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--- radar:fmcw [2026/04/29 13:11] – mauro
+++ radar:fmcw [2026/04/29 13:14] (current) – mauro
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-====== Frequency Modulated CW Radar ======
+{{ :media:radar_fmcw_radarlab_wiki_turco.pdf |}}
-===== Abstract =====
-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.
------
-===== 1. Introduction =====
-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.
------
-===== 2. Principles of FMCW Radars =====
-==== 2.1 Target Distance and Range Resolution ====
-As an example, a sawtooth modulation is considered.
-{{:media:fmcw_li.png|Figure 1: Principles of FMCW system}}
-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
------
-==== 2.1.1 Relationship Between Bandwidth, Resolution and Range ====
-{{:media:chirp_ba.jpg|Figure 2: Chirp signal}}
-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
------
-==== 2.2 Block Diagram and Isolation ====
-{{:media:block_diagram_generic_fmcw_radar.jpg|Figure 4: FMCW radar block diagram}}
-The receiver uses:
-  * mixer
-  * low-pass filter
-  * FFT processor
-Key issue:
-  * transmitter-receiver coupling
-Solutions:
-  * low-noise oscillators
-  * shielding
-  * circulators
-  * RPC (Reflected Power Canceller)
------
-===== 3. Modulation Techniques =====
-==== 3.1 Linear Modulation ====
-{{:media:linear_modulation.jpg|Figure 6: Linear modulation}}
-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>
------
-==== 3.1.1 Triangular Modulation ====
-{{:media:triangular_modulation.jpg|Figure 7: Triangular modulation}}
-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>
------
-==== 3.1.2 Sawtooth Modulation ====
-{{:media:dente_di_sega.jpg|Figure 11: Sawtooth wave}}
-Limitation:
-  * Doppler cannot be measured
-  * introduces range errors if target moves
------
-==== 3.2 Coded Modulation =====
-Uses binary sequences (+1 / -1) to modulate phase.
-Advantage:
-  * bandwidth control
-Drawback:
-  * ambiguity with Doppler
------
-==== 3.3 Square-wave Modulation (FSK) ====
-{{:media:rectangular_wave.jpg|Figure 13: Square wave}}
-Distance measurement is based on phase difference:
-<math>
-\Delta \phi
-</math>
-Limitation:
-  * very small unambiguous range
------
-==== 3.4 Sinusoidal Modulation ====
-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.
------
-===== 4. Applications =====
-==== 4.1 Radar Altimeters ====
-{{:media:altimetro_fm.jpg|Figure 16: Radar altimeter}}
-Characteristics:
-  * frequency: 4.2–4.4 GHz
-  * range: up to 1200 m
-  * accuracy: ~30 cm
------
-==== 4.2 ADAS Systems ====
-{{:media:received_fmcw_radar_signal.png|Figure 18}}
-Applications:
-  * adaptive cruise control
-  * emergency braking
-Typical specs:
-  * frequency: 77 GHz
-  * range: 80–200 m
------
-==== 4.3 Through-the-Wall Detection ====
-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>
------
-===== 5. Advantages and Disadvantages =====
-==== Advantages ====
-  * high resolution
-  * low power
-  * LPI capability
-==== Disadvantages ====
-  * limited long-range performance
-  * sensitive to interference
-  * more complex hardware
------
-===== References =====
-  * [1] Sistemi Radar – Galati
-  * [2] radartutorial.eu
-  * [3] TI mmWave tutorial
-  * ...