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WERA HF Radar Chirp Start Correction

Reason for Chirp Start Variations

WERA uses two independent DDS chirp generators for transmit and receive, which are started simultaneously. Under rare conditions, it can happen that although the start signal is passed to both DDS chips in parallel, the generated chirps behave different. The problem can probably be tracked down to a short "forbidden" time window, where the start signal should not be sent to the DDS. In the end this results in one of the chirps (e.g. RX) beeing one DDS clock longer than the other one (e.g. TX), leading to a small frequency shift on the direct path signal (from TX to RX) and of course also shifting all measured Doppler spectra by this amount.

In the latest hardware revision of the commercial WERA system by Helzel Messtechnik, this problem is avoided by using the same DDS for transmit and receive during measurement cycles. The second DDS is only used for calibration purposes.

A software solution is now implemented, which corrects the chirp start variation without the need of harware modifications.

Magnitude of Frequency Shift and Current Velocity Deviation

The frequency shift depends on:
Range Resolution R_HF 1.5 km
Speed of Light c 299.792458 km/s
DDS Clock Frequency F_dds 181.48430768 MHz
Chirp Length T_chirp 0.26 s
Radar Frequency Freq 16.0 MHz

Bandwidth, frequency shift, current velocity deviation can be calculated as follows:
Bandwidth B = 0.5 * c / R_HF 99.930819 kHz
Frequency Shift F_err = B / (F_dds * T_chirp) 0.00211781 Hz
Current Deviation v_err = 0.5 * c * F_err / Freq 1.9840735 cm/s

The following table shows some typical values:
R_HF T_chirp Freq F_err v_err
1.500 km 0.260 s 45.000 MHz 0.00211781 Hz 0.70544834 cm/s
1.500 km 0.260 s 30.000 MHz 0.00211781 Hz 1.05817251 cm/s
1.500 km 0.260 s 12.000 MHz 0.00211781 Hz 2.64543127 cm/s
1.500 km 0.260 s 8.000 MHz 0.00211781 Hz 3.96814690 cm/s
1.000 km 0.260 s 16.000 MHz 0.00317672 Hz 2.97611018 cm/s
0.300 km 0.260 s 45.000 MHz 0.01058905 Hz 3.52724169 cm/s
1.500 km 0.520 s 16.000 MHz 0.00105891 Hz 0.99203673 cm/s
1.500 km 0.130 s 16.000 MHz 0.00423562 Hz 3.96814690 cm/s

How Chirp Start Variations are Corrected

In a first step, the frequency shift F_err, which might exist in the data, is calculated using the equation shown above. In a second step, the five cases -2*F_err, -F_err, 0.0, +F_err, +2*F_err are evaluated by modulating (adding a frequency shift of F_err) the time series of the signals at range cell 1 (where the direct path signal is mapped to) for all antennas and by calculating the average power of the three spectral lines left and right of DC. The case giving the best balance of the power on both sides of DC is chosen to be the correct one and applied to the signals of all ranges and antennas. In case F_err=0.0 is identified to give the best balance, no modification is done.

Modified Processing Programs

The following programs have been extended to compensate for chirp start variations:
Comments to: gurgel@ifm.uni-hamburg.de (Klaus-Werner Gurgel)