## 9.3 Exercises

EXERCISE 9.8.

Repeat exercise 9.1 using a different basic pulse for the transmitted waveform:

• – bipolar code without return to zero;
• – triangular pulse;
• – Manchester code.

Compare the theoretical and experimental error probabilities obtained from a large number of simulations.

EXERCISE 9.9.

An active early warning radar transmits a pulse burst (1200 pulses/s) with an amplitude A, using a uniformly rotating antenna (15 rotations/min) with the mainlobe width of 1.5°.

1. How many pulses are backscattered by a scanned target?

2. Using an appropriate process, the N pulses backscattered by the scanned target form an observation vector having N components, corrupted by a zero-mean additive white Gaussian noise with a standard deviation σ.

The detection is performed using the Neyman-Pearson criterion, which fixes the false alarm probability level and maximizes the detection probability. Prove that this criterion is equivalent to comparing the sum of N components to a threshold which should be defined. Evaluate the results obtained for: A = 1, σ = 0.6, N = 20, PFA = 10−10.

Write a MATLAB code to predict the detection performance for different values of the involved parameters and to plot the ROC (receiver operating characteristics) curves. These curves illustrate the variation of the detection probability as a function of the false alarm probability, for different values of the signal-to-noise ratio.

EXERCISE 9.10.

Consider a random signal s(t) corrupted by a white noise ...

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