HW10

ECE 380 Introduction to Communication Systems
Homework Assignment 10 Due: No need to submit
Problem 1. In an M-ary ASK digital communication system, the channel has bandwidth 1400 Hz. Select a symbol rate and a signal constellation size to achieve a 9600 bit per second error-free signal transmis- sion.
Problem 2. test.
(a) Find the average transmit energy and minimum distance of the constellation shown in the following figure:
(b) Find a better constellation with 8 elements and justify your answer.
Hint: try to minimize the average symbol energy without sacrificing/decreasing the minimum distance.
Problem 3. In a digital transmission system. The signal constellation is A = {−1, 1}. The received signal is y = a + n,
where a is the transmitted signal and n is the noise.
(a) The minimum distance rule is used for detection. What is the decision rule?
(b) If n is Gaussian with zero-mean and unit variance, what is the probability of error using the decision rule in (a) when a = 1?
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