🎯 FMCW Radar Virtual Laboratory

Frequency Modulated Continuous Wave Radar Simulation & Analysis

ECE 514E - Radar & Satellite Engineering

🎯 Learning Objectives

Upon completion of this virtual laboratory, students will be able to:

📚 Theoretical Background

1. FMCW Radar Principle

Frequency Modulated Continuous Wave (FMCW) radar transmits a continuous wave with frequency varying linearly over time (chirp). The received signal from a target is delayed due to round-trip propagation time. By mixing the transmitted and received signals, a beat frequency is generated that contains target range and velocity information.

Range Measurement

The beat frequency due to range is:

fb_range = (2 × R × B) / (c × Tc)

Where:
R = Target range (m)
B = Chirp bandwidth (Hz)
c = Speed of light (3×108 m/s)
Tc = Chirp duration (s)

Velocity Measurement

Doppler shift due to target velocity:

fd = (2 × v × fc) / c

Where:
v = Target velocity (m/s)
fc = Carrier frequency (Hz)
c = Speed of light

2. Combined Beat Frequency

fbeat = (2 × R × B) / (c × Tc) ± (2 × v × fc) / c

Note: The sign depends on the direction of target movement (+ for approaching, - for receding) and the chirp direction (up-ramp or down-ramp).

3. Range Resolution

Resolution Limit

ΔR = c / (2 × B)

Range resolution depends only on bandwidth B, not on chirp duration. Higher bandwidth provides better range resolution.

Maximum Unambiguous Range

Rmax = (c × Tc) / 2

Determined by the chirp repetition interval. Targets beyond this range appear aliased (folded).

4. Velocity Resolution

Δv = c / (2 × fc × Tframe)

Where Tframe is the total duration of multiple chirps used for Doppler processing. More chirps provide better velocity resolution but slower update rate.

🔬 Interactive Simulation

24 GHz
150 MHz
100 μs
50 m
20 m/s
20 dB

📊 Calculated Results

Range Resolution
1.0 m
Max Unambiguous Range
15.0 m
Beat Frequency
50.0 kHz
Doppler Shift
3.2 kHz
Measured Range
50.2 m
Measured Velocity
20.1 m/s

🧪 Experimental Procedure

Pre-Lab Preparation: Review the theoretical equations and calculate expected beat frequencies for the given parameter ranges before starting the simulation.
Static Target Analysis (Range Measurement Only)
Set the target velocity to 0 m/s. Vary the target range from 10 m to 200 m in steps of 20 m. For each step:
  • Record the simulated beat frequency
  • Calculate theoretical beat frequency using fb = (2RB)/(cTc)
  • Plot measured vs. theoretical beat frequency
  • Calculate percentage error and analyze sources
Bandwidth vs. Resolution Study
Set target range to 50 m and velocity to 0 m/s. Systematically vary the chirp bandwidth:
  • Test bandwidths: 50 MHz, 100 MHz, 200 MHz, 400 MHz
  • Measure the -3dB width of the peak in the beat frequency spectrum
  • Verify that range resolution ΔR = c/(2B)
  • Discuss the trade-off between resolution and processing bandwidth
Moving Target Analysis (Range-Doppler Coupling)
Set bandwidth to 200 MHz and chirp duration to 200 μs. Vary velocity from -50 m/s to +50 m/s:
  • Observe the up-chirp and down-chirp beat frequencies
  • Use fbeat_up = frange - fdoppler and fbeat_down = frange + fdoppler
  • Solve simultaneous equations to extract true range and velocity
  • Analyze velocity ambiguity and maximum unambiguous velocity
Noise Performance Analysis
Set target range to 100 m, velocity to 30 m/s. Vary SNR from 0 dB to 30 dB:
  • Measure detection probability (ability to distinguish peak from noise)
  • Calculate RMS error in range and velocity measurements
  • Determine minimum SNR required for reliable detection (< 5% error)
  • Plot error vs. SNR curve
Multi-Target Resolution
Simulate two targets at different ranges (separation variable from 1 m to 10 m):
  • Determine minimum separation for distinct peak detection
  • Verify agreement with theoretical range resolution
  • Analyze sidelobe levels and windowing effects

📝 Laboratory Report Guidelines

1. Title Page & Abstract (5%)

  • Clear title, student name, date, course information
  • Abstract (150-200 words): Brief overview of objectives, methodology, and key findings
  • List of equipment/parameters used in simulation

2. Introduction & Theory (20%)

  • Background on FMCW radar applications (automotive, altimetry, security)
  • Detailed derivation of beat frequency equations
  • Explanation of range resolution and Doppler shift principles
  • Diagrams illustrating the frequency-time relationship (chirp plots)

3. Experimental Setup & Methodology (15%)

  • Description of simulation parameters and their nominal values
  • Justification for parameter choices in each experiment
  • Step-by-step procedure followed (refer to steps 1-5 above)
  • Data collection methods and sampling criteria

4. Results & Analysis (40%)

Required Elements:

  • Tables comparing theoretical vs. simulated values for all experiments
  • Plots with proper labels, titles, and grid lines:
    • Beat frequency vs. Target range (Experiment 1)
    • Range resolution vs. Bandwidth (Experiment 2)
    • Up/Down chirp frequencies vs. Velocity (Experiment 3)
    • Measurement error vs. SNR (Experiment 4)
  • Error analysis: Calculate percentage error, standard deviation, and discuss systematic vs. random errors
  • Discussion of range-Doppler coupling and its resolution

5. Discussion & Conclusions (15%)

  • Interpretation of results in context of radar theory
  • Discussion of practical limitations (hardware constraints, atmospheric effects not modeled)
  • Comparison with alternative radar techniques (pulsed radar, FSK)
  • Recommendations for improving measurement accuracy

6. References & Appendices (5%)

  • Citations in IEEE format (minimum 3 peer-reviewed sources)
  • Appendix: Sample calculations, additional plots, or code snippets if applicable
Grading Rubric Emphasis:
  • Accuracy of theoretical calculations (30%)
  • Quality of data presentation and graphs (25%)
  • Depth of analysis and error discussion (25%)
  • Clarity of writing and organization (20%)

❓ Post-Lab Assessment

Answer the following questions in your report:

  1. Why does FMCW radar use triangular (up-down) chirp modulation instead of sawtooth (up-only) when measuring both range and velocity?
  2. If the chirp bandwidth is doubled while keeping the duration constant, how does this affect:
    • Range resolution?
    • Maximum unambiguous range?
    • Processing requirements?
  3. Explain the phenomenon of "range-Doppler coupling" and how it affects measurement accuracy in high-speed scenarios.
  4. Calculate the required bandwidth to achieve 10 cm range resolution at 77 GHz automotive radar frequency.
  5. Why is the beat frequency typically much lower than the RF carrier frequency, and what advantages does this offer?