The aim of this work is to present the main aspects of FMCW radars. After mentioning the main characteristic of this kind of radar, that is the ability to detect target range, focus is given on the description of the relationship among signal bandwidth, radar resolution and maximum unambiguous range.

Monostatic and bistatic configurations are presented in order to provide a comparison among their limitations. Moreover, a series of modulation techniques are reported giving particular attention to linear-triangular modulation.

Applications mostly concern short-range scenarios, as examples altimeters radars, Advanced Driver Assistance Systems (ADAS) and Through The Wall Detection technologies.

Frequency Modulated Continuous Wave (FMCW) radars are radars where the electromagnetic signals are continuously transmitted in time and the operating frequency can vary during measurements.

As continuous wave radars, they have:

• low peak power
• reduced instantaneous bandwidth
• no ambiguity in Doppler velocity
• Low Probability of Intercept (LPI)

Unlike simple CW radars, FMCW radars are able to determine target range by measuring the frequency difference between transmitted and received signal.

As an example, a sawtooth modulation is considered.

The target distance is obtained from:

<math> R = \frac{c_0 \Delta t}{2} = \frac{c_0 \Delta f}{2 \cdot \frac{\delta f}{\delta t}} </math>

Where:

• $c_0$ is the speed of light
• $\Delta t$ is the time delay
• $\Delta f$ is the frequency difference
• $\frac{\delta f}{\delta t}$ is the chirp slope

If the target is moving, a Doppler shift affects the received signal.

The maximum unambiguous range is:

<math> R_{max} = \frac{0.1 c_0 t_m}{2} </math>

Where:

• $t_m$ is the modulation period

The range resolution is:

<math> \Delta R = \frac{c_0}{2B} </math>

Where:

• $B = f_1 - f_0$ is the bandwidth

The beat frequency is:

<math> f_b = S \cdot t_d = \frac{2 R S}{c_0} </math>

Where:

• $S$ is the chirp slope
• $t_d$ is the delay

Important observations:

• Beat frequency ∝ distance
• Maximum range depends on ADC sampling rate
• Resolution depends only on bandwidth

The receiver uses:

• mixer
• low-pass filter
• FFT processor

Key issue:

• transmitter-receiver coupling

Solutions:

• low-noise oscillators
• shielding
• circulators
• RPC (Reflected Power Canceller)

The delay is:

<math> t_d = \frac{2R}{c_0} </math>

The beat frequency:

<math> f_b = \frac{2 R \Delta F}{c_0 t_m} </math>

Beat frequencies:

<math> f_{b1} = \frac{2R \Delta F}{c_0 t_m} </math>

<math> f_{b2} = -f_{b1} </math>

Range:

<math> R = \frac{c_0 t_d}{2} </math>

Number of FFT bins:

<math> N_F = \Delta F \cdot t_m </math>

Limitation:

• Doppler cannot be measured
• introduces range errors if target moves

Uses binary sequences (+1 / -1) to modulate phase.

Advantage:

• bandwidth control

Drawback:

• ambiguity with Doppler

Distance measurement is based on phase difference:

<math> \Delta \phi </math>

Limitation:

• very small unambiguous range

The transmitted signal:

<math> s(t) = U_s \sin(\Omega_0 t + \frac{\Delta \Omega}{\omega_m} \sin \omega_m t) </math>

Distance is extracted from spectral analysis.

Characteristics:

• frequency: 4.2–4.4 GHz
• range: up to 1200 m
• accuracy: ~30 cm

Applications:

• adaptive cruise control
• emergency braking

Typical specs:

• frequency: 77 GHz
• range: 80–200 m

Uses UWB FMCW radar.

Radar equation:

<math> P_r = \frac{P_t T_{wall}^2 G_t G_r \lambda^2 \sigma}{(4\pi)^3 R^4} </math>

• high resolution
• low power
• LPI capability

• limited long-range performance
• sensitive to interference
• more complex hardware

• [1] Sistemi Radar – Galati
• [2] radartutorial.eu
• [3] TI mmWave tutorial
• …