This full README file was written by Guilherme Cardoso.
This is the first simulator developed at the course 47064 - Network Performance and Dimension, at University of Aveiro.
On a given network link supporting the exchange of data packets, the average bit error rate (i.e., the probability of each bit being received with error due to propagation or interference factors) is q, with 0 < q ≪ 1. It is assumed that errors in different bits are statistically independent (in this case, the number of errors in a data packet is a binomial random variable). It is considered that the following bit error rate values q=10E-7, q=10E-6 and q=10E-5. In this link, data packets are sent with a 32 bytes field with appropriate information for the receiver to be able to correct 1 error and to detect 2 or more errors. So, each data packet is accepted if it has 0 or 1 error and is discarded if it has 2 or more errors.
The probability function of a binomial random variable with parameter n and q is calculated as the following:
And the probability of a geometric random variable with parameter p is:
task1.m contains analytical analysis for the probability of a packet being received with 0 ,1 or 2 or more errors, given a bit error rate.
All in all, the following variables are available in task1.m:
| Variable | Description |
|---|---|
| q | Array of bit error values to compute |
| error_rates | Error rate probability |
| B | Size of the packet (bits) |
Also in the same m-file there's also analysis that computes the same values for packets sizes of an according probability and packet sizes with a size of B plus a geometric random value with the parameter p.
In task2.m the scenario we considered is a wireless link used by two stations for data communications. The link can be either in a normal state with a probability of p or in an interference state with a probability of 1 – p. The two stations exchange from time to time a set of n consecutive control frames to decide if the link is in interference state. The probability of a control frame being received with one or more errors is at most pEF1 (0.01%) in normal state and is at least pEF2 (50%) in interference state.
Both stations determine with a 100% probability if the control frames have been received with errors. The stations decide that the link is in interference state when the n consecutive control frames are received with errors.
Using Bayes'Law we determined the following probabilities:
- For several p probability of being in the normal state, we determined the probability of the link being in the interference state and in the normal state when one control frame is received
- For same scenario the probability of false positives
- For the same scenario the probability of false negatives
In the task3.m case it was considered a wireless link between multiple stations for data communications. The bit error rate (ber) introduced by the wireless link due to the variation along with time of the propagation and interference factors is approximately given by the following Markov chain:
State transitions are in number of transitions per hour.
Birth-dead Markov chain was used to calculate the following values:
- Average time in each state
- Average bit error rate of the link
- Average time duration (in minutes) that the link is in each state
- If a link is considered in interference state when its bit error rate is p the probability of a link being in the interference state
According to probability of state 0:
and the steady-state probability of state n>0: