How is the beat signal generated in FMCW radar?

The beat signal is generated by the dechirp process: 1) The transmitter generates a linear frequency chirp (ramp) sweeping from f_start to f_start + BW over time T_chirp. For 77 GHz automotive: f_start = 76 GHz, BW = 4 GHz, T_chirp = 40 μs. 2) The echo returns after round-trip delay τ = 2R/c, which is a time-shifted copy of the transmitted chirp. 3) A mixer multiplies the transmitted and received signals. Because both are chirps with the same slope S = BW/T_chirp, the mixer output contains the sum and difference frequencies. 4) A low-pass filter removes the sum (at ~154 GHz) and passes the difference (the beat signal). The beat frequency equals: f_beat = S × τ = S × 2R/c = (2R × BW) / (c × T_chirp). The beat signal is a low-frequency sinusoid (kHz to MHz range) that can be digitized by a low-cost ADC, dramatically simplifying the receiver architecture compared to pulsed radar.

What determines the ADC requirements for the beat signal?

The ADC must sample the highest beat frequency in the system, which corresponds to the maximum detection range: f_beat_max = (2 × R_max × S) / c. For typical automotive radar: Long-range (R_max = 300 m, BW = 1 GHz, T_chirp = 40 μs, S = 25 MHz/μs): f_beat_max = 2 × 300 × 25×10⁶ / 3×10⁸ = 50 kHz. ADC rate: 100+ kSPS. Short-range (R_max = 30 m, BW = 4 GHz, T_chirp = 10 μs, S = 400 MHz/μs): f_beat_max = 2 × 30 × 400×10⁶ / 3×10⁸ = 80 kHz. ADC rate: 160+ kSPS. In practice, automotive radar SoCs (TI AWR2944, NXP S32R45) use 12-14 bit ADCs at 20-80 MSPS, significantly oversampled to provide anti-aliasing margin and support multiple receive channels (4-12 Rx). Higher bandwidth chirps produce higher beat frequencies at the same range, requiring faster ADCs.

How are range and velocity extracted from the beat signal?

Range and velocity extraction uses a 2D FFT process: 1) Range FFT (fast-time): The beat signal from one chirp is sampled and FFT'd. Each FFT bin corresponds to a range bin: ΔR = c/(2×BW). For BW = 4 GHz: ΔR = 3.75 cm. Targets appear as peaks at their corresponding range bins. 2) Doppler FFT (slow-time): For each range bin, the phase of the beat signal is tracked across N_chirps consecutive chirps. A second FFT across chirps extracts Doppler frequency: f_Doppler = 2v/λ. Velocity resolution: Δv = λ/(2×N_chirps×T_chirp). For λ = 3.9 mm, N = 256, T = 40 μs: Δv = 3.9×10⁻³/(2×256×40×10⁻⁶) = 0.19 m/s. 3) The result is a 2D range-Doppler map where each cell contains the complex amplitude of targets at that (range, velocity) pair. CFAR detection identifies targets above the noise floor.

FMCW Radar

Beat Signal (Automotive Radar)

/beet SIG-nul/

The IF output from mixing the transmitted FMCW chirp with the received echo. Beat frequency is proportional to range: f_beat = 2R × S / c, where S = BW/T_chirp (chirp slope). For 77 GHz radar with 4 GHz BW, 40 µs chirp (S = 100 MHz/µs): target at 100 m produces f_beat = 66.7 kHz. Range resolution ΔR = c/(2×BW) = 3.75 cm. Velocity from Doppler FFT across chirps: Δv = λ/(2×N×T). ADC: 12 to 14 bit, 20 to 80 MSPS.

Range: ΔR = c/(2BW)

ADC: 20–80 MSPS

Freq: 77 GHz band

Understanding the Beat Signal

The beat signal is the elegant foundation of FMCW radar. By mixing the transmitted chirp with the delayed echo, the high-frequency radar signal (77 GHz) is converted to a low-frequency signal (kHz to MHz) that can be digitized by an inexpensive ADC. This "dechirp" process replaces the wideband high-speed digitization that pulsed radar requires, making FMCW the dominant architecture for automotive radar.

The linear relationship between beat frequency and range means that a simple FFT of the beat signal produces a range profile where each spectral peak corresponds to a target at a specific distance. The peak's magnitude indicates target reflectivity (RCS), and its phase carries velocity information extracted by a second FFT across multiple chirps.

Beat Signal Equations

Beat Frequency:
f_beat = 2R × S / c
S = BW / T_chirp (chirp slope)
4 GHz / 40 µs = 100 MHz/µs

Range Resolution:
ΔR = c / (2 × BW)
c = 3×10⁸, BW = 4 GHz:
ΔR = 3.75 cm

Velocity Resolution:
Δv = λ / (2 × N_chirps × T_chirp)
λ = 3.9 mm, N=256, T=40 µs:
Δv = 0.19 m/s

Max Unambiguous Range:
R_max = f_s × c / (2 × S × 2)
(Nyquist-limited by ADC sample rate f_s)

Automotive Radar Beat Signal Comparison

Parameter	Long-Range (LRR)	Short-Range (SRR)
R_max	300 m	30 m
BW	1 GHz	4 GHz
T_chirp	40 µs	10 µs
S (slope)	25 MHz/µs	400 MHz/µs
f_beat at R_max	50 kHz	80 kHz
ΔR	15 cm	3.75 cm

Common Questions

Frequently Asked Questions

How is it generated?

Dechirp: mixer multiplies Tx chirp × Rx echo. LPF removes sum frequency. Output: beat sinusoid at f_beat = S×2R/c. Low-frequency IF (kHz to MHz) digitized by low-cost ADC. Key advantage of FMCW vs. pulsed.

ADC requirements?

Sample f_{beat_max} = 2×R_max×S/c. LRR 300 m: ~50 kHz. SRR 30 m (S=400 MHz/µs): ~80 kHz. Automotive SoCs: 12 to 14 bit at 20 to 80 MSPS (oversampled for margin + multi-Rx).

Range + velocity extraction?

Range FFT (fast-time, per-chirp): peaks at range bins. Doppler FFT (slow-time, across N chirps): velocity per range bin. Result: 2D range-Doppler map. CFAR detection identifies targets.

Related Terms

← Beat Frequency BeCu Cable →

Automotive Radar

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