** DUE DATE FOR DIGITAL COMMUNICATION PART
CHANGED TO THURSDAY, FEBRUARY 22 **
Chapter 1: 1.8.2, 1.9.1, and 1.9.6.We will have a short quiz on February 13.
** DUE DATE FOR DIGITAL COMMUNICATION PART CHANGED TO THURSDAY, FEBRUARY 22 **
Recall that the observations at the receiver are modeled as
x = s + n
where the signal s and noise n are independent and take on the following values with the indicated probabilities:
n P[n] s P[s] -- ---- -- ---- -2 0.1 -1 0.5 -1 0.2 +1 0.5 0 0.4 +1 0.2 +2 0.1
We discussed various "decision rules" in class whose purpose is to decide whether a -1 or +1 was transmitted based on the noisy observation x. We also calculated the probability of a bit error (also called bit error rate or BER) using mathematical analysis. Now we will use MATLAB to simulate the digital communication system and evaluate the BER for various situations, as described below.
Sample MATLAB programs digcom1.m and digcom2.m are available to help you get started. These are the programs that we discussed in class on February 8.
Derive a formula for the BER as a function of r for this case in which each bit is transmitted three times. Compare your simulation results with the analytical BER.
Hint: When developing the analytical BER, think of the conditional probability of a bit error given that s = -1 was transmitted, and do the same given that s = +1 was transmitted. Then you should be able to obtain the correct analytical BER.
If you would like, repeat using five transmissions of each bit, and compare analysis with simulation. (This is not required.)
Please submit printouts of your MATLAB programs, BER results from running your programs (you will need to decide how many "trials" should be performed to get accurate results), and compare your simulation results with the analytical BER. You should explain clearly and completely how the analytical BER is calculated for each case. If you do things correctly, you should obtain excellent agreement between the simulated BER and the analytical BER!