This set of Radar Multiple Choice Questions & Answers (MCQs) focuses on “Probabilities of Detection and False Alarm”.

1. Which of the following combinations are used to obtain an envelope detector?

a) Local oscillator, matched filter & threshold decision

b) IF amplifier, matched filter & video amplifier

c) IF amplifier, second detector & video amplifier

d) Mixer, IF amplifier & second detector

View Answer

Explanation: The combination of IF amplifier, second detector & video amplifier acts as an envelope detector which is used to pass pulse modulation and reject the carrier frequency i.e. the high frequency components of the signal.

2. If a square law characteristic is easier to handle mathematically, which out of the following is preferred in practice?

a) Power law

b) Inverse square law

c) Linear law

d) Lanchester’s square law

View Answer

Explanation: A linear law is preferred in practice because unlike square law characteristic which is assumed when the effect on the detection probability is relatively insensitive to the choice, linear law allows a larger dynamic range than the square law.

3. What does ψ_{0} stands for in the equation of probability of false alarm?

a) Bandwidth of radar

b) Mean square value

c) False alarm time

d) Probability of finding the noise voltage

View Answer

Explanation: ψ

_{0}is used to represent mean square value of the noise voltage (mean noise power) in false alarm. Here the Gaussian pdf is used to describe the receiver noise at the input to the IF filter. So when Gaussian noise is passed through the IF filter, the pdf of the envelope R is given in the form of Rayleigh pdf.

4. Which out of the following equations correctly represent the probability of a false alarm?

a) P_{fa} = exp (- V_{T}^{2} / 2ψ_{0})

b) P_{fa} = exp (V_{T}^{2} / 2ψ_{0})

c) P_{fa} = exp (- VT / 2ψ_{0})

d) P_{fa} = exp (- V_{T}^{2} / ψ_{0})

View Answer

Explanation: The probability of a false alarm is represented by the equation P

_{fa}= exp (- V

_{T}

^{2}/ 2ψ

_{0}). Even though this equation is used to represent false alarm, however it won’t indicate whether or not a radar will be troubled by excessive false indications of targets which can only be done by false alarm time.

5. The average duration of a threshold crossing by noise <tk>_{av} is approximately the reciprocal of ______

a) IF bandwidth

b) RF bandwidth

c) 2^{nd} detector

d) Threshold

View Answer

Explanation: It is approximately the reciprocal of IF bandwidth in false alarm time where t

_{k}is the time between crossings of the threshold V

_{T}by the noise envelope because it’s the envelope of IF amplifier output which is applied to the threshold detector due to which the signal noise is able to cross it.

6. The false alarm probabilities of radars are generally quite large and bandwidth is usually small.

a) True

b) False

View Answer

Explanation: The false alarm probability of radar is generally small since a decision is made as to whether a target is present or not every 1/B seconds. The bandwidth is usually large so there are many opportunities during one second for a false alarm to occur.

7. The probability that the envelope R will exceed the threshold V_{T} is called as ______

a) probability of indication

b) probability of false alarm

c) probability of increased bandwidth

d) probability of detection

View Answer

Explanation: The probability of detecting the signal is the probability that the envelope R will exceed the threshold V

_{T}(set by the need to achieve some specified false alarm time), and in order to evaluate the probability of detection P

_{d}, numerical and empirical methods were used.

8. The empirical formula which is given in order to relate S/N, P_{d}, and P_{fa} is called as ________

a) Albersheim’s detection equation

b) Taylor’s detection equation

c) Goldman’s detection equation

d) Dixon’s detection equation

View Answer

Explanation: Albersheim’s detection equation was used to relate S/N, P

_{d}and P

_{fa}which is S/N = A + 0.12AB + 1.7B where A = ln [0.62/P

_{fa}] and B = ln [P

_{d}/ (1-P

_{d})]. Albersheim’s detection equation is quite simpler to use compared to lengthy computer programs with all sorts of quantitative information.

9. It is more easy to use signal to noise power ratio S/N instead of A^{2}/2 ψ_{0} in radar system analysis.

a) True

b) False

View Answer

Explanation: In radar system analysis it is more convenient to use signal to noise ratio S/N rather than A

^{2}/2 ψ

_{0}because the probability of detection P

_{d}can then be expressed in terms of S/N and the ratio of the threshold to noise ratio V

_{T}

^{2}/ 2ψ

_{0}.

10. During probability of detection for a sine wave in noise, why is it accurate to take the values in dB?

a) To provide greater values of P_{d} and lower values of P_{fa}

b) To provide lower values of P_{d} and greater values of P_{fa}

c) To provide greater values of P_{d} and greater values of P_{fa}

d) To provide lower values of P_{d} and lower values of P_{fa}

View Answer

Explanation: The probability of detection for a sine wave in noise as a function of the signal to noise ratio and the probability of false alarm is given in dB since its suitable for rough calculations for greater values of P

_{d}and lower values of P

_{fa}and this applies for a single pulse only.

**Sanfoundry Global Education & Learning Series – Radar.**

To practice all areas of Radar, __ here is complete set of Multiple Choice Questions and Answers__.