L8 Pre-flight

L8 Pre-flight#

Block 1: Radar Fundamentals — Lesson 8: Detection Theory Work this before L8. Pre-flights are never collected — in class, anyone may be cold-called to present any question at the board, and that recitation is the participation grade.

Assumed pre-class reading#

  • L7 wrap-up

  • The Jupyter Book Reading page for L8: thermal noise floor \(kTB\), SNR, \(P_d\) / \(P_{fa}\), ROC curves, and integration gain.

Quiz questions (5 items, ~5 minutes)#

Q1. (Multiple choice) The cold-receiver thermal noise floor at room temperature is approximately:

  • [ ] (a) \(-100\) dBm/Hz

  • [ ] (b) \(-114\) dBm/Hz

  • [ ] (c) \(-174\) dBm/Hz

  • [ ] (d) \(-200\) dBm/Hz

Q2. (Multiple choice) For a receiver with bandwidth \(B = 1\) MHz and noise figure \(\text{NF} = 5\) dB, the noise floor is approximately:

  • [ ] (a) \(-114\) dBm

  • [ ] (b) \(-109\) dBm

  • [ ] (c) \(-99\) dBm

  • [ ] (d) \(-79\) dBm

Q3. (Multiple choice) Raising the detection threshold causes:

  • [ ] (a) \(P_d\) rises, \(P_{fa}\) rises

  • [ ] (b) \(P_d\) rises, \(P_{fa}\) falls

  • [ ] (c) \(P_d\) falls, \(P_{fa}\) falls

  • [ ] (d) \(P_d\) falls, \(P_{fa}\) rises

Q4. (Short answer) In one sentence, why does coherent integration of \(N\) pulses give a \(+10\log_{10} N\) dB SNR gain while non-coherent integration only gives roughly \(+5\log_{10} N\) dB?

Q5. (Multiple choice) In the radar range equation, the parameter \(S_{\min}\) is best understood as:

  • [ ] (a) A fixed receiver constant, read straight off the data sheet

  • [ ] (b) The receiver’s own thermal noise floor, \(kTB \cdot \text{NF}\)

  • [ ] (c) The signal level a chosen \(P_d/P_{fa}\) contract requires

  • [ ] (d) The transmit power \(P_t\) the radar’s amplifier delivers

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