(Using running correlation to detect reflected radar pulses) lab2 data.mat also contains three other signals: radar pulse, radar received, and radar noise. The received signal contains several reflections of the transmitted radar pulse and noise. The signal radar noise contains noise with similar characteristics to the noise in the received signal without the reflected pulses.
a (Examining the radar signals) First, let’s take a look at the first two signals.
i Calculate the energy of radar pulse, E(x). (2 marks)
ii Use subplot to plot radar pulse and radar received in separate axes of the same figure. (3 marks)
iii Can you identify the reflected pulses in the received signal by visual inspection alone? (1 mark)
b (Perform running correlation) Use run corr to correlate radar received with radar pulse.
i Plot the resulting correlation signal. (3 marks)
ii Where are the received pulses? Visually identify sample locations of each pulse in the correlation signal. (2 marks)
iii Compare the heights of the peaks to the energy of the radar pulse and explain why the peaks are larger/smaller than the energy. (2 marks)
iv Given that the speed of light is 3 × 108 m/s and the sampling frequency of the detector is 107 samples per second, what is the approximate distance to each object9 ?
c (Estimating error rates, as in Section 2.2.5) In a real radar detector, the correlation signal would be compared to a threshold to perform the detection. To estimate the error rates for such a detector, let’s consider a threshold that is equal to one-half the energy of the transmitted pulse, i.e. c = E(x)/2. Perform running correlation between radar pulse andradar noise call the resulting correlation signal noise c.
i Plot noise c. (2 marks)
ii For how many samples is noise c greater than this threshold? Use this value to estimate the false alarm rate. (3 marks)
iii For how many samples is noise c less than this threshold minus the energy of the transmitted pulse? Use this value to estimate the miss rate. (3 marks)
iv What is the total error rate for this threshold? (2 marks)
d (Determining error rates from a histogram) As discussed in Section 2.2.5, we can use a histogram to judge the number of errors as well.
i Plot the histogram of noise c using 100 bins. (3 marks)
ii Describe how you could derive the error numbers in problem 4c from the histogram. (3 marks)
e (Setting the threshold to achieve a particular error rate) Suppose that detector false alarms are considered to be more serious than detector misses. Thus, we have determined that we want to raise the threshold so that we achieve a false alarm rate of approximately 0.004. Find a threshold that satisfies this requirement.
i What is your threshold? (3 marks)
ii What is the false alarm rate on this noise signal with your threshold? (3 marks)
iii What is the miss rate on this noise signal with your threshold? (3 marks)
iv What is the total error rate for the new threshold? Compare this to the total error rate of the threshold used in problem 4c. (3 marks)
