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# Engineering Homework Help

ECE 4260 Communication Systems, Winter 2021
Assignment 5
Due: 5. April, 11:59 PM
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An anti-aircraft missile launching system is shown below.
pulse
Surveillance
antenna
Reflection
Noise from aircraft
Y
N X A
Missile
launcher
This system works as follows. A RADAR transmitter periodically transmits a pulse whose amplitude is A. If there is an aircraft in the target area, the pulse will be reflected by the aircraft as shown in the figure. The probability that an aircraft appears during a pulse period is P0 (assume that no more than one aircraft can appear during a pulse period). Engineering Homework Help.

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A nearby missile launcher listens the reflected pulse using a surveillance
antenna whose output signal is Y = X + N, where X is a random variable
representing the reflected pulse and N is noise. Note that
X =

A if a reflection occurs
0 otherwise.
Noise N is a random variable whose probability density function is shown
below.
5A 0 5A N
The launcher fires a missile whenever the antenna output Y exceeds the level
A
2
. You will realize that the operation of this system is equivalent to that of
a digital communication system.
1. On one occasion, a missile is fired by the launcher. Determine the
probability that it is a false alarm.
2. Suppose an observer sitting nearby notices an aircraft in the sky. Determine the probability that she/he will witness a missile being fired
by the launcher.
3. Determine the fraction of missiles that will be wasted in the long run.

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