Chapter 1: 1.8.2, 1.9.1, and graduate students also do 1.9.6.
Chapter 2: 2.2.3, 2.2.4, 2.2.5 (draw a tree), 2.2.6, and 2.2.9 (in part d, n refers to the number of tries before generating a busy signal).
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.
A sample MATLAB program digcom1.m is available to help you get started. This is the program that we developed in class on February 11.
Hint: Your BER results may not agree with your analysis on homework 3 (even if you received full-credit). 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.
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!