Wireless Network Design: Optimization Models and Solution ...

2 Introduction to Wireless Communications 29
follows. Let there be N distributed nodes that are sharing the wireless medium. Traffic
arrivals at each node is modeled as a random process, such as a Poisson point
process. Some basic assumptions are typically made to enable simple analysis of
these protocols. For instance, if two or more nodes transmit a packet at the same
time, a collision is said to occur and the receiver will be unable to accurately decode
either of these packets. 1 It is also assumed that some form of instantaneous feedback
mechanism exists from the receiver to the transmitter indicating whether a packet
is received successfully or not. This feedback in turns enables the transmit node to
retransmit packets that are not received correctly.
The earliest and simplest form of multiple access is the well known Aloha
method [1]. In an Aloha system, users simply transmit their packets whenever they
have data to be sent. Clearly, such a scheme might cause significant amount of collisions
if multiple packets are sent simultaneously. Further, if a collision is detected,
the nodes which are involved in the collision, delay their subsequent retransmissions
by random amounts. This randomization will allow the multiple competing nodes
to reduce their probability of collision in their retransmissions. It turns out that the
maximum throughput of Aloha is severely limited. Specifically, if the wireless chan-
Fig. 2.11 Depiction of convolutional code using a trellis.
1 This assumption has been modified in recent years to address the issue of capture, which is
discussed later.