# Stanford EE259 I 2023 I Lecture 12 (Extra Session)

()

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

• 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.

• 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.

• 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.

## Introduction

• 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.

## Conclusion

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