BWR-1 · simulations/link-budget · v3
FMCW weather-radar link budget
Zmin per configuration, separating meteorological power, post-range-FFT noise, detection statistics and an explicit engineering margin. These are design estimates, not demonstrated sensitivity.
Summary
Headline value: Doppler-band filtered estimator plus engineering margin. The detailed table also shows the alternative estimators.
Scenarios
Common parameters
Engineering Zmin vs range
Dashed orange line: target. Dotted vertical line: evaluation range.
Detailed results
Model and assumptions
- Antennas:
G = η(πD/λ)²,θ₃dB ≈ 70λ/D. - Meteorological power (Probert-Jones with distinct TX/RX beams):
Pr = Pt·Gt·Gr·θ²ef·(2ΔR)·π³·|K|²·Z / (1024·ln2·λ²·R²),θ²ef = 2θt²θr²/(θt²+θr²),2ΔR = c/B. - Rain attenuation: ITU-R P.838-3, horizontal polarization, coefficients interpolated in log-frequency; two-way; applied only over the given path length.
- Noise per range bin:
N = −174 + NF + 10log(ENBW/T). - Precipitation spectrum:
B_w = √(2π)·2σv/λ; PRF = 1/T. - (a) Independent looks (model v2):
SNR_chirp + 5log(min(N_chirps, dwell·B_w)). Right for estimate precision when SNR ≳ 0 dB; pessimistic for detection at low SNR. - (b) Radiometer:
SNR_chirp + 5log(N_chirps). At low SNR the limit is noise fluctuation, which is independent from chirp to chirp. - (c) Doppler-band filtered (primary): slow-time FFT, summing only the band occupied by precipitation,
B_sel = min(B_w, PRF):SNR = Pr − (−174 + NF + 10log(ENBW·B_sel)),M = min(N_chirps, dwell·B_sel), significanceSNR + 5log M. Assumes the echo spectral position is estimated (standard spectral processing). - Zmin = test Z − (significance − threshold). Engineering = plus an explicit margin for TX→RX leakage, phase noise on clutter, ADC and model error.
- The √N approximation holds for large N and low-to-moderate per-sample SNR.
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