How 77 GHz FMCW Automotive Radar Measures Range and Velocity

Modern automotive safety systems rely on 77-gigahertz (GHz) Frequency-Modulated Continuous-Wave (FMCW) radar transceivers to simultaneously track the distance and relative speed of surrounding vehicles. This article provides a technical breakdown of how these sensors function, explaining the transmission of rapid frequency-modulated "chirps," the extraction of intermediate beat frequencies to calculate distance, and the measurement of phase shifts across multiple signal transmissions to determine relative velocity using two-dimensional Fast Fourier Transforms (2D-FFT).

The Fast-Chirp FMCW Signal Architecture

Unlike traditional pulsed radar, an FMCW radar transceiver continuously emits an electromagnetic signal whose frequency changes linearly over time. This frequency sweep is known as a "chirp." In 77 GHz automotive radar, the transceiver sweeps across a wide bandwidth—typically up to 4 GHz (from 77 GHz to 81 GHz)—within a fraction of a millisecond.

The transceiver transmits a sequence of these rapid chirps, grouped together into what is called a "chirp frame." When the transmitted signal strikes a target vehicle, it reflects back to the radar's receiving antenna. Because the signal travels at the speed of light, the received echo is time-delayed relative to the signal currently being transmitted.

Measuring Vehicle Range via Beat Frequency

To measure the distance (range) to a target, the radar transceiver routes both the currently transmitting signal and the incoming reflected signal into an electronic component called a mixer. The mixer subtracts the frequency of the received signal from the frequency of the transmitted signal.

This subtraction produces a much lower frequency signal called the Intermediate Frequency (IF), or "beat frequency." Because the frequency of the chirp increases linearly with time, the beat frequency is directly proportional to the round-trip time delay of the echo.

  • Close targets reflect the signal quickly, resulting in a small time delay and a low beat frequency.
  • Distant targets result in a longer time delay and a higher beat frequency.

An Analog-to-Digital Converter (ADC) samples this IF signal, and a Digital Signal Processor (DSP) applies a Fast Fourier Transform ( Range-FFT) to the data. The Range-FFT converts the time-domain signal into the frequency domain, showing distinct peaks at specific frequencies. These peaks directly correspond to the distance of the detected vehicles.

Resolving Range-Velocity Ambiguity

If a target vehicle is moving, the reflected signal undergoes a Doppler frequency shift in addition to the time delay. In older, slow-chirp FMCW systems, this creates a problem: a single beat frequency contains both range and velocity information intertwined, making it impossible to tell if a frequency shift is caused by the target's distance or its movement.

Modern 77 GHz transceivers solve this by using "fast-chirp" modulation. By making each individual chirp extremely short (usually between 10 and 100 microseconds), the Doppler shift within a single chirp becomes negligible compared to the frequency shift caused by the distance. Therefore, the beat frequency of a single chirp is used almost exclusively to determine the target's range.

Measuring Relative Velocity via Phase Shift

To find the relative velocity simultaneously, the radar transceiver analyzes the reflected signals across a sequence of multiple consecutive chirps within a frame.

While a moving vehicle does not travel far enough between two microsecond-long chirps to noticeably change the beat frequency, its tiny movement (even just a few millimeters) causes a significant, measurable change in the phase of the reflected carrier wave. At 77 GHz, the wavelength of the radar signal is roughly 3.9 millimeters. A tiny shift in distance results in a massive shift in the wave's phase.

By transmitting a frame of \(N\) chirps at regular time intervals, the radar measures the progression of this phase shift from chirp to chirp. The rate at which the phase changes over time is directly proportional to the Doppler frequency, which correlates to the radial velocity of the target vehicle.

Simultaneous Extraction Using 2D-FFT

To output range and velocity at the same time, the radar's processor builds a two-dimensional data matrix for every chirp frame and performs a Two-Dimensional Fast Fourier Transform (2D-FFT):

  1. 1st Dimension (Range-FFT): As each chirp arrives, the DSP performs a Range-FFT to sort targets into "range bins." At this stage, the radar knows the distance of the targets, and it records the phase of the signal in each range bin.
  2. 2nd Dimension (Doppler-FFT): Once all the chirps in the frame are collected, the DSP runs a second FFT across the sequence of chirps for each specific range bin. This Doppler-FFT analyzes the phase shifts from chirp to chirp, separating the targets into "velocity bins."

The result of the 2D-FFT is a Range-Doppler map. Even if two vehicles are at the exact same distance from the radar, they will appear as separate points on the map if they are traveling at different speeds, as their phase shifts across the chirp frame will differ. This simultaneous, real-time extraction of range and relative velocity allows automotive electronics to reliably execute functions like Adaptive Cruise Control (ACC) and Autonomous Emergency Braking (AEB).