The Complete OFDM Radar Processor

The OFDM radar processor builds on Chapter 22's framework:

1. Transmit $M$ OFDM symbols with $N$ subcarriers
2. Receive echo with delay $\tau$ and Doppler $f_d$
3. Element-wise division $Z[k,m] = Y[k,m]/X[k,m]$
4. IFFT along subcarriers $\to$ range
5. FFT along symbols $\to$ Doppler
6. CFAR detection on the 2D range-Doppler map

For a 2D range-Doppler map, 2D CFAR uses a rectangular window of training cells around the CUT:

def cfar_2d(rd_map, n_train_r, n_train_d, n_guard_r, n_guard_d, pfa):
    Nr, Nd = rd_map.shape
    n_total = (2*n_train_r+2*n_guard_r+1)*(2*n_train_d+2*n_guard_d+1) \
              - (2*n_guard_r+1)*(2*n_guard_d+1)
    alpha = n_total * (pfa**(-1/n_total) - 1)
    detections = np.zeros_like(rd_map, dtype=bool)
    for r in range(n_train_r+n_guard_r, Nr-n_train_r-n_guard_r):
        for d in range(n_train_d+n_guard_d, Nd-n_train_d-n_guard_d):
            window = rd_map[r-n_train_r-n_guard_r:r+n_train_r+n_guard_r+1,
                            d-n_train_d-n_guard_d:d+n_train_d+n_guard_d+1].copy()
            window[n_train_r:n_train_r+2*n_guard_r+1,
                   n_train_d:n_train_d+2*n_guard_d+1] = 0
            noise_est = np.sum(window) / n_total
            if rd_map[r, d] > alpha * noise_est:
                detections[r, d] = True
    return detections