Ad Hoc Radio Networks
• Radio Network is a collection of transmitter-receiver devices
(denoted as notes). Each node can transmit data to nodes which
exist within its transmitting capability region.
• A radio network can be modeled by a directed graph G=(V,E),
where V denotes a set of nodes and when a node u can transmit
to a node v, there exists an edge (u,v) in E.
• Nodes in a radio network work per round synchronized by a
global clock. At each round, each node transmits data or receives
data. At every round, each node transmits data or receives data. A
node acting as a receiver in a given round gets a message iff
exactly one of its neighbors transmits in this round.
• A collision occurred at a node if at least its two neighbors
transmits in a given round.
• Nodes have a collision detection
-- Nodes can distinguish that no neighbor transmits data and that
two or more neighbors transmit data.
• Radio Broadcasting (RB)
-- Transmitting a message from the source node to all other nodes.
• Acknowledged Radio Broadcasting (ARB)
-- Achieving RB and inform the source about finishing RB.
Model for the following RB and ARB algorithms
• A radio network with a collision detection
• Its reachability graph is symmetric
• Every node knows its own ID and whether itself is source.
• Only source knows the starting round of the algorithms.
• A node v acting as a receiver in a given round hears
 if at least one of its neighbors acts as a trasmitte r in this round,
otherwise v hears signal . In order to distingusi h  and 
for reception of a message, nodes transmit 1 - bit data
(referred as contact message).
RB algorithm
Suppose that (a1 , a2 ,...ar ) is a binary representa tion of
the source message.
Method for transm itting one bit ai
Transmission
Transmitting bit or signal
0
1
Start (end) signal
First round
Second round
No action
No action
Transmission
No action
Transmission
Transmission
Reception
First round
signal 
signal 
signal 
Second round Reception bit or signal
signal 
signal 
signal 
0
1
start or end
Algorithm:
(1)The source transmits a source message (the nodes
whose distance from the source is 1 receive the
source message) and then take no action in the
remaining steps.
(2) the other nodes received source message transmit
the source message. After that, they take no actions
(i.e., the nodes whose distance from source is 1
transmit the source message and the nodes whose
distance from source is 2 receive the source
message, and so on.)
Time complexity: the source message is delivered as if
ripple spreads every 2r+4 rounds. RB algorithm can be
completed in O(r  ecc) rounds, where ecc is the largest
distance from source to any other node.
Improved RB algorithm
• Improve the algorithm to run in only O(r+ecc) round
using a pipelined fashion.
Using 6 rounds to receive or send ai to prevent collision :
(1) Source node trasmits ai in the first 2 rounds and takes
no actions in the next 4 rounds.
(2) The nodes receiving ai (in 2 rounds) transmit it in
the next 2 rounds and take no actions in the following 2 rounds.
Time complexity: Improved RB algorithm can be
completed in 6r+2ecc rounds.