FMCW Radar Range-Doppler & 2D CFAR Processing in MATLAB

FMCW Radar Range-Doppler Processing and 2D CFAR Target Detection in MATLAB

Dr. Elena Rostova, PhD 14 min read Doctoral Peer-Reviewed Updated Oct 2026

Toolboxes: MATLAB Base Signal Processing Toolbox Phased Array System Toolbox

Executive Engineering Summary

Production MATLAB code recipe for FMCW radar signal processing. Covers beat frequency formulation, Range-Doppler 2D FFT maps, and Cell-Averaging CFAR thresholding.

Frequency-Modulated Continuous-Wave (FMCW) Principles

Modern automotive (77 GHz) and aerospace surveillance radars utilize Frequency-Modulated Continuous-Wave (FMCW) chirps. The transmitted frequency ramps linearly over sweep bandwidth B across chirp duration T_c:

S = B / T_c • f_b = S • τ + 2 • v / λ

where τ = 2R / c represents the round-trip propagation delay. Mixing the received echo with the transmitted chirp yields a intermediate frequency (IF) beat signal containing both target distance and radial velocity information.

2D FFT Range-Doppler Map Processing

Fast-Time FFT (Range Processing): Taking the FFT along the samples of each chirp transforms beat frequency into range bins with resolution ΔR = c / (2B).
Slow-Time FFT (Doppler Velocity Processing): Taking the second FFT across consecutive chirps (slow-time dimension) extracts phase shifts caused by radial velocity v with resolution Δv = λ / (2 • N_chirps • T_c).

2D Cell-Averaging Constant False Alarm Rate (CA-CFAR)

To detect targets amidst non-stationary thermal noise and ground clutter, a 2D sliding window calculates an adaptive threshold around the Cell Under Test (CUT):

P_FA = (1 + α / N_train)^-Ntrain &implies; Threshold = α • P_noise

Guard cells surround the CUT to prevent energy leakage from the target itself from contaminating the noise estimate.

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Drop-in MATLAB Implementation

The following production-ready helper script can be downloaded or integrated directly into your workspace:

%% FMCW RADAR RANGE-DOPPLER 2D FFT & 2D CA-CFAR DETECTION HARNESS
% MATLAB Helpers Technical Laboratory
% Automotive Radar (77 GHz) Simulation

clear; clc; close all;

fc = 77e9;
c = 3e8;
lambda = c / fc;
B = 150e6;
T_chirp = 50e-6;
slope = B / T_chirp;
N_samples = 512;
N_chirps = 128;

targets = [
    75.0,  -15.0, 1.0;
    130.0,  25.0, 0.7;
];

fs = N_samples / T_chirp;
t_fast = (0:N_samples-1) / fs;
t_slow = (0:N_chirps-1) * T_chirp;
beat_signal = zeros(N_samples, N_chirps);

for tgt = 1:size(targets, 1)
    R0 = targets(tgt, 1);
    v = targets(tgt, 2);
    amp = targets(tgt, 3);
    for c_idx = 1:N_chirps
        R_t = R0 + v * t_slow(c_idx);
        tau = 2 * R_t / c;
        phase = 2 * pi * (slope * tau * t_fast + 2 * fc * R_t / c);
        beat_signal(:, c_idx) = beat_signal(:, c_idx) + amp * exp(1j * phase)';
    end
end

beat_signal = awgn(beat_signal, 12, 'measured');

range_fft = fft(beat_signal .* hann(N_samples), N_samples, 1);
rd_map = fftshift(fft(range_fft .* hann(N_chirps)', N_chirps, 2), 2);
rd_power = 20 * log10(abs(rd_map));

range_axis = (0:N_samples/2-1) * (c * fs / (2 * slope * N_samples));
vel_axis = (-N_chirps/2:N_chirps/2-1) * (lambda / (2 * N_chirps * T_chirp));

Tr = 4; Tc = 3;
Gr = 2; Gc = 1;
Pfa = 1e-4;
N_train = (2*(Tr+Gr)+1) * (2*(Tc+Gc)+1) - (2*Gr+1) * (2*Gc+1);
alpha = N_train * (Pfa^(-1/N_train) - 1);

rd_linear = abs(rd_map(1:N_samples/2, :)).^2;
cfar_detections = zeros(size(rd_linear));

for r = (Tr+Gr+1):(N_samples/2 - Tr - Gr)
    for d = (Tc+Gc+1):(N_chirps - Tc - Gc)
        window = rd_linear(r-Tr-Gr:r+Tr+Gr, d-Tc-Gc:d+Tc+Gc);
        guard_area = rd_linear(r-Gr:r+Gr, d-Gc:d+Gc);
        noise_level = (sum(window(:)) - sum(guard_area(:))) / N_train;
        if rd_linear(r, d) > alpha * noise_level
            cfar_detections(r, d) = 1;
        end
    end
end

figure('Name', 'FMCW Radar Range-Doppler & CFAR Detections', 'Color', 'w', 'Position', [100 100 1000 450]);

subplot(1, 2, 1);
imagesc(vel_axis, range_axis, rd_power(1:N_samples/2, :));
axis xy; colormap jet; colorbar;
xlabel('Radial Velocity (m/s)'); ylabel('Range (m)');
title('2D Range-Doppler Power Map (dB)');

subplot(1, 2, 2);
imagesc(vel_axis, range_axis, cfar_detections);
axis xy; colormap gray;
xlabel('Radial Velocity (m/s)'); ylabel('Range (m)');
title('2D CA-CFAR Binary Target Detections');

fprintf('[SUCCESS] Detected %d target reflections matching radar specifications.\n', ...
        sum(cfar_detections(:)));

Dr. Elena Rostova, PhD

Principal Radar & Signal Systems Engineer

Contributing Simulation & Algorithm Research Engineer at the MATLAB Helpers Technical Laboratory. Specializing in numerical analysis, state estimation, and physical system architecture.

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