This repository contains a comprehensive simulation of a Frequency-Modulated Continuous-Wave (FMCW) radar system. The project is divided into two parts to demonstrate both the fundamental signal processing mathematics and a realistic system implementation using MATLAB's Phased Array System Toolbox.
The goal of this project is to simulate the complete radar processing chain:
- Signal Generation: Creating linear frequency modulated (LFM) chirps.
- Propagation Physics: Simulating time delay (range) and Doppler shift (velocity).
- Signal Processing: Mixing (de-chirping) and performing FFT analysis to detect targets.
- Hardware Simulation: Modeling antenna gain, transmitter power, and thermal noise.
In this section, the radar logic is built from the ground up using raw mathematical formulas (Euler's formula) without relying on high-level radar toolboxes. This demonstrates a deep understanding of the underlying physics.
Key Concepts Implemented:
-
Chirp Generation: Manual creation of the complex baseband signal
$e^{j\pi \alpha t^2}$ . -
Echo Simulation: Modeling the round-trip delay
$\tau$ and Doppler shift$f_d$ . -
De-chirping: Implementing the mixer mathematically as
Beat = Rx * conj(Tx). - Spectral Analysis: Using FFT to extract range information from the beat frequency.
Results:
Beat signal: "Beat Signal" is obtained by mixing the transmitted and received signals.
Transmitted Signal (Spectrogram): The spectrogram below visualizes the linear frequency ramp (Up-Chirp) generated in the simulation. The frequency increases linearly over time, covering the bandwidth required for the target resolution.
Spectrum comparison:
As illustrated above, a single chirp measurement results in Range-Doppler ambiguity. The frequency shift caused by distance and velocity is superimposed in a single spectrum, making it impossible to decouple these two parameters without a chirp sequence.
This section upgrades the simulation to a professional level using MATLAB's System Objects. It introduces realistic hardware constraints and advanced processing for moving targets.
System Configuration:
- Frequency: 77 GHz (Automotive standard)
- Bandwidth: Calculated for 0.5 m range resolution.
- Hardware: Includes antenna aperture (
$6.06 \text{ cm}^2$ ), gain calculations, and receiver noise figure ($4.5 \text{ dB}$ ). - Processing: Range-Doppler processing using 2D-FFT on a frame of 64 chirps.
Simulation scenario:
- Radar Velocity: 10 km/h
- Target Velocity: -96 km/h (Closing in / Head-on scenario) or Receding.
- Environment: Free space path loss model with Radar Cross Section (RCS) simulation.
Results: Range-Doppler Map
The final output is a Range-Doppler Map generated by processing a coherent processing interval (CPI) of 64 pulses.
- X-Axis: Velocity (Relative speed of the target).
- Y-Axis: Range (Distance to the target).
- Color: Signal power (dB).
The map clearly distinguishes the target based on both its distance and relative velocity, resolving the range-velocity ambiguity inherent in single-chirp processing.
Understanding raw radar data processing is a prerequisite for implementing robust Sensor Fusion algorithms (e.g., fusing Radar point clouds with Camera data via Kalman Filters) in autonomous mobile robots.
