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) \(P_d\) up, \(P_{fa}\) up

  • [ ] (b) \(P_d\) up, \(P_{fa}\) down

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

  • [ ] (d) \(P_d\) down, \(P_{fa}\) up

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 from the data sheet

  • [ ] (b) The thermal noise floor

  • [ ] (c) The signal level required to meet a chosen \(P_d / P_{fa}\) contract, accounting for integration

  • [ ] (d) Equal to the transmit power \(P_t\)

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