Page 148 - Fundamentals of Communications Systems

4.24 Chapter Four

Figure 4.22 An airborne air traffic control radar example.

(a) What is the actual complex envelope, x z (t), produced by this implementation
as a function of ˜x I (t), ˜x Q (t), and θ?
(b) Often in communication systems it is possible to correct this implementation
error by preprocessing the baseband signals. If the desired output complex
envelope was x z (t) = x I (t) + jx Q (t), what should ˜x I (t) and ˜x Q (t) be set to
as a function of x I (t), x Q (t), and θ to achieve the desired complex envelope
with this implementation?

Problem 4.14. A commercial airliner is flying 15,000 feet above the ground and
pointing its radar down to aid traffic control. A second plane is just leaving the
runway as shown in Figure 4.22. The transmitted waveform is just a carrier
√
tone, x z (t) = 1or x c (t) = 2 cos(2π f c t).
The received signal return at the radar receiver input has the form
√ √
y c (t) = A P 2 cos(2π(f c + f P )t + θ P ) + A G 2 cos(2π(f c + f G )t + θ G ) (4.42)

where the P subscript refers to the signal returns from the plane taking off and
the G subscript refers to the signal returns from the ground. The frequency shift
is due to the Doppler effect you learned about in your physics classes.
(a) Why does the radar signal bouncing off the ground (obviously stationary)
produce a Doppler frequency shift?
(b) Give the complex baseband form of this received signal.
(c) Assume the radar receiver has a complex baseband impulse response of
h z (t) = δ(t) + βδ(t − T ) (4.43)

where β is a possibly complex constant, find the value of β which eliminates
the returns from the ground at the output of the receiver. This system was a
common feature in early radar systems and has the common name Moving
Target Indicator (MTI) as stationary target responses will be canceled in
the filter given in Eq. (4.43).

Modern air traffic control radars are more sophisticated than this problem
suggests. An important point of this problem is that radar and communication
systems are similar in many ways and use the same analytical techniques for
design.