ECEE 3468 NOISE AND STOCHASTIC PROCESSES


FINAL MATLAB PROJECT
Consider a radar system used for local traffic control at an airport. Short duration pulses are carried by an
electromagnetic wave which is transmitted via an antenna. When the wave is reflected by a target, the
reflected energy is delivered to the receiver and used to extract information on the location and the velocity
of the target.
Let 1 denote the event that a target is present with prior probability [1] and denote the event that
there is no target with prior probability [].
To simplify the model, we assume that the receiver is able to sample the received signal at appropriate time
instants. Each received sample, has an information component denoted by and a noise component
denoted by where =+
We also assume that the signal component if present has a fixed voltage plus the noise which is Gaussian
(0, ). At the receiver, the received signal is compared to a threshold, if the signal is above the threshold, a
target is detected. The probability of detection, [] is the probability that the signal level is above the
threshold when a target is present. The probability of false alarm, [] is the probability that the received
signal level is above the threshold when no target is present.

= {
1 = [ = 1] =
0 = 0 [ = 0] = 1 −
} (1)

a. Write a MATLAB code to simulate the radar system as described above and calculate [] and [],
assume = 0.55, = 2 , = 1.6 and the threshold voltage obtained using the maximum a
posteriori probability, MAP, decision rule
ℎ =

2
+
2


[0]
[1]
(2)
b. Increase the standard deviation of the noise, use = 2 and = 3, observe how [] and []
are affected by and comment on your results. What does increasing physically mean?
c. Assume that the threshold is determined using the Neyman Pearson Binary Hypothesis testing
decision rule. The probability of false alarm is set to [] = 0.25 to obtain the threshold. Assume
= 0.55, = 2 , = 1.6 . Use the simulation to compute [] and []. Compare to the
results in part (a). Confirm that the simulated [] matches the set value of 0.25.
d. Assume that the threshold is determined using the maximum likelihood ratio test. Assume = 0.55,
= 2 , = 1.6 . Use the simulation to compute [] and []. Compare to the results in part (a).
e. To improve the performance, a system is designed to transmit multiple pulses at non overlapping
times or using multiple antennas and observe the reflections (returns). The decision is then made
based on the average received signal. The received signal at each trial is represented by a vector
[ 1 2 … … . . ]
′ where = + . is the signal component which is the same in each return.
is the noise component in the
ℎ return. The average received signal = (1 + 2 + ⋯ )/ is
ECEE 3468 NOISE AND STOCHASTIC PROCESSES

compared to the threshold. Take the number of returns = 3 and assume the noise components in
all received returns are independent and have the same = 1.6 , use = 0.55, = 2 and the
threshold voltage ℎ =

2
. Observe the results of the simulation and compare to part . Was the
probability of detection improved? Was the probability of false alarm improved?
f. Gradually increase the number of returns, , until the probability of detection is at least 95%, what
is the minimum value of ? What is the corresponding probability of false alarm?
g. Now assume the noise components in the different returns are correlated. Assume the standard
deviation of all noise components is the same, and the correlation coefficient between any two
components = 0.2 ≠ . Use = 1.6 , = 0.55, = 2 , ℎ =

2
and = 3. Observe
the simulation results and compare to part . How does the correlation between the returns affect
the performance of the system? Increase = 0.6 and comment on the results. Do the
simulation results agree with your prediction? Explain
h. Assume the receiver instead of computing the average of the received returns, it uses a different
processing approach and it makes a decision based on the strongest signal = max (1, 2, … ).
Use = 1.6 , = 0.55, = 2 , ℎ =

2
and = 3. Assume all returns are uncorrelated. Find
[] and []. Compare to part and to explain your results.