Wireless and Optical Sensing for IoT · Study deck

FMCW mmWave Radar: Range, Doppler, and Angle

Radio Remi is checking a loading bay where dust hides painted floor marks.

Radio Remi is your guide for this deck.

fmcw-radar-basicsiot-sensing
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After studying this chapter

Learning objectives

You will be able to:

  • Relate chirp slope and beat frequency to target range.
  • Explain how repeated chirps and antenna phase support Doppler and angle estimates.
  • Connect bandwidth, timing, aperture, SNR, resolution, and ambiguity to an IoT claim.
  • Explain: Radio Remi is checking a loading bay where dust hides painted floor marks.
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Major section

Start With the Story

Radio Remi is checking a loading bay where dust hides painted floor marks.

  • A camera loses contrast, but a radar return still needs careful reading.
  • Remi sends a rising chirp, mixes the delayed echo with the current transmit signal, and finds a beat tone.
  • Repeating the chirp adds motion evidence.
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Major section

Chirp, delay, and beat frequency

Ignoring target motion for this first step, beat frequency is slope times delay, so range is c times beat frequency divided by twice the slope.

  • The approximation is useful only within the radar's sampling, calibration, and propagation assumptions.
  • The mixer removes most of the carrier frequency and leaves a slower beat signal that an analogue-to-digital converter can sample.
  • Leakage between transmitter and receiver can occupy near-range bins and mask a weak reflector.
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Major section

Walk through the radar cube

The output is a detection with range, radial velocity, angle, strength, and uncertainty—not a camera-like object record.

  • The arrows show processing order, not proof that the final output is correct in every setting.
FMCW radar pipeline from chirp and echo through range, Doppler, and angle processing.
FMCW radar pipeline from chirp and echo through range, Doppler, and angle processing.
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Major section

Resolution and ambiguity

Ideal range resolution is approximately c divided by twice the swept bandwidth, so more bandwidth separates closer reflectors.

  • Doppler resolution improves with a longer coherent observation, while frame rate and target change limit how long samples remain comparable.
  • Sampling rate bounds beat frequency and unambiguous range.
  • Pulse timing bounds unambiguous velocity.

Why it matters

Windowing reduces spectral leakage but widens peaks.

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Deck summary

Key takeaways

Radio Remi is checking a loading bay where dust hides painted floor marks.

  • Ignoring target motion for this first step, beat frequency is slope times delay, so range is c times beat frequency divided by twice the slope.
  • The output is a detection with range, radial velocity, angle, strength, and uncertainty—not a camera-like object record.
  • Ideal range resolution is approximately c divided by twice the swept bandwidth, so more bandwidth separates closer reflectors.
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Retrieval practice

Recall check 1 of 3

Radio Remi says: answer from memory, then check your reasoning.

Q1What mainly improves ideal FMCW range resolution?

APrinting additional decimal places on the displayed range.
BIncreasing the FMCW sweep bandwidth for finer range bins.
CReducing receive antenna count without changing bandwidth.
DReplacing held-out range tests with repeated training samples.
Show answer

Answer: B Ideal FMCW range resolution is approximately c/(2B); increasing swept bandwidth B improves separation of nearby reflectors.

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Retrieval practice

Recall check 2 of 3

Radio Remi says: answer from memory, then check your reasoning.

Q2For stationary reflectors measured with the same chirp slope and calibration, one reflector gives a higher beat frequency. What does the simple range model indicate?

AA longer round-trip delay and a farther reflector.
BA shorter round-trip delay and a nearer reflector.
CThe same range because beat frequency is unrelated to delay.
DOnly a wider antenna angle, with no range information.
Show answer

Answer: A The simple static-target model links beat frequency to delay through chirp slope and then to range.

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Retrieval practice

Recall check 3 of 3

Radio Remi says: answer from memory, then check your reasoning.

Q3A radar team widens its sweep and claims it can measure targets at any distance. Which check is still needed?

ACheck sample support for beat frequencies at the claimed target ranges.
BAssume a wider sweep removes range limits because broad frequency coverage resolves beat-sampling ambiguity.
CAdd display decimals to a range the sampler may not represent.
DUse antenna count alone to validate the claimed distant ranges.
Show answer

Answer: A Resolution and unambiguous range depend on different waveform and sampling constraints.

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Print reference

Answers

Answer key.

  1. B · Ideal FMCW range resolution is approximately c/(2B); increasing swept bandwidth B improves separation of nearby reflectors.
  2. A · The simple static-target model links beat frequency to delay through chirp slope and then to range.
  3. A · Resolution and unambiguous range depend on different waveform and sampling constraints.
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