Digital Signal Processing Reference
In-Depth Information
3.3 Wireless Transmission Model
Wireless transmission is error prone with non-stationary error characteristics.
Bit error rates as bad as or are reported [3]. They are caused by path
loss, fast fading due to movement and multipath propagation, slow fading due
to moving beyond large obstacles, noise and interference from other networks
or devices like microwave ovens.
A widely used model for the error characteristics of a wireless channel is the
Gilbert-Elliot two state Markov model [20][21][8], where each state represents a
Binary Symmetric Channel (BSC). Each state is assigned a specific constant Bit
Error Rate (BER): in the “good” state (G) errors occur with low probability
while in the “bad” state (B) they happen with high probability
Within one state errors are assumed to occur independently from each other. For
a complete specification of the model the values and that represent
the probability to switch from the good state to the bad state and vice versa, are
necessary and sufficient.
The steady state probabilities of being in the states G and B are
respectively. Hence the average bit error rate produced by the Gilbert-Elliot
channel is
As established by measurements, BER's of the order of and are typ-
ical for the good and bad state, respectively. For simplicity we assume that state
transitions occur only at multiples of 20 ms and that a packet is entirely sent in
one of the two states (no state transitions occur in the middle of a packet.)
Given these restrictions we can express the packet error probability as a func-
tion of the packet size: with a
b
-bit packet and a BER of the packet will be
considered corrupted and therefore discarded with probability
For a Gilbert-Elliot channel the packet error rate can then be expressed as
where and are the packet size (in bit) during the channel good and bad
states, respectively.
If retransmissions are allowed at the MAC level the source station can trans-
mit a packet at most N times before discarding it. The perceived correct rate at
