Question

A radar signal sn = A cos(2Tfon), n = 1, ... , N is received corrupted by AWGN

with 2=1, Design a detector that maintains PFA=10-8 including the
formula for the decision threshold. If fo= 1/4 and N =25, find the probability
of detection PD versus A and plot it for A = [0, 5], You will need to evaluate
the inverse of the Q function, for which you can use qfuncinv . m or erfinv . m.
For what values of the frequency fo is your detection the most accurate (the
deflection coefficient is the largest)?

Answer 1

To design a detector that maintains a Probability of False Alarm (PFA) of 10^-8, we need to find the decision threshold and calculate the Probability of Detection (PD) versus A. The values of fo that maximize the accuracy of detection can be determined by finding the values of fo that correspond to the maximum PD for different values of A.

Step-by-step explanation:

To design a detector that maintains a Probability of False Alarm (PFA) of 10^-8, we need to find the decision threshold. For a given signal sn = A cos(2πfon), where A is the amplitude and fon is the frequency, the decision threshold is given by td = qfuncinv(PFA) * sqrt(2/N), where qfuncinv is the inverse of the Q function.

To find the Probability of Detection (PD) versus A, we need to calculate the value of A that maximizes the deflection coefficient. The deflection coefficient is given by PD = 1 - qfunc(A * sqrt(N/2)), where qfunc is the Q function. We can plot PD versus A for A ranging from 0 to 5 to visualize the relationship.

The values of fo that maximize the accuracy of detection (largest deflection coefficient) can be determined by finding the values of fo that correspond to the maximum PD for different values of A.