FMCW Radar Systems: Principles and Equations

This page covers the FMCW radar system and its equation. This radar system is based on the FM CW signal.

FMCW radar, or Frequency Modulated Continuous Wave radar, is a type of radar where the carrier signal frequency ($f_0$) is frequency modulated by a frequency $f_m(t)$. This results in a transmitted frequency ($f_i$) that can be expressed as:

$f_i = f_0 + f_m(t)$

Doppler radar isn’t typically used for distance or range measurement because it lacks a mechanism for marking the transmit and receive time stamps. This time stamp difference is crucial for determining range information.

To address this limitation, FMCW radar exploits the change in frequency over time to determine the range. This principle is illustrated in the FMCW radar waveform shown below.

As shown in the waveform, the received signal ($f_{ir}$) can be expressed as:

$f_{ir} = f_0 + f_m(t - T_e)$

Where $T_e$ is the time of the echo after the transmission. The frequency difference ($f_d$) is:

$f_d = f_m(t) - f_m(t - T_e)$

The range of the FMCW radar system can then be calculated using the following equation:

$Range = \frac{c \cdot f_d}{2 \cdot a}$

Where:

• c = speed of light
• $a = \frac{f_d}{T_e}$

FMCW radar typically operates at comparatively lower power levels than pulse radar. It’s particularly well-suited for detecting targets at very short ranges.

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