Stanford EE259 I 2023 I Lecture 12 (Extra Session)

Stanford EE259 I 2023 I Lecture 12 (Extra Session)

Fundamentals of Radar Systems

  • The basics of antenna theory, including calculating electric and magnetic fields and finding radiated power density.
  • Understanding radiation efficiency and directivity of an antenna.

Radar Range Equation

  • Calculation used to determine the maximum range that a radar system can detect.
  • Factors considered in the equation: transmit power, antenna gain, target radar cross section, and system losses.

Types of Radar Systems

  • Pulse radar and continuous wave radar.
  • Single-input single-output (SISO) and multiple-input multiple-output (MIMO) systems.
  • Differences and applications of each system in robotics and autonomy.

Frequency-Modulated Continuous Wave (FMCW) Radar

  • Introduction to FMCW radar and its usage in robotics.
  • Discussion on how FMCW radar works and its application in estimating range and velocity using the Doppler effect.

Performance of Radar Systems

  • Range, resolution, field of view, and velocity estimation capabilities of radar systems.
  • Mention of a commercially available chip for FMCW radar and its integration into a radar system.


  • Discussion on the signal model involving the complex conjugate of a received waveform multiplied by a transmitted waveform.
  • Simplification of the model by expressing it as complex exponentials.

Doppler Shift and Range

  • Explanation that the instantaneous frequency of the signal includes contributions from both target range and velocity.
  • Proportional relationship between Doppler shift and radial velocity.
  • Complexity in interpreting the frequency due to coupling between range and velocity.

Decoupling Range and Velocity

  • Mention that coupling between range and velocity is typically insignificant in robotic applications.
  • Doppler shift is usually much smaller than the frequency shift from range.
  • Demonstration with specific numbers to show the negligible Doppler shift.

Simplifying Range Estimation

  • Explanation that in FMCW radar, the frequency of the intermediate frequency (IF) signal is assumed to be equal to the frequency shift from range.
  • Estimation of range by multiplying the frequency shift by the speed of light and dividing by twice the bandwidth.

Multiple Targets

  • Discussion on extending ranging estimation technique to multiple targets.
  • IF signal being the sum of individual IF terms corresponding to each target, with different frequency shifts proportional to their ranges.
  • Visualization with an example of three targets hit by a wide radiation pattern.


  • Concluding the video and mentioning the continuation of the discussion in the next installment.
  • Inviting the audience to ask questions.

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