Frequency Modulated Continuous Wave (FMCW) radar has revolutionized the field of radar technology, offering numerous benefits over traditional pulsed radar systems. This chapter delves into the fundamental principles of FMCW radar, exploring its advantages, applications, and the mathematical foundations that underpin its operation. We will also set up the MATLAB environment and provide practical examples to illustrate the concepts discussed throughout this chapter.

FMCW Radar high-level block diagram

FMCW Radar high-level block diagram

Above is the block diagram of a Frequency Modulated Continuous Wave (FMCW) radar system, which illustrates the key components and signal flow in the transmitter and receiver chains.

The transmitter (Tx) chain consists of a ramp generator that produces a linear frequency sweep signal. This ramp signal is fed to a Voltage Controlled Oscillator (VCO), which generates a chirp signal whose frequency varies linearly with the input voltage. The chirp signal is then amplified by a Power Amplifier (PA) before being transmitted through the antenna.

In the receiver (Rx) chain, the reflected chirp signal from the target is captured by the receiving antenna. The received signal is first amplified by a Low Noise Amplifier (LNA) to improve the signal-to-noise ratio while minimizing the noise introduced by the receiver.

The amplified received signal is then mixed with a portion of the transmitted chirp signal in the mixer. This process, known as deramping or stretch processing, produces a beat signal whose beat-frequency is proportional to the round-trip delay and, consequently, the range of the target.

The beat signal continues to the Analog to Digital Converter (ADC), which digitizes the signal for subsequent processing. The Signal Processor performs various operations on the digitized beat signal, such as filtering, Fourier analysis, and target detection, to extract the desired range and velocity information.

Finally, the processed data can be displayed to the user through a suitable interface, such as a graphical display or a control panel.

The block diagram provides a high-level overview of the FMCW radar system architecture, highlighting the essential components and the flow of signals between them. Understanding this architecture is crucial for designing, analyzing, and troubleshooting FMCW radar systems.

1.1 Principles of FMCW Radar

At its core, FMCW radar relies on the continuous transmission of a frequency-modulated signal, typically a chirp, which exhibits a linear increase or decrease in frequency over time. This transmitted signal interacts with targets in the radar's field of view, and the reflected signal is then processed to extract valuable information about the target's range and velocity.

1.1.1 Frequency Modulation The key to FMCW radar's operation lies in the frequency modulation of the transmitted signal. The instantaneous frequency of the chirp signal can be mathematically expressed as:

$$ f(t) = f_0 + \frac{BW}{T_c} t, $$

where:

• $f_0$ is the starting frequency in Hz
• $BW$ is the chirp bandwidth in Hz
• $T_c$ is the chirp/sweep time in seconds
• $t$ is the time variable in seconds

The phase function $\phi(t)$ of the chirp signal is the integral of the instantaneous frequency: