 100 150 200 250 300 350 400

50

100

150

200

250

300

350

400

α = 2γ = 6

α = 4γ = 9

α = 2γ = 3

Topology ModelingA 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 selectednode 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

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

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. β determines the edge density while α determines the ratio of long to short edges

Common Topology Models

Previous two models have limited clustering effectsBarabasi-Albert graph: evolves network topologies by adding

vertices. New vertices prefer to connect with high degree verticesThe probability P that a new vertex attaches to I

Start with m0 connected vertices and a predefined node degree k. Every time period a new vertex is added. This vertex l has probability P(kl) that it is connected to j randomly selected nodes

Common Topology Models

Random Graph Random Geometric Graph Barabasi-Albert Graph

Dijkstra’s Routing Algorithm

Shortest Path TreeShortest path tree from u

Forwarding table for node u:

Destination Next hop Cost

v v 2

x x 1

y x 2

w x 3

z x 4