Chapter 4: Network Model

A wireless communications network is a collection of nodes being capable of communicating with each other over wireless communications links. Let

$\mathsf{N}:=\{1,\dotsc,N\}$

be the set of nodes, and let (

n

,

m

) with

n

≠

m

represent a wireless link from node

n

∈

N

to node

m

∈

N

. We say that there is a wireless link (

n

,

m

) with

n

≠

m

if both

1

node

n

is allowed to transmit data to node

m

, and

2

a minimum signal-to-noise ratio (SNR), being necessary for successful transmission, can be achieved on link (

n

,

m

), in the absence of interference and with transmit power on this link subject to some power constraints.

It is reasonable to assume that wireless links are bidirectional in the sense that (

n

,

m

) exists if and only if there exists (

m

,

n

). We label links (in any particular way) by the integers

$1,2,\dotsc,L$

and use

$\mathsf{L}=\{1,\dotsc,L\}$

to denote a set of all wireless links. The pair (

N

,

L

) is referred to as the network topology. With any network, we associate the topology graph, which is an undirected graph where a vertex corresponds to a node in the network, and an edge between two vertices represents a wireless link between the corresponding nodes.